Physical and Analytical Chemistry

Transcription

1 S. Y. B. Sc. Textbook as per syllabus of University of Mumbai Physical and Analytical Chemistry Dr. Bapu R Thorat Dr. Ramesh S Yamgar Miss. Vaishali Bapu Thorat Government of Maharashtra, Ismail Yusuf College, Jogeshwari (East), Mumbai Patkar Varde College, Goregaon (West), Mumbai IES, Junior College, Bandra (East), Mumbai ISBN

2 S. Y. B. Sc. Textbook as per syllabus of University of Mumbai Physical and Analytical Chemistry Dr. Bapu R Thorat Dr. Ramesh S Yamgar Miss. Vaishali Bapu Thorat Published by Ramesh Yamgar Research Group ISBN

3 S. Y. B. Sc. CHEMISTRY USCH301 No. of credit = 02 Unit Topic Page No. I 1.1. Chemical Thermodynamics II: Free energy functions: Helmholtz free energy, Gibbs free energy, Variation of Gibbs free energy with pressure and temperature, Gibbs- Helmholtz equation Thermodynamics of open system: Partial molal properties, chemical potential and its variation with pressure and temperature, Gibbs Duhem equation Concept of fugacity and activity Chemical equilibrium and equilibrium constant: Equilibrium constant, K P and K C and their inter relation, van t Hoff reaction isotherm, van t Hoff reaction isochore Photochemistry Introduction, Difference between thermal and photochemical reactions, Laws of Photochemistry, Grothus-Draper Law, Stark-Eistein law, Einstein of energy Quantum efficiency, determination using actinometer Photochemical reactions - primary and secondary processes. Reactions with high (formation of HCl) and low quantum efficiency (formation of HBr), Reasons for high and low quantum efficiency Photochemical phenomenon: fluorescence, phosphorescence, chemiluminiscence, ozone depletion 1.3. Chemical Kinetics II Types of complex chemical reactions: reversible or opposing, consecutive and parallel reactions (no derivations, only examples expected), Thermal chain reactions H 2 and Br 2 reaction (steps involved only, no kinetics expressions needed) Effect of temperature on rate of reaction, Arrhenius equation, Concept 3

4 of energy of activation (E act ). (Numerical on Arrhenius equation expected). II III 2.1. Electrochemistry I Variation of molar conductance with dilution Arrhenius theory of electrolytic dissociation and its limitations Debye Huckel s theory of strong electrolyte electrophoretic and relaxation effect Mobility of ions Kohlrausch s law of independent migration, applications of Kohlrausch s law determination of degree of dissociation, solubility of sparingly soluble salt, etc Titrimetric Analysis II Construction of titration curves and choice of indicators in titration of weak acid against strong base, strong acid against weak base, weak acid against weak base, polybasic acid against strong base. End point evaluation choice and suitability of indicators in each case Titrimetric Analysis III Complexometric titration Introduction, EDTA titrations, advantageous and limitations of EDTA as a chelating agent, absolute and conditional formation constants of metal EDTA complexes, Construction of titration curves, types of EDTA titrations, Methods of increasing the selectivity of EDTA as a titrant Metallochromic indicators theory and applications Separation Techniques Types of separation techniques Filtration, distillation, chromatography, solvent extraction, etc Solvent extraction partition coefficient and distribution ratio, Types of solvent extraction Batch and continuous process, extraction efficiency, separation factor, role of complexing agents in solvent extraction, chelation, ion pair formation, solvation. 4

5 USCH401 No. of credit = 02 Unit Topic Page No. I II 4.1. Electrochemistry II Migration of ions, velocity of ions and change in concentration around electrodes (unattackable) Transport number definition and determination by moving boundary method Factors affecting transport number of ions Relation between transport number and ionic conductance Nuclear chemistry II Factors affecting stability of nucleus: Mass defect of nucleus, binding energy, binding energy per nucleon, binding energy curve, N/P ratio, odd-even number rule, magic numbers Basic units of radioactivity and dosimetry: exposure units, absorbed dose and equivalent dose, external dose due to natural sources Liquid state Surface tension: Introduction, method of determination of surface tension drop number method, parachor value and applications of surface tension Viscosity: Introduction, coefficient of viscosity, relative viscosity, Ostwald viscometer method for viscosity determination Liquid crystals: Introduction, classification and structure of thermotropic phases (nematic, smectic and chlolesteric phases), applications of liquid crystals. 5.1.Phase equilibria Liquid liquid mixtures: A. Completely miscible liquids: Raoult s law, Ideal and non-ideal solutions (positive and negative deviations). B. Partially miscible liquids: Partially miscible liquids with upper critical 5

6 solution temperature (e.g. phenol-water system), partially miscible liquids with lower critical solution temperature (e.g. triethylamine-water system), partially miscible liquids with lower and upper critical solution temperature (e.g. nicotine-water system) Spectroscopy II Energy of light, Intensity of light, polychromic and monochromic light, wavelength of maximum absorption, Transmittance, percentage transmittance, Absorbance, molar extinction coefficient, Lambert s Law, Beer s law, Beer Lambert s law, Deviations from Beer Lambert s law, Quantitative analysis by calibration curve method Instrumentation: Single beam and double beam photoelectric colorimeter (detail of components expected), principle, construction & working Photometric titrations: Principle, instrumentation, types of photometric titration curves with examples including estimation of Cu (II) and Bi (III), Advantageous and limitations. III 6.1.Statistical treatment of analytical data Performance characteristics of an analytical method: Accuracy, precision, sensitivity, specificity, robustness, ruggedness, linearity range, limit of quantification, limit of detection, signal to noise ratio Errors in chemical analysis: Types of errors determinate and indeterminate errors, constant and proportionate errors, absolute and relative errors, minimization of errors Measures of central tendency and dispersion: A. Measure of central tendency: Mean, median and mode. B. Measure of dispersion: Deviation, arange, standard deviation, variance, correlation coefficient, and relative standard deviation Titrimetric Analysis IV: Precipitation titrations Argentimetric titrations, construction of titration curves, Volhard s method, Mohr s method, Adsorption indicators theory and applications. 6

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8 Unit - I 1.1. Free Energy and Equilibrium II According to the first law of thermodynamics, when heat is supplied to the system, some part of it is converting into work and remaining part is rejected or used to increase internal energy of the system. How much quantity of heat is used to increase the internal energy or rejected to surrounding is determined from the entropy change. But how much quantity of heat is used to performed work done is determined by mew thermodynamic state function is called as free energy. The heat energy is supplied in the form of internal energy or enthalpy. [Heat energy (E or H)] = (Heat available to perform work done) + (Heat unavailable to perform work done) If heat energy is supplied in the form of internal energy, the part of internal energy available to perform work is called Helmholtz free energy. It is denoted by the latter A. The internal energy unavailable to perform the work done is TS, S-is entropy at temperature T. Heat energy (E)] = (E available to perform work done) + (E unavailable to perform work done) E = A + TS A = E - TS 1 If heat energy is supplied in the form of enthalpy, the part of enthalpy available to perform work is called Gibbs free energy. It is denoted by the latter G or F. The enthalpy unavailable to perform the work done is TS, S-is entropy at temperature T. [Heat energy (H)] = (H available to perform work done) + (H unavailable to perform work done) H = G + TS G = H - TS Helmholtz free energy: Helmholtz free energy of any system A is defined as- A = E - TS Where, E and S are internal energy and entropy of the system respectively. A, E, S and T are state functions. The change in A during any process is given as- ΔA = A 2 - A 1 = (E 2 T 2 S 2 ) (E 1 T 1 S 1 ) = (E 2 - E 1 ) (T 2 S 2 T 1 S 1 ) = ΔE ΔTS.. 3 1

9 Equation (3) is the general definition of ΔA. For isothermal process T 2 = T 1, then equation (3) becomes- ΔA = ΔE TΔS 4 Equation (4) explain physical interpretation (significance) of ΔA, under isothermal conditions TΔS = q r (according to the definition of entropy). ΔA = ΔE q r.. 5 According to the first law of thermodynamics for reversible and isothermal processq r = ΔE + W m or W m = q r - ΔE. a From equation (5) and (a)- ΔA = -W m. 6 The equation (6) indicates that, at constant temperature the maximum work done by the system is due to expense of (decrease in) Helmholtz free energy of the system. Therefore, A is called as Work function of a system. Variation of A with V and T: According to the definition of A [i.e. from equation (1)]- A = E - TS Differentiate it completely as- da = de - TdS - SdT 7 According to the definition of entropy- dq r = TdS Therefore equation (7) becomes- da = de - dq r - SdT. 8 According to the first law of thermodynamics- dq r = de + PdV (for reversible process) Or -PdV = de - dq r Therefore equation (8) becomes - da = -PdV - SdT 9 Equation (9) indicates that A is most conveniently expressed in terms of a T and V as the independent variables, we have - A = f (T,V) Differentiate it completely - da = dt + dv Comparing equation (9) and (10) we have - = -P

10 = -S.. 12 An alternative equation for the variation of A with T can be obtained as follows - Differentiate with respect to T at constant V gives - = = = = 13 Equation (9) shows that the dependence of A for a pure substance on both T and V, these can be shown by (12) and (13) for T and (11) for V. Gibb s free Energy: If heat energy is supplied in the form of enthalpy, the part of enthalpy available to perform work is called Gibbs free energy. It is denoted by the latter G or F. The enthalpy unavailable to perform the work done is TS, S-is entropy at temperature T. [Heat energy (H)] = (H available to perform work done) + (H unavailable to perform work done) H = G + TS G = H - TS 1 Where, H and S are enthalpy and entropy of the system respectively. G, H, S and T are state functions. The change in G during any process is given as- ΔG = G 2 - G 1 = (H 2 T 2 S 2 ) (H 1 T 1 S 1 ) = (H 2 - H 1 ) (T 2 S 2 T 1 S 1 ) = ΔH ΔTS.. 2 Equation (2) is the general definition of ΔG. For isothermal process T 2 = T 1, then equation (2) becomes - ΔG = ΔH TΔS.. 3 Relationship between G and A: 3

11 Consider equation (3) is- ΔG = ΔH TΔS But H is also state function- ΔH = ΔE + PΔV (at constant P) Therefore, ΔG = ΔE + PΔV TΔS = (ΔE TΔS) + PΔV (But, ΔA = ΔE TΔS) ΔG = ΔA + PΔV.. 4 In general- G = A + PV.. 5 The equation (4) and (5) shows the relationship between G and A. Physical significance of G: At constant temperature, TΔS = q r and at constant pressure, ΔH = ΔE + PΔV. Put these values into equation (3) - ΔG = (ΔE + PΔV) q r = - (q r - ΔE - PΔV) But according to the first law of thermodynamics, q r = ΔE + W m or W m = q r - ΔE Therefore, ΔG = - (W m - PΔV).. 6a Or -ΔG = (W m - PΔV) 6b Equation (6b) shows that ΔG is the available free energy for the work done other than P-V type at constant T and P. the work is done due to expense of Gibb s free energy. Variation of G with P and T: According to the definition of G [i.e. from equation (1)] - G = H - TS Differentiate it completely as - dg = dh - TdS - SdT. 7 According to the definition of entropy and first law of thermodynamics - dq r = TdS = de + PdV (for reversible process).. 8 According to the definition of enthalpy - H = E + PV Differentiate it completely - dh = de + PdV + VdP. 9 Therefore equation (8) and (9) dh = VdP + TdS. 10 From equation (7) and (10) - dg = VdP + TdS -TdS -SdT dg = VdP - SdT 11 4

12 Equation (11) indicates that G is function of a T and P as the independent variables, we have - G = f (T,P) Differentiate it completely - dg = dt + dp 12 Comparing equation (11) and (12) we have- = V = - S.. 13 An alternative equation for the variation of G with T can be obtained as follows- Differentiate G/T with respect to T at constant P gives- = = = = 14 Equation (11) shows that the dependence of G for a pure substance on both T and P, these can be shown by (14) and (13) for T. ΔG for reaction: For any chemical reaction such as - aa + bb +... cc + dd +... ΔG for such reaction is sum of the G s for the products minus a similar sum of for the reactants. ΔG = ΣG p ΣG R... 1 ΔG = [H p H R ] T[S p - S R ] ΔG = ΔH - TΔS at constant T.. 2 ΔH and ΔS are change in enthalpy and entropy of the reaction respectively at constant temperature T and pressure P. Also ΔG is function of T and P as - d(δg) = dt + dp.. 3 5

13 These derivatives are also obtained by differentiate equation (2) with respect to T at constant P and with respect to P at constant T. = - T ΔS But = C p therefore = ΔC p and = ΔC p - ΔS = ΔS 4 Also, = V p V R = ΔV 5 Where, ΔV is change in molar volume during the reaction. From equation (3), (4) and (5), we haved(δg) = ΔV dp ΔS dt.. 6 From equation (4) and (2) - ΔG = ΔH + 7 The equation (7) is called as Gibb s-helmholtz equation where (δδg/δt) p is called as temperature coefficient of a reaction. Significance of Gibb s-helmholtz equation Gibb s-helmholtz equation is - ΔG = ΔH + 7 Consider the reaction: Zn + CuSO 4 (sol) ZnSO 4 (sol) + Cu. When this reaction is carried out in open beaker by adding zinc to a solution of CuSO 4, heat of reaction is equal to ΔH. If same reaction is carried out reversibly in a cell by applying the external voltage which is infinitely smaller than that of cell emf. The work is done denoted by the later ΔG instead if heat evolved. The difference between these two i.e. (ΔG - ΔH) is equal to a either TΔS or T[δ(ΔG)/δT] p. From equation (2) and (7) - - TΔS =.. 8 But by the definition of the entropy - TΔS = q r. Therefore, -q r =. 9 And equation (7) becomes - ΔG = ΔH - q r 6

14 Or q r = ΔH ΔG 10 The equation (8) represents the heat interchange between the system and its surroundings when process is conducted isothermally and reversibly. Case - I: when ΔH > ΔG, q r is positive; heat is absorbed from the surrounding. Case - II: when ΔH < ΔG, q r is negative; heat is evolved to the surrounding. Case - III: when ΔH = ΔG, heat is neither absorbed nor evolved with the surrounding. 7

15 Thermodynamics of open system We need a set of concepts that enable us to apply thermodynamics to mixtures of variable composition. For a more general description of the thermodynamics of mixtures we have to introduce other partial properties, each one being the contribution that a particular component makes to the mixture. The equilibrium thermodynamic state of a simple one-component open system can be specified by T, P, and n, the amount of the single component. This gives the differential relation for a general extensive quantity, X, in a one-component system: In a one-component system the molar quantity X m is given by The molar quantity X m is an intensive quantity. Because an intensive quantity cannot depend on an extensive quantity, X m depends only on T and P. Therefore In a one-component system any partial molar quantity is equal to the corresponding molar quantity. The most important examples are (for one component system) For ideal gas system,, therefore above equation become Where, is the molar Gibbs energy in the standard state. It is equal to μ, the chemical potential in the standard state. The standard state for the Gibbs energy of an ideal gas is the ideal gas at pressure (exactly 1 bar). Also, we derived the equation,, therefore, equation for S m is 8

16 where Also the partial molar enthalpy of a one-component ideal gas is obtained from = = = The molar enthalpy of an ideal gas does not depend on pressure. The equation for molar volume is - (for one component system) The equation for molar Helmholtz energy can be derived from the equation A = G PV, = According to Dalton s law of partial pressures, each gas in a mixture of ideal gases behaves as though it were alone in the container. The equation for applies to any substance in an ideal gas mixture: Where, is the chemical potential of substance i in the standard state at pressure and is its partial pressure. All of the other equations for one-component ideal gases apply as well. Partial Molal Quantities: A partial molar property is the contribution (per mole) that a substance makes to an overall property of a mixture. Dependence of one variable with respect to particular variable by keeping other variables constants is called as partial molal quantities. Consider a solution composed of j constituents and n 1, n 2, n 3,.,n j be the number of moles of various constituents present. Let X is any extensive property of the system is said to be function of P and T and the number of moles of the various constituents present as - X = f (P, T, n 1, n 2, n 3,.,n j ) 1 Partial differentiation of equation (1) gives dx as - dx = (dx dt) P,ni dt + (dx dp) T,ni dp + (dx dn 1 ) P,T,ni dn 1 + (dx dn 2 ) P,T,ni dn (dx dn j ) P,T,ni dn j 2 Where, n i represents in each instance all the n s except the one with respect to which X is differentiated then, 9

17 (dx dn i ) P,T,nj is called as partial molal quantity and is denoted by drawing bar over the symbol of that property. Therefore, X 1 = (dx dn 1 ) P,T,nj, X 2 = (dx dn 2 ) P,T,nj,.., X j = (dx dn j ) P,T,ni.. 3 Put eq. (3) in eq. (2), dx = (dx dt) P,ni dt + (dx dp) T,ni dp + X 1 dn 1 + X 2 dn X j dn j 4 At constant temperature and pressure, eq. (4) becomes- (dx) T,P = X 1 dn 1 + X 2 dn X j dn j.. 5 On integration equation (5) become- (by Euler s theorem for homogeneous function)- X = X 1 n 1 + X 2 n X j n j 6 Equation (6) shows that any extensive property of a solution at constant T and P, is expressed as a sum of X x n for individual components of solution. In each product, the n represents a capacity factor and X represents a partial molal quantity represent an intensive factor i.e. partial molal quantities are intensive properties of a solution. Differentiating equation (6) completely- (dx) T,P = X 1 dn 1 + X 2 dn X j dn j + n 1 dx 1 + n 2 dx n j dx j (dx) T,P = (dx) T,P + n 1 dx 1 + n 2 dx n j dx j Or n 1 dx 1 + n 2 dx n j dx j = 0 7 For binary solution, j = 1 and 2. n 1 dx 1 + n 2 dx 2 = 0 or dx 1 = -n 2 /n 1 dx 2 8 The equation (7) and (8) is called as Gibb s-duhem equation. This equation shows that a partial molal quantity depends on each others. These are determined by variety of methods both graphical and analytical. When X = G, n 1 dg 1 + n 2 dg 2 = 0 Partial molal volume: Imagine a huge volume of pure water. When a further 1 mol H 2 O is added, the volume increases by 18 cm 3. However, when we add 1 mol H 2 O to a huge volume of pure ethanol, the volume increases by only 14 cm 3. The quantity 18 cm 3 mol 1 is the volume occupied per mole of water molecules in pure water; 14 cm 3 mol 1 is the volume occupied per mole of water molecules in virtually pure ethanol. In other words, the partial molar volume of water in pure water is 18 cm 3 mol 1 and the partial molar volume of water in pure ethanol is 14 10

18 cm 3 mol 1. In the latter case there is so much ethanol present that each H 2 O molecule is surrounded by ethanol molecules and the packing of the molecules results in the water molecules occupying only 14 cm 3. Partial molal volume of the i th component is denoted by later V i and defined as- V i = (dv dn i ) P,T,nj The subscript n j means that the number of moles of each component except i th component is constant. Partial molal volume is the change in volume (V) when one mole of component is added to large quantity of system at constant temperature and pressure. For binary solution, V = f (P, T, n 1, n 2 ) Partial differentiation of V gives dv asdv = (dv dt) P,n1,n2 dt + (dv dp) T, n1,n2 dp +( dv dn 1 ) P,T,ni dn 1 +( dv dn 2 ) P,T,ni dn 2 At constant temperature and pressure, (dv) T,P = V 1 dn 1 + V 2 dn 2 On integrating, (V) T,P = V 1 dn 1 + V 2 dn 2 Example: What is the total volume of a mixture of 50.0 g of ethanol and 50.0 g of water at 25 C? Solution: Calculate the amounts by using - n J = m J /M J. The molar masses of CH 3 CH 2 OH and H 2 O are g mol 1 and g mol 1, respectively. Therefore the amounts present in the mixture are - = 1.09 mol = 2.77 mol For a total of ( ) 3.86 mol. Hence x ethanol = and x water = The partial molar volumes of the two substances in a mixture of this composition are 56 cm 3 mol 1 (density of ethanol is g/lit) and 18 cm 3 mol 1, respectively, so from the total volume of the mixture is - V = (1.09 mol) (56 cm 3 mol 1 ) + (2.77 mol) (18 cm 3 mol 1 ) = cm 3 = 110 cm 3 11

19 Partial molal free energy: The partial molar Gibbs energy has exactly the same significance as the partial molar volume. For instance, ethanol has a particular partial molar Gibbs energy when it is pure (and every molecule is surrounded by other ethanol molecules), and it has a different partial molar Gibbs energy when it is in an aqueous solution of a certain composition (because then each ethanol molecule is surrounded by a mixture of ethanol and water molecules). The partial molar Gibbs energy is so important in chemistry that it is given a special name and symbol. From now on, we shall call it the chemical potential and denote it μ (mu). The name chemical potential is very appropriate, for it will become clear that μ i is a measure of the ability of i th component to bring about physical and chemical change. A substance with a high chemical potential has a high ability, in a sense we shall explore, to drive a reaction or some other physical process forward. Partial molal free energy of the i th component is denoted by later G i (called chemical potential, denoted by later μ i ) and defined as- G i = μ i = (dg dn i ) P,T,nj The subscript n j means that the number of moles of each component except i th component is constant. Partial molal free energy or chemical potential is the change in free energy when one mole of component is added to large quantity of system at constant temperature and pressure. Suppose a substance J occurs in different phases in different regions of a system. For instance, we might have a liquid mixture of ethanol and water and a mixture of their vapours. Let the substance J have chemical potential μ j (l) in the liquid mixture and μ j (g) in the vapour. We could imagine an infinitesimal amount, dμ j, of J migrating from the liquid to the vapour. As a result, the Gibbs energy of the liquid phase falls by μ j (l)dμ j and that of the vapour rises by μ j (g)dμ j. The net change in Gibbs energy is - dg = μ j (g)dμ j μ j (l)dμ j. = { μ j (g) μ j (l)} dμ j. There is no tendency for this migration (and the reverse process, migration from the vapour to the liquid) to occur if dg = 0. The argument applies to each component of the system. Therefore, for a substance to be at equilibrium throughout the system, its chemical potential must be the same everywhere. For binary solution, G = f (P, T, n 1, n 2 ) 12

20 Partial differentiation of G gives dv asdg = (dg dt) P,n1,n2 dt + (dg dp) T, n1,n2 dp +(dg dn 1 ) P,T,ni dn 1 +(dg dn 2 ) P,T,ni dn 2 At constant temperature and pressure, (dμ i ) T,P = (dg) T,P = G 1 dn 1 + G 2 dn 2 On integrating, (μ i ) T,P = (G) T,P = G 1 dn 1 + G 2 dn 2 It is extensive property, is independent on the size of system. This equation is called as Gibb s- Duhem equation. Variation of chemical potential with temperature and pressure (Chemical potential for gaseous): The general expression for the differential change of the Gibbs energy, G, is given by: dg = - S dt + V dp 1 Where, S is the entropy, V the volume, P is the pressure, and T is the absolute temperature. From equation (1) we have a relation between the change of G with respect to a change of pressure at constant temperature, i.e.,.. 2 If we rewrite Equation (2) as a differential relation, we can calculate the Gibbs free energy as a function of pressure, namely -. 3 Where, the temperature is held constant. Since PV = nrt fo r an ideal gas, with R the gas constant and n the number of moles, we find = = nrt ln.. 4 In equation (4) an arbitrary pressure reference, P ref, corresponds to the pressure where Gibbs free energy is equal to G 0. Thus, the Gibbs free energy of an ideal gas at constant T is given by:. 5 In practice the values of P ref defined a set of conditions called standard state. Usually one atmosphere or one bar is chosen for all gases; in the present discussion we will leave P ref as a value to be defined. In this case the molar Gibbs free energy or chemical potential, μ, is given by: 13

21 6 According to equation (6), when P is equal to the reference pressure, P ref, the molar Gibbs free energy is equal to the standard state molar Gibbs free energy. If one considers interactions between particles, i.e., non-ideal gases, one has to replace the argument of the natural logarithm by the fugacity, f. Thus we have - 7 where, f(p) = P exp. 8 where, = 9 Equation (8) is the chemical potential for an arbitrary standard state defined by the reference pressure, P ref. When P ref = 1, then equation (6) become 10 The chemical potential becomes negatively infinite as the pressure tends to zero. As the pressure is increased from zero, the chemical potential rises to its standard value at 1 bar (because ln 1 = 0), and then increases slowly (logarithmically, as ln p) as the pressure is increased further. This conclusion is consistent with the interpretation of the chemical potential as an indication of the potential of a substance to be active chemically: the higher the partial pressure, the more active chemically the species. In this instance the chemical potential represents the tendency of the substance to react when it is in its standard state (the significance of the term μ) plus an additional tendency that reflects whether it is at a different pressure. The molar Gibbs energy of a pure substance is the same in all the phases at equilibrium. A system is at equilibrium when the chemical potential of each substance has the same value in every phase in which it occurs. The total Gibbs energy of the two substances A and B mixture by using an expression G = n A G A + n B G B Or G = n A μ A + n B μ B At constant temperature and pressure, when an amount na of A and nb of B of two gases mixture 14

22 ΔG = nrt {x A ln x A + x B ln x B } ( Where n = n A + n B, The crucial feature is that because x A and x B are both less than 1, the two logarithms are negative (ln x < 0 if x < 1), so ΔG < 0 at all compositions. Therefore, perfect gases mix spontaneously in all proportions. Chemical potential for solvent: In the case of solutions, where the solvent is at equilibrium with its vapor, we know that - μ solvent = μ vapour Since equation (11) applies to the chemical potential of an ideal vapor (from equation 6), we have μ solvent = μ vapour μ 12 For a pure solvent, P is the equal to the pure solvent vapor pressure, P*. Thus the pure liquid chemical potential is given by: solvent μ 13 Solving this equation for μ and substituting in equation (12) we get μ solvent 14 In the case of an ideal solution, Raoult's law is satisfied. Therefore, the following relation between the vapor pressure and composition is observed: = 15 Where, X is the mole fraction. Therefore for ideal solutions we have notice that now the reference point is the pure solvent. μ solvent 16 For a non-ideal solution, the following relation is defined: 17 Where, is defined as the activity and as the activity coefficient. In this case the solvent chemical potential of a non-ideal solution is given by: μ solvent 18 15

23 Equation (18) is the most general expression for the solvent's chemical potential where the nonideality is taken in consideration in the activity coefficient. Also notice that for pure solvent the activity and the activity coefficient are equal to unity. 16

24 Concept of activity: For an ideal gas, either pure or in a mixture, equation for chemical potential is -. 1 For a component of an ideal solution or for the solvent in a dilute solution, we have = 2 Where, is the chemical potential of substance i in the appropriate standard state and a i, the activity of substance i. The activity is - (pressure) = (mole fraction) = (molality) = (concentration) The activity is a dimensionless quantity that is equal to unity if the substance is in its standard state. Each measure of the activity corresponds to a different standard state. For example, the standard state for a component in an ideal solution or a solvent in an arbitrary solution is the pure substance. The standard state for a solute that obeys Henry s law is the hypothetical pure substance that has a vapor pressure equal to k i, the Henry s law constant. The standard state of a dilute solute in the molality description is a hypothetical solute with a molality of 1 mol kg 1 such that Henry s law is obeyed at this composition. The standard state of a dilute solute in the concentration description is a hypothetical solute with a molar concentration of 1 mol m 3 or 1 mol L 1 such that Henry s law is obeyed at this composition. The standard state of a pure solid or liquid is the pure substance at pressure. If the substance is at a pressure P not equal to, =.. 3 Where we assume that the solid or liquid has a nearly constant volume. By comparison with equation (2),. 4 The activity of a pure liquid or solid at pressure P is given by (For pure solid or liquid) 5 The exponent in equation (5) is generally quite small unless P differs greatly from. For ordinary pressures we will assume that the activity of a pure solid or liquid is equal to unity. The activity of a non-ideal gas to be the ratio of the fugacity to : (for non-ideal gas) 6 17

25 We define the activity coefficient γ i of a non-ideal gas as 7 So that the activity coefficient of a gas equals the ratio of the fugacity to the pressure: = 8 The activity coefficient of an ideal gas equals unity. The chemical potential of a non-ideal gas can be written = =. 9 The activity coefficient of a gas is also known as the fugacity coefficient and is sometimes denoted by φ i instead of by γ i. If the value of the activity coefficient of a real gas is greater than unity, the gas has a greater activity and a greater chemical potential than if it were ideal at the same temperature and pressure. If the value of the activity coefficient is less than unity, the gas has a lower activity and a lower chemical potential than if it were ideal. Concept of fugacity: For an ideal gas, we have.. 1 Where, is the value of the chemical potential for a particular pressure. When a gas requires corrections for non-ideality we write a new equation in the same form as equation (1), replacing the pressure by the fugacity, f, which has the dimensions of pressure. The fugacity plays the same role in determining the molar Gibbs energy of a real gas as does the pressure in determining the molar Gibbs energy of an ideal gas. The quantity (T) is the molar Gibbs energy of the gas in its standard state. The standard state of a real gas is defined to be the corresponding ideal gas at pressure. For a real gas, one defines the chemical potential as 2 The formula in following equation is equivalent to integrating from the standard - state pressure down to zero pressure with the ideal gas, and then integrating back up to pressure P with the real gas. This procedure gives the difference between the real gas at pressure P and the ideal gas 18

26 at pressure as. Now, the difference between the real and ideal chemical potential can be written. 3 Where, we have used the compressibility, Z(P) =. From equation (3), we get following equation for The real gas and the corresponding ideal gas become identical in the limit of zero pressure. Since real gases at low pressures behave ideally, equation (3) reduces to. 5 Therefore we pick an and such that.. 6 The equation (6) indicates that.. 7 But on the other hand, the value of the chemical potential is independent of the reference pressure i.e.,.. 8 Where P ref is the reference pressure that defines the standard state. Hence, we find the following relation between reference chemical potential But, 11 Where the fugacity is defined by 19

27 12 The final expression for the chemical potential for a real gas is given by:.. 13 Finally, we have to choose. From equation (12), we notice that 14 Consequently we pick = 0. 20

28 Chemical equilibrium: Many chemical reactions do not go to completion but instead attain a state of chemical equilibrium. Chemical equilibria are important in numerous biological and environmental processes. For example, equilibria involving O 2 molecules and the protein hemoglobin play a crucial role in the transport and delivery of O 2 from our lungs to our muscles. Similar equilibria involving CO molecules and hemoglobin account for the toxicity of CO. The another example is - When a liquid evaporates in a closed container, molecules with relatively higher kinetic energy escape the liquid surface into the vapour phase and number of liquid molecules from the vapour phase strike the liquid surface and are retained in the liquid phase. It gives rise to a constant vapour pressure because of an equilibrium in which the number of molecules leaving the liquid equals the number returning to liquid from the vapour. Chemical equilibrium is state in which the rates of the forward and reverse reactions are equal and the concentrations of the reactants and products remain constant. Equilibrium is a dynamic process in which the conversions of reactants to products and products to reactants are still going on, although there is no net change in the number of reactant and product molecules. The mixture of reactants and products in the equilibrium state is called an equilibrium mixture. Based on the extent to which the reactions proceed to reach the state of chemical equilibrium, these may be classified in three groups. (i) The reactions that proceed nearly to completion and only negligible concentrations of the reactants are left. In some cases, it may not be even possible to detect these experimentally. (ii) The reactions in which only small amounts of products are formed and most of the reactants remain unchanged at equilibrium stage. (iii) The reactions in which the concentrations of the reactants and products are comparable, when the system is in equilibrium. For a better comprehension, let us consider a general case of a reversible reaction, A + B C + D 21

29 With passage of time, there is accumulation of the products C and D and depletion of the reactants A and B (as shown in following fig.). This leads to a decrease in the rate of forward reaction and an increase in the rate of the reverse reaction. Eventually, the two reactions occur at the same rate and the system reaches a state of equilibrium. Similarly, the reaction can reach the state of equilibrium even if we start with only C and D; that is, no A and B being present initially, as the equilibrium can be reached from either direction. There are number of important questions about the composition of equilibrium mixtures: What is the relationship between the concentrations of reactants and products in an equilibrium mixture? How can we determine equilibrium concentrations from initial concentrations? What factors can be exploited to alter the composition of an equilibrium mixture? The last question in particular is important when choosing conditions for synthesis of industrial chemicals such as H 2, NH 3, CaO etc. To answer these questions, let us consider a general reversible reaction: A + B C + D where A and B are the reactants, C and D are the products in the balanced chemical equation. On the basis of experimental studies of many reversible reactions, the Norwegian chemists Cato Maximillian Guldberg and Peter Waage proposed in 1864 that the concentrations in an equilibrium mixture are related by the following equilibrium equation, K C = a A m C x C b B l L CM x C CA, CB, CM, CL are the molar concentrations of A, B, C and D respectively. where K c is the equilibrium constant and the expression on the right side is called the equilibrium constant expression. The equilibrium equation is also known as the law of mass action because in the early days of chemistry, concentration was called active mass. Equilibrium constant : The law of mass action gives relationship between concentration of reactant and rate of reaction at any temperature T. It is also stated as- the rate of a chemical reaction at any instant is proportional to the molar concentration of the reacting substance at that instant. Consider the simplest reaction 22

30 A product. If C A is the concentration of the reactant at time t, then- Rate = α An equation which shows that how the rate of chemical reaction is related to the concentration is called as rate law or rate equation. The proportionality constant in the above rate equations is called rate constant or velocity constant or specific rate constant. From above equation α C A = k C A If C A = 1, then rate = = k i.e. Rate constant of reaction is the rate of reaction when all the reactants are at unit concentration or activity. The chemical reactions shows (exhibiting) the tendency to reverse themselves are called as reversible or opposing reaction. In reversible or opposing reactions, the products formed are also react and gives back the reactants. Initially rate of product formation (forward reaction) is very large and is goes on decreasing with time whereas initially rate of opposing reaction or backward reaction (reactant formation) is zero and is increasing with time. After some time t, a stage is reached when two rates are equals. It is called as equilibrium stage. It is dynamic in nature i.e. all the species are reacting at the rate at which they are being formed. At equilibrium stage, overall rate of reaction is zero i.e. = 0. Consider following reversible reaction- A k f Where, k f and k b are the rate constants for the forward and backward reactions respectively. Depending on the physical state of the reactants and products, two physical constants for reversible reaction is defined as K P and K C. At gaseous state, the equilibrium constant K P is in terms of partial pressures of reactants and products while in other state, it is denoted by K C which is in terms of partial concentrations. Consider general reaction- k b B 23

31 aa + bb ll + mm A & B are reactants (behaves ideally) L & M are products (behaves ideally) a & b and c & d are number of moles of reactants and products respectively. When concentrations of both reactants and products are expressed in molar terms, then K C is- Where, are the molar concentrations of A, B, C and D respectively. Characteristics of K c : 1. Expression for equilibrium constant is applicable only when concentrations of the reactants and products have attained constant value at equilibrium state. 2. The value of equilibrium constant is independent of initial concentrations of the reactants and products. 3. Equilibrium constant is temperature dependent having one unique value for a particular reaction represented by a balanced equation at a given temperature. 4. The equilibrium constant for the reverse reaction is equal to the inverse of the equilibrium constant for the forward reaction. 5. The equilibrium constant K for a reaction is related to the equilibrium constant of the corresponding reaction, whose equation is obtained by multiplying or dividing the equation for the original reaction by a small integer. Magnitude of K c : i. If the K c value is large (K c >> 1), the equilibrium lies to the right and the reaction mixture contains mostly products. ii. If the K c value is small (K c <<1), the equilibrium lies to the left and the reaction mixture contains mostly reactants. iii. If the K c value is close to 1 (0.10 < K c < 10), the mixture contains appreciable amounts of both reactants and products. Because gas pressures are easily measured, equilibrium equations for gas-phase reactions are often written using partial pressures rather than molar concentrations. For the gaseous state, the partial pressure is also measure the activity of the component, K P is- Where, are the molar concentrations of A, B, C and D respectively. 24

32 Relationship between K P and K C : Consider general reaction - Therefore, A & B are reactants (behaves ideally) aa + bb ll + mm L & M are products (behaves ideally) a & b and c & d are number of moles of reactants and products respectively. K p = a A m P x P b B l L PM x P PA, PB, PM, PL are the partial molar pressure of A, B, C and D respectively. For n mole of ideal gas- pv = nrt p = = But n/v = C, therefore, p = C R T. Substituting this value of p in above K P equation, then- K p = (C RT) A x m (C RT) x (C RT) M a (C RT) B L b l K p = But (l + m)-(a + b) = n, therefore, a A m C x C B l L CM x C (RT) (l+m)-(a-b) K p = K C (RT) n This is the relationship between K P and K C. When n = 0, then K P = K C. The Reaction isotherm (Van t Hoff s Isotherm): A quantitative relation of the free energy change during the chemical reaction has been developed which is known as Reaction isotherm Van t Hoff s isotherm. Van t Hoff s isotherm gives the net work done that can be obtained from gaseous reactants at constant temperature, when both reactants and products are at suitable orbitary pressure. Consider a general reactionaa + bb +... cc + dd +... Where a, b, c and d are number of moles of reactants A and B and products C and D respectively. If a A, a B, a C and a D are activities of reactants A, B and products C, D respectively. The free energies of each of these substances per mole at T is- G A = + RT. 1 G B = + RT. 2 25

33 G C = + RT. 3 G D = + RT. 4 Where,,, and are the free energies at unit activity of the A, B, C and D respectively or are the standard free energies of A, B, C and D respectively. Therefore the free energy change of the chemical reaction is difference between sum of free energies of product and sum of free energies of reactants. ΔG = ΣG p ΣG R = [c G C + d G D +.] [a G A +b G B +..] = [c + RT + d + RT +.] [a + RT + b + RT +..] = [(c + d + ) (a + b + )] + RT[( + +.) ( + RT +..)] ΔG = ΔG o + RT ln 5 Where ΔG o is the free energy change of the reaction in standard condition or state i.e. free energy change involved when the starting materials and the product formed having unit activity at constant T. The equation (5) is called as the Van t Hoff s isotherm or reaction isotherm. When activities of all reactants and products are equal to one them ΔG = ΔG o. For any reaction, ΔG o is constant at any given temperature and is completely independent on the pressure. The variation of ΔG o with temperature is explain by using following equation- ΔG o = ΔH o - TΔS o At equilibrium step of the reaction- ΔG = 0 0 = ΔG o + RT ln At equilibrium, according to the law of mass action, K a = Therefore, 0 = ΔG o + RT ln K a Or ΔG o = - RT ln K a.. 6 K a = e -ΔGo/RT.. 7 Form equation (5) and (6) - 26

34 ΔG = RT ln - RT ln K a = RT ln Q a - RT ln K a where Q a = = RT ln ( ) 8 Where Q a is called reaction quotient, is the resulting value when we substitute reactant and product concentrations into the equilibrium expression. 1. If Q > K, the reaction will go to the left. The ratio of products over reactants is too large & the reaction will move toward equilibrium by forming more reactants. 2. If Q < K, the reaction will go to the right. The ratio of products over reactants is too small & the reaction will move toward equilibrium by forming more products. 3. If Q = K, the reaction mixture is already at equilibrium, so no shift occurs. For gases activities are proportional to the partial pressures of the components of reaction mixture hence the activities of the equation (5) can be replaced by the partial pressures, therefore- ΔG = ΔG o + RT ln. 9 = RT ln Q p - RT ln K p 10 Where K p is the equilibrium constant and Q p = At equilibrium state, ΔG = ΔG o and Q p = 1. ΔG o = - RT ln K p = -W or K p = e -ΔGo/RT.. 11 i.e. net work done of the reaction is equal to the decrease in free of the system and it is calculated by using expression- RT ln K p or 2.303RT ln K p. It will be observed that, ΔG is positive when K p is less than unity. If ΔG is negative when K p is greater than unity and is zero when K p =0. Van t Hoff Isochore: The Van t Hoff isochore is obtained by comparing the Van t Hoff isotherm with Gibbs- Helmeholtz equation. The Gibbs Helmeholtz equation is ΔG = ΔH + T 27

35 Or - ΔH = T - ΔG Dividing both side by T 2 gives:- = The right hand side of the above equation is obtained by differentiating ΔG/T w.r.t. T at constant P- = = 12 According to Van t Hoff isotherm- ΔG = - RT ln K p.. 13 Dividing both side by T and differentiating it w.r.t. T at constant P- = R. 13a Comparing equation (13) and (12), we have- = R Or = d (ln K p ).. 14 The above equation is known as Van t Hoff isochore. For applying isochore to any chemical reaction, it is essential to integrate it. If ΔH remains same over the range of temperature, we have on integrationln K p = = + constant of integration. Appling the limits T 1 and T 2 at the equilibrium constants K p1 and K p2 respectively, we havelnk p2 - lnk p1 = ln = ln =. 15 By using this equation, equilibrium constant at any temperature or heat of reaction is calculated. In reversible reaction, the sign of ΔG o indicates whether the forward or reverse reaction is spontaneous as- ΔG o = RT log K p 28

36 i) If ΔG o is negative; log K must be positive & K is greater than one and reaction proceeds spontaneously in forward direction. ii) If ΔG o is positive; log K must be negative & K is less than one and reaction proceeds spontaneously in reverse direction. iii) If ΔG o is zero; log K must be zero & K is equal to one and reaction is in equilibrium state. Van t-hoff equation in terms of K c : We known that equilibrium constant in terms of partial pressure K p and in terms of concentration K c are related to each other by the equation as- K p = K c (RT) Δn Taking logarithm of both sideln K p = ln K c + Δn ln (RT) Differentiate it with respect to temperature, we get- = + 16 From equation (16) and (14)- = + = = = But (ΔH ΔnRT) = ΔE, =. 19 Where, ΔE is the heat of reaction at constant volume. 29

37 1.2. Photochemistry: Introduction: Important developments in the study of photochemistry occurred in the early 1800s. In 1817 the German physicist Theodor von Grotthus recognized that in order for light to be effective in producing a chemical change it had to be absorbed. In 1841 the American chemist John William Draper studied the reaction between moist hydrogen and chlorine gases. This reaction was observed first about 1801 and may have been the first recognized photochemical reaction. Draper noted that after a certain inhibition period the rate of the reaction was proportional to the intensity of the light absorbed. These observations led to the first law of photochemistry (the Grotthus-Draper law), which states that the amount of photochemical reaction is proportional to the quantity of light absorbed. The development of the quantitative aspects of photochemistry began in earnest with the enunciation of the quantum theory by Max Planck in 1900 and its elucidation by Albert Einstein in Planck, who is regarded as the founder of the quantum theory, espoused that an atom or a molecule can absorb only fixed quantities (quanta) of light energy. Many reactions can be initiated by the absorption of electromagnetic radiation. The most important of all are the photochemical processes that capture the radiant energy of the Sun either ultra violet or visible light. Electromagnetic radiation in the ultraviolet and visible region spans a wavelength range of about nm corresponding to energies of kcal mole -l. A molecule in an excited electronic state can possibly undergo a chemical reaction that is inaccessible in the ground level. If the excited state was reached directly or indirectly by absorption of radiation, the reaction is a photochemical reaction. Most photochemical reactions are governed by the Stark Einstein law of photochemistry, which states that absorption of one photon causes the reaction of one molecule. However, the number of molecules that react is not necessarily equal to the number of photons absorbed. Some of the excited molecules might undergo internal conversion, intersystem crossing, fluorescence, or phosphorescence processes leading to unreactive states and therefore not react chemically. A chain reaction might occur in which the reaction of one molecule can lead to the reaction of other molecules without 30

38 absorption of additional radiation. The quantum yield of a photochemical reaction,, is defined by.. 1 Equation (1) can also be stated in terms of moles of reactant and moles of photons. One mole of photons is called an Einstein, so that 2 In a chain reaction, can exceed unity, but in a non-chain reaction, 1. Example: Upon radiation with ultraviolet light of 300 nm to 350 nm wavelength, benzophenone undergoes a reaction with 2-propanol to form benzpinacol and acetone. Most photochemical reactions can be considered to occur in three stages: 1. Absorption of electromagnetic radiation to produce electronically excited states. 2. Primary photochemical reactions involving excited electronic states. 3. Secondary or dark reactions whereby the products of the primary photochemical reaction are converted to stable products. Terms used in photochemistry: The ground states of most molecules all electrons are paired; excited states also can have all electrons paired. Such states with paired electrons are called singlet states. The excited singlet state (S 1 ), ground singlet state curve (S 0 ). Excited states also can have unpaired electrons. States with two unpaired electrons are called triplet states (T) and normally are more stable than the corresponding singlet states because, by Hund's rule, less inter-electronic repulsion is expected with unpaired than paired electrons. Thermal and photochemical reactions: Thermal reactions: Thermochemistry is the study of the energy and heat associated with chemical reactions. If a reaction releases energy and heat, it is called exothermic reaction. The opposite is the endothermic reaction, when energy and heat is absorbed. 31

39 Photochemical reactions: Some reactions do not take place in the dark but take place only in the presence of light or some other radiation. Such reactions are known as photochemical reactions. For example: Photosynthesis of HCl gas: H 2 (g) + Cl 2 (g) + hν -> 2 HCl (g) Light is a form of energy. Hence it provides the necessary activation energy for the reaction to take place. Features of photochemical reactions: 1. Photochemical reactions do not take place in dark but take place in the presence of light by absorbing it. 2. Since different colored radiations in the range of visible light have different frequencies and hence different energies, therefore all radiations may not be able to initiate a particular reaction. For example, a photon of violet light has highest frequency and hence the highest energy. Hence a reaction which is initiated by violet light may not be initiated by other colored radiations 0of visible light. On the other hand, a photon of red light has lowest frequency and energy. Therefore a reaction that can be initiated by all other radiations as well. 3. Temperature has very little effect on the rate of a photochemical reaction. Instead, the intensity of light has marked effect on the rate of photochemical reaction. 4. The free energy change of a photochemical reaction may not be negative. 5. There are many substances which do not react directly when exposed to light. However, if another substance is added, the photochemical reaction starts. Difference between photochemical reactions and thermochemical reactions are discussed below: Thermochemical reactions Photochemical reactions These reactions involve absorption or evolution of heat. They can take place even in absence of light i.e. dark. These reactions involve absorption of light. The presence of light is the primary requisite for the reaction to take place. Temperature has significant effect on the rate Temperature has very little effect on the rate of a photochemical reaction. Instead, the 32

40 of a thermochemical reaction. The free energy change G of a thermochemical reaction is always negative. They are accelerated by the presence of a catalyst. intensity of light has a marked effect on the rate of a photochemical reaction. The free energy change G of a photochemical reaction may not be negative. Some of these are initiated by the presence of a photosensitizer. However a photosensitizer acts in a different way than a catalyst. Laws of Photochemistry: The study of chemical reactions, isomerizations and physical behavior that may occur under the influence of visible and/or ultraviolet light is called Photochemistry. Two fundamental principles are the foundation for understanding photochemical transformations: 1. Grotthus-Draper law or the first law of photochemistry 2. Stark-Einstein law or the second law of photochemistry Grotthus-Draper law or the first law of photochemistry: Only the light which is absorbed by a molecule can be effective in producing photochemical changes in the molecules. h R R* Product Ground state Excited state The probability or rate of absorption is given by the Lambert-Beer law. The Lambert law states that the fraction of incident radiation absorbed by a transparent medium is independent of the intensity of incident radiation and that each successive layer of the medium absorbs an equal fraction of incident radiation. The Beer law states that the amount of radiation absorbed is proportional to the number of molecules absorbing the radiation that is the concentration C of the absorbing species. Where, is the proportionality constant. The quantity C dl, measures the amount of solute per unit area of the layer, dl being the thickness of the layer. On integrating, we have 33

41 Where is absorption coefficient is function of frequency or wavelength of radiation.. 3 Where,, is called the molar extinction coefficient and is a function of frequency of radiation, the concentration is expressed in moles per litre and l is the optical path length in cm. The quantity is commonly known as the optical density OD or absorbance A. Stark-Einstein law or the second law of photochemistry: It is also known as the photochemical equivalence law or photoequivalence law. The second law of photochemistry was first enunciated by Stark (1908) and later by Einstein (1912). The Stark-Einstein law states that: One quantum of light is absorbed per molecule of absorbing and reacting substance that disappears or The absorption of light by a molecule is a one-quantum process for low to moderate light intensity, e.g., to quanta/sec. Number of activated molecules = Number of quanta of radiation absorbed 1 R + 1 h 1 R* Ground state Excited state Molecules which absorb photons become physically excited, and this must be distinguished from becoming chemically active. Excited molecules may lose their energy in nonchemical ways, or alternatively may trigger off thermal reactions of large chemical yield. The so-called law, therefore, rarely holds in its strict sense, but rather provides essential information about the primary photochemical act. Einstein energy: For any chemical reaction, energy is required in two ways: (i) as energy of activation ΔE act, and (ii) as enthalpy or heat of reaction ΔH. The need for energy of activation arises because on close approach, the charge clouds of the two reacting partners repel each other. The reactants must have sufficient energy to overcome this energy barrier for fruitful interaction. The enthalpy of reaction is the net heat change associated with the breaking and making of bonds leading to reaction products. In thermal or dark reactions, the energy of activation is supplied as heat energy. In photochemical reactions, the energy barrier is by passed due to electronic excitation and one of the products may appear in the excited state. 34

42 The bond dissociation energy per mole for most of the molecules lie between 150 kj and 600 kj. These energies are available from Avogadro s number of photons of wavelengths lying between 800 nm and 200 nm respectively, which correspond to the visible and near ultraviolet regions of the electromagnetic spectrum. The same range of energies is required for electronic transitions in most atoms and molecules. From Bohr s relationship, the energy equivalent of a photon (Einstein - An Avogadro number of photons is called an einstein) of this wavelength is calculated as E = E 2 E 1 = hν Where, h = Planck s constant and ν is the frequency of absorbed radiation. When expressed in wave number ( ) in reciprocal centimeter (cm 1 ) or wavelength ( ) in nanometer (nm) and substituting the values for h and c (the velocity of light), we get. 4 In this system, the unit of length is a metre (m), the unit of mass is kilogram (kg) and the unit of time is second (s). All the other units are derived from these fundamental units. The unit of thermal energy, calorie, is replaced by Joule (1J = 10 7 erg) to rationalize the definition of thermal energy. 35

43 Quantum efficiency: The concept of quantum yield or quantum efficiency was first introduced by Einstein. The quantum yield of a process is the probability that an absorbed photon undergoes one particular process. Thus, one can define a quantum yield for fluorescence, a quantum yield for phosphorescence, or a quantum yield for other pathways. Each quantum yield is typically a number between 0 and 1 (except under unusual circumstances), and the total of all quantum yields for a particular absorption event should sum to one. To express the efficiency of a photochemical reaction, the quantity quantum efficiency φ is defined as.. 5 When high intensity light sources as from flash lamps or lasers are used biphotonic photochemical effects may occur which modify the application of the Einstein law. At very high intensities a molecule may absorb two photons simultaneously; a more common effect, however, is for a second photon of longer wavelength to be absorbed by a metastable (triplet or radical) species produced by the action of the first photon. The nature of the photo-products and the quantum yields are here dependent on the light intensity. The concept of quantum yield can be extended to any act, physical or chemical, following light absorption... 6 Determination of Quantum efficiency using actinometer: The mechanism of photochemical reaction has been measured by number of ways, some of them are: (1) detection of the products in a photochemical reaction, as many as 10 or 15; (2) in measuring kinetics, there are more variables, since we can study the effect of the intensity or the wavelength of light on the rate of reaction; (3) in the detection of intermediates by spectra we can use the technique of flash photolysis, which can detect extremely short-lived intermediates. In addition to these methods, there are two additional techniques. 36

44 1. The use of emission (fluorescence and phosphorescence) as well as absorption spectroscopy: the presence of as well as the energy and lifetime of singlet and triplet excited states can often be calculated. 2. The study of quantum yields. The quantum yield is the fraction of absorbed light that goes to produce a particular result. There are several types. A primary quantum yield for a particular process is the fraction of molecules absorbing light that undergo that particular process. Product quantum yields are much easier to measure. The number of quanta absorbed can be determined by an instrument called an actinometer, which is actually a standard photochemical system whose quantum yield is known. The physical device is converted incident photon energy into a quantifiable electrical signal however; a chemical actinometer is the most widely used device in which quantum yield of the reference substance undergoing a photochemical reaction is determined and calibrated. Working principle of Physical actinometer: An actinometer is a chemical system or physical device which determines the number of photons in a beam integrally or per unit time. This name is commonly applied to devices used in the ultraviolet and visible wavelength ranges. For example, solutions of iron(iii) oxalate can be used as a chemical actinometer, while bolometers, thermopiles, and photodiodes are physical devices giving a reading that can be correlated to the number of photons detected. Following are the basic steps employed in the working principle of chemical actinometer a. The gas of interest is filled into a photolysis reactor. b. Actinometer is exposed to heat radiation. c. The photochemical rate is measured. The actinometer gas is exposed to actinic flux without altering the radiation intensity and spectral composition. For this reason, a transparent quartz cell having a suitable geometrical shape is used, and gases with small optical absorbance value is used. Based on these conditions, the photolysis frequency can be easily evaluated. There are two basic modes of actinometric operation: static batch mode and flowing gas mode. In the static bath mode, the photolysis reactor is filled with actinometer gas, sealed off by a gas valve and covered with a opaque hood to prevent exposure to sunlight. During measurement, the actinometer is uncovered and exposed to heat radiation for a fixed of time. Following this, the actinometer is closed again and analyzed for change in the gas composition. 37

45 In another mode of operation, the actinometer gas is constantly passed into the reactor that is exposed to solar radiation. In this case, the time interval is considered to be the mean residence time of the gas in the illuminated reactor. When gas passes through the reactor, its composition is analyzed using online gas detector along with continuous moderation of photolysis frequencies. Working principle of Chemical actinometer: Chemical actinometry involves measuring of radiant flux via the yield from a chemical reaction. It requires a chemical with a known quantum yield and easily analyzed reaction product. Potassium ferrioxalate is commonly used, as it is simple to use and sensitive over a wide range of relevant wavelengths (254 nm to 500 nm). Irradiation of ferrioxalate solution results in the reduction of Fe 3+ to Fe 2+ which is estimated calorimetrically by using o-phenanthrolin as complexing agent. The OD at 510 nm of the deep red color produced is compared with a standard. The quantum yield for Fe 2+ formation is nearly constant within the wavelength range and shows negligible variation with temperature, solution composition and light intensity. The recommended actinometric solution, for wavelength up to 400 nm contains M K 3 Fe(ox) 3 in 0.1 N H 2 SO 4. For longer wavelengths, a 0.15 M solution is more convenient. Quantum yields vary between 1.2 (λ nm) to 1.1 at longer wavelengths. Other actinometers include malachite green leucocyanides, vanadium(v) iron(iii) oxalate and monochloroacetic acid, however all of these undergo dark reactions, that is, they react in the absence of light. This is undesirable since it will have to be corrected for. Other actinometers are more specific in terms of the range of wavelengths at which quantum yields have been determined. Reinecke s salt K[Cr(NH 3 ) 2 (NCS) 4 ] reacts in the near-uv region although it is thermally unstable. Uranyl oxalate has been used historically but is very toxic and cumbersome to analyze. Applications: 1. The actinometers are chiefly used in meteorology to measure solar radiation transmitted by the sun, reflected by the earth or scattered by the atmosphere. 2. They are used in photochemical experiments that involve complex irradiation geometry. 3. They are used for calibrating photochemical detectors used for radiation measurements. 4. In combination with joulemeters, it is used for measuring laser pulse energies. 38

46 Photochemical reactions: Ordinary reactions occur by absorption of heat energy from outside. The reacting molecules are energized and molecular collisions become effective. These bring about the reaction. The reactions which are caused by heat and in absence of light are called thermal or dark reactions. On the other hand, some reactions proceed by absorption of light radiations. These belong to the visible and ultraviolet regions of the electromagnetic spectrum (2000 to 8000 Å). The reactant molecules absorb photons of light and get excited. These excited molecules then produce the reactions. A reaction which takes place by absorption of the visible and ultraviolet radiations is called a photochemical reaction. Time span of photochemical reaction: Electronic transitions caused by absorption of ultraviolet and visible radiation occur within s. We expect, then, that the upper limit for the rate constant of a first-order photochemical reaction is about s 1. Fluorescence is slower than absorption, with typical lifetimes of s. Therefore, the excited singlet state can initiate very fast photochemical reactions in the femtosecond (10 15 s) to picoseconds (10 12 s) timescale. Examples of such ultrafast reactions are the initial events of vision and of photosynthesis. Typical intersystem crossing (ISC) and phosphorescence times for large organic molecules are s and s, respectively. As a consequence, excited triplet states are photochemically important. Indeed, because phosphorescence decay is several orders of magnitude slower than most typical reactions, species in excited triplet states can undergo a very large number of collisions with other reactants before deactivation. The overall photochemical reaction may consist of: (a) A primary reaction (b) Secondary reactions A primary reaction proceeds by absorption of radiation. A secondary reaction is a thermal reaction which occurs subsequent to the primary reaction. For example, the decomposition of HBr occurs as follows: HBr + hv + Primary reaction HBr + H 2 + Secondary reaction + Br 2 Secondary reaction 39

47 2HBr + hv H 2 + Br 2 Overall reaction Evidently, the primary reaction only obeys the law of photochemical equivalence strictly. The secondary reactions have no concern with the law. Cause of high quantum yield: When one photon decomposes or forms more than one molecule, the quantum yield φ > 1 and is said to be high. The chief reasons for high quantum yield are: (a) Reactions subsequent to the Primary reaction: One photon absorbed in a primary reaction dissociates one molecule of the reactant. But the excited atoms that result may start a subsequent secondary reaction in which a further molecule is decomposed. AB + hv A + B Primary AB + A A 2 + B Secondary Obviously, one photon of radiation has decomposed two molecules, one in the primary reaction and one in the secondary reaction. Hence the quantum yield of the overall reaction is 2. (b) A reaction chain forms many molecules per photon: When there are two or more reactants, a molecule of one of them absorbs a photon and dissociates (primary reaction). The excited atom that is produced starts a secondary reaction chain. A 2 + hv 2A... (1) Primary A + B 2 AB + B... (2) Secondary B + A 2 AB + A... (3) Reaction chain It is noteworthy that A consumed in (2) is regenerated in (3). This reaction chain continues to form two molecules each time. Thus the number of AB molecules formed in the overall reaction per photon is very large. Or that the quantum yield is extremely high. Examples of high quantum yield: The above reasons of high quantum yield are illustrated by citing examples as below: (i) Decomposition of Hl: The decomposition of hydrogen iodide is brought about by the absorption of light of less than 4000 Å. In the primary reaction, a molecule of hydrogen iodide absorbs a photon and dissociates to produce H and I. This is followed by secondary steps as shown below: HI + hv H + I... (1) Primary H + HI H 2 + I... (2) Secondary I + I I 2... (3) 2HI + hv H 2 + I 2 Overall reaction 40

48 In the overall reaction, two molecules of hydrogen iodide are decomposed for one photon (hv) of light absorbed. Thus the quantum yield is 2. (ii) Hydrogen-Chlorine reaction: This is a well known example of a photochemical chain reaction. A mixture of hydrogen and chlorine is exposed to light of wavelength less than 4000 Å. The hydrogen and chlorine react rapidly to form hydrogen chloride. In the primary step, a molecule of chlorine absorbs a photon and dissociates into two Cl atoms. This is followed by the secondary reactions stated below: Cl 2 + hv 2Cl... (1) Primary reaction Cl + H 2 HCl + H... (2) H + Cl 2 HCl + Cl... (3) The Cl atom used in step (2) is regenerated in step (3). Thus the steps (2) and (3) constitute a self-propagating chain reaction. This produces two molecules of HCl in each cycle. Thus one photon of light absorbed in step (1) forms a large number of HCl molecules by repetition of the reaction sequence (2) and (3). The chain reaction terminates when the Cl atoms recombine at the walls of the vessel where they lose their excess energy. 2Cl Cl 2 The number of HCl molecules formed for a photon of light is very high. The quantum yield of the reaction varies from 10 4 to Causes of low quantum yield: The chief reasons of low quantum yield are: (a) Deactivation of reacting molecules: The excited molecules in the primary process may be deactivated before they get opportunity to react. This is caused by collisions with some inert molecules or by fluorescence. A + hv A * A * A + hv Activation Fluorescence (b) Occurrence of reverse of primary reaction: Here the primary reaction generally yields a polymer. The product then undergoes a thermal reaction giving back the reactant molecules. h 2 A A 2 Thermal The reverse thermal reaction proceeds till the equilibrium state is reached. 41

49 (c) Recombination of dissociated fragments: In a primary process, the reactant molecules may dissociate to give smaller fragments. These fragments can recombine to give back the reactant. (AB) + hv A + B A + B (AB) Thus the secondary reactions involving the fragments to form the product will not occur. This will greatly lower the yield. The yield of particular photochemical reaction may be lower than expected for more than one reason cited above. Examples of low quantum yield: The examples listed below will illustrate the above causes of low quantum yield: (i) Dimerization of Anthracene. When anthracene, C 14 H 10, dissolved in benzene is exposed to ultraviolet light, it is converted to dianthracene, C 28 H 20. h 2 C 14 H 10 C 28 H 20 Obviously, the quantum yield should be 2 but it is actually found to be 0.5. The low quantum yield is explained as the reaction is accompanied by fluorescence which deactivates the excited anthracene molecules. Furthermore, the above reaction is reversible. h 2 C 14 H 10 C 28 H 20 Thermal The transformation of the product back to the reactant occurs till a state of equilibrium is reached. This further lowers the quantum yield. (ii) Combination of H 2 and Br 2 : When a mixture of hydrogen and bromine is exposed to light, hydrogen bromide is formed. The reaction occurs by the following possible steps. Br 2 + hv 2Br Br + H 2 HBr + H... (2) H + Br 2 HBr + Br... (3) H + HBr H 2 + Br... (4) Br + Br Br 2... (5) (1) Primary reaction The reaction (2) is extremely slow. The reactions (3), (4) and (5), depend directly or indirectly on (2) and so are very slow. Therefore most of the Br atoms produced in the primary process recombine to give back Br 2 molecules. Thus the HBr molecules obtained per quantum is extremely small. The quantum yield of the reaction is found to be 0.01 at ordinary temperature.

50 Photochemical phenomenon: Fluorescence: George Gabriel Stokes named the phenomenon fluorescence in Radiative decay between states of same spin multiplicity (i.e. S=0). Emission of electromagnetic radiation, usually visible light, caused by excitation of atoms in a material which then reemit immediately (within about 10-8 seconds). The initial excitation is usually caused by the absorption of energy from incident radiation of particles, such as X-Rays or electrons. Because reemission occurs so quickly the fluorescence ceases as soon as the exciting source is removed, unlike phosphorescence, which persists as an afterglow. E.g. A fluorescent light bulb is coated on the inside with a powder and contains a gas; electricity causes the gas to emit ultraviolet radiation, which then stimulates the tube coating to emit light. Fluorescence has many practical applications, including mineralogy, gemology, chemical sensors, fluorescence labeling, dyes, biological detectors, and, most commonly, fluorescent lamps. The most striking examples of fluorescence occur when the absorbed radiation is in the ultraviolet region of the spectrum, and thus invisible and the emitted light are in the visible region. Phosphorescence: Radiative decay between states of different spin multiplicity (i.e. S 0). The emission of light from a substance exposed to radiation and persisting as an afterglow after the 43

51 exciting radiation has been removed. Unlike fluorescence, in which the absorbed light is spontaneously emitted about 10-8 seconds after excitation, phosphorescence requires additional excitation to produce radiation and may last from about 10-3 seconds to days or years depending on the circumstances. In simple term phosphorescence is a process in which energy absorbed by a substance is released relatively slowly in the form of light. Phosphorescent substances have the ability to store up light and release it gradually. If the molecules of the substance can get from the ground state to a metastable state, and if the metastable state can slowly decay back to the ground state via photon emission, then we have phosphorescence. Metastable state: In physics and chemistry, particular excited state of an atom, nucleus, or other system that has a longer lifetime than the ordinary excited states and that generally has a shorter lifetime than the lowest, often stable, energy state, called the ground state. A metastable state may thus be considered a kind of temporary energy trap or a somewhat stable intermediate stage of a system the energy of which may be lost in discrete amounts. Chemiluminescence: It is the generation of electromagnetic radiation as light by the release of energy from a chemical reaction. While the light can, in principle, be emitted in the ultraviolet, visible or infrared region, those emitting visible lights are most common. Chemiluminescent reactions can be grouped into three types: 1. Chemical reactions using synthetic compounds and usually involving a highly oxidized species such as peroxide are commonly termed chemiluminescent reactions. 2. Light-emitting reactions arising from a living organism, such as the firefly or jellyfish, are commonly termed bioluminescent reactions. 3. Light-emitting reactions which take place by the use of electrical current are designated electrochemiluminescent reactions. Chemiluminescence differs from fluorescence in that the electronic excited state is derived from the product of a chemical reaction rather than the more typical way of creating electronic excited states, namely absorption. Here, light is generated from a chemically exothermic reaction. 44

52 Internal Conversion: Radiationless transition between states of same spin multiplicity (e.g. S n to S m or T n to T m, m<n). Internal conversion is a transition from a higher to a lower electronic state in a molecule or atom. It is sometimes called "radiationless de-excitation", because no photons are emitted. Intersystem Crossing: Radiationless transitions between states of differing spin multiplicity (e.g. S n to T n ). This process, intersystem crossing is the non-radiative conversion of a singlet state to a lower energy triplet state, or vice versa and is slower than internal conversion. Excited State Quenching: When a second molecule interacts with a molecule in an excited state, new ways may be created for the excited state species to lose its energy of excitation. Such interactions (collisions) can induce the loss of energy in the form of heat, which is called physical quenching, or it can cause the energy to be transferred to the second molecule with or without the transfer of an electron. The former is called simply energy transfer (second molecule get excited), and the latter electron transfer (forming ions). Ozone Depletion: Ozone layer depletion, is simply the wearing out (reduction) of the amount of ozone in the stratosphere. Unlike pollution, which has many types and causes, Ozone depletion has been pinned down to one major human activity. Industries that manufacture things like insulating foams, solvents, soaps, cooling things like Air Conditioners, Refrigerators and Take-Away containers use something called chlorofluorocarbons (CFCs). These substances are heavier than air, but over time, (2-5years) they are carried high into the stratosphere by wind action. Depletion begins when CFC s get into the stratosphere. CFCs are molecules made up of chlorine, fluorine and carbon. Because they are extremely stable molecules, CFCs do not react with other chemicals in the lower atmosphere, but exposure to ultraviolet radiation in the stratosphere breaks them apart, releasing chlorine atoms. Free chlorine (Cl) atoms then react with ozone molecules, taking one oxygen atom to form chlorine monoxide (ClO) and leaving an oxygen molecule (O 2 ). If each chlorine atom released from a CFC molecule destroyed only one ozone molecule, CFCs would pose very little threat to the ozone layer. However, when a chlorine monoxide molecule encounters a free atom of oxygen, the oxygen atom breaks up the chlorine monoxide, stealing the oxygen atom and releasing the chlorine atom back into the stratosphere to destroy another ozone molecule. These two reactions happen over 45

53 and over again, so that a single atom of chlorine, acting as a catalyst, destroys many molecules (about 100,000) of ozone. Fortunately, chlorine atoms do not remain in the stratosphere forever. Free chlorine atoms react with gases, such as methane (CH 4 ), and get bound up into hydrogen chloride (HCl) molecules. These molecules eventually end up back in the troposphere where they are washed away by rain. Therefore, if humans stop putting CFCs and other ozone-destroying chemicals into the stratosphere, stratospheric ozone will eventually return to its earlier, higher values. There are other Ozone Depleting Substances (ODS) such as methyl bromide used in pesticides, halons used in fire extinguishers, and methyl chloroform used in making industrial solvents. 46

54 1.3. Chemical Kinetics II: Introduction: Chemical kinetics is the branch of physical chemistry which concern with the study of the rates of chemical reactions and is used to determine the mechanism of the chemical reaction with which it is proceeds. Thermodynamics does not explain, how rapidly and by what mechanism does a reaction can be takes place? Thermodynamics consider only the relation between reactants and the product of the reaction. It does not explain the stages through which the reactants get converted into products and also does not explain the rate at which the equilibrium is attained. Chemical kinetics provides such information along with thermodynamics. There are some reactions which are very fast. e.g.- Ionic and explosive reactions so that their rate is measured by using special instrument and some reactions are also very slow; that are completed within months or years are necessary to complete at ordinary temperature, their rates are measured. The rate of the chemical reactions are depends on the nature of the reacting substance, the temperature and the concentration of the reacting substances. As temperature increases, the rate of the reaction increases rapidly and is almost double when temperature increased by 10 0 C or doubled. Rate of chemical reaction means speed or the velocity of the reaction. In a chemical reaction, the reactants are consumed i.e. concentration of the reactants goes on decreasing while those of the products increase with time. Rate of a chemical reaction is defined as- rate of change of concentration of reactants or product with time t. Consider a simple chemical reaction, A B. As reaction proceeds, concentration of A decrease while that of product, B increase with time. Rate = Rate of disappearance of A with time t = - dc A /dt OR Rate = Rate of appearance of B with time t. = dc B /dt. On the basis of above chemical conversion, rate of a reaction is defined as- The decrease in concentration of a reactant in unit time or increase in concentration of a product in unit time. e.g. Consider a chemical reaction 47

55 aa + bb cc + dd. If C A, C B, C C and C D are the concentrations of reactant A, B and products C, D respectively then the rate with respect to A, B, C and D are- dc A /dt, dc B /dt, dc C /dt and dc D /dt respectively. These rates are related to each other by the equation- (1/a)dC A /dt = (1/b)dC B /dt = (1/c)dC C /dt = (1/d)dC D /dt The dimentations of the rate of the reaction is- Rate = [conc.]/[time] = [conc.][time] -1. The law of mass action gives relationship between concentration of reactant and rate of reaction at any temperature T. It is also stated as- the rate of a chemical reaction at any instant is proportional to the molar concentration of the reacting substance at that instant. If the stoichiometric equation of a chemical reaction containing more than one reactant, then rate of chemical reaction is proportional to the product of the concentration of reactants with each concentration raise to the power equal to number of molecules of each starting molecule (species) participating in the reaction shown by stoichiometric equation. Consider the simplest reaction- A product. If C A is the concentration of the reactant at time t, then- Rate = - dc A /dt α C A 1 An equation which shows that how the rate of chemical reaction is related to the concentration is called as rate law or rate equation. Consider following reactions - A + B product. Rate = - dc A /dt = - dc B /dt α C A x C B 2 A + 2B product. Rate = - dc A /dt = -(1/2)dC B /dt α C A x C 2 B. 3 In general - a aa + bb product. Rate = - (1/a)dC A /dt = -(1/b)dC B /dt α C A x C b B 4 Dependence of rate of reaction with concentration is determined experimentally i.e. rate equation has been formed experimentally. The proportionality constant in the equations (1), (2), (3) and (4) is called rate constant or velocity constant or specific rate constant. The rate constant is the 48

56 characteristic of the reaction and is different for different reactions. It is also depends on the temperature and change with change in temperature. From equation (1) - dc A /dt α C A - dc A /dt = k C A. 5 If C A = 1, then rate = - dc A /dt = k i.e. Rate constant of reaction is the rate of reaction when all the reactants are at unit concentration or activity. For equation (2), (3) and (4) - - dc A /dt = - dc B /dt = k C A x C B 6 - dc A /dt = -(1/2)dC B /dt = k C A x C 2 B.. 7 a - (1/a)dC A /dt = -(1/b)dC B /dt = k C A x C b B 8 The significance of the rate constant can be understood by considering the following examples as e.g. Decomposition of benzene diazonium chloride in water: k = 4.2 x 10-4 sec.-1 at 40 0 C i.e. from one molar aqueous solution of benzene diazonium chloride, 4.2 x 10-4 mole will be decomposed in one second at 40 0 C. Rate constant of a reaction is used to decide the rapidity (speed) of the reaction i.e. High value of k indicates that reaction is rapid and vice-versa. Units of k: Consider - dc A /dt = k C A a x C B b from equation (8). a k = -dc A /dt [C A x C b B ] If concentration is given in mole/lit and time is in second, then dimensions of k isk = [mole/lit] x [mole/lit] -a x [mole/lit] -b x [second] -1. = [mole/lit] 1-(a-b) x [second] -1. ORDER OF CHEMICAL REACTION: 1. It is an experimentally determined quantity and it is calculated from the rate equation applicable to the reaction. 2. Consider a chemical reaction 49

57 aa + bb + cc products. Rate = k. C a A. C b B. C c C Then, rate of reaction is proportional to the a th power of the concentration of reactant A, to the b th power of the concentration of reactant B, to the c th power of the concentration of reactant C, etc. The reaction is said to be a th ordered with respect to A, b th ordered with respect to B, c th ordered with respect to C, etc. The overall order of the reaction is n - n = a + b + c The order of the reaction with respect to particular reactant is equal to the power of the concentration of that reactant raised in the rate equation. The overall order of the reaction involving two or more reactants is the sum of powers of the concentrations of various reactants involving in the rate equation. 4. In rate equation only those reactants appears whose concentration undergoes changing during the chemical reaction. (a) The reactants which are present in large (excess) amount will not appear in the rate equation because the change in concentration is immeasurably small. (b) The concentration of the catalyst also will not appear in the rate equation even though the catalyst actually takes part in the reaction. MOLECULARITY OF REACTION: 1. It is a theoretical concept and is based on the mechanism of the reaction. The chemical reactions are broadly classified into two types a) Simple reactions:- A chemical reactions are completed in single step. b) Complex reactions:- A chemical reactions are undergoes completion in two or more intermediate steps in which at least one of the step is slow called rate determining step of reaction. The slow step decides the rate of reaction. 2. The number of atoms or molecules that are involved in slow step of reaction is called as molecularity of the reaction. 3. The molecularity and order of the reaction may be or may not be same. e.g.- 1. H 2 + I 2 2HI, order = molecularity = 2. 50

58 2. CH 3 COOEt + H 2 O (excess) CH 3 COOH + EtOH. Order of reaction = 01 and molecularity of reaction = During deciding molecularity of the reaction, if catalyst or the reagent which is taken in excess is participating in the rate determining step of reaction are taken in consideration. 5. The molecularity of the reaction can never be zero and fractional. e.g.- Molecularity of the following reaction is 02. H 2(g) + D 2(g) 2HD (g). 6. The molecularity of the reaction does not alter (changed) when we change the experimental conditions. e.g.- concentration, temperature, nature of the reagent/reactant, etc. Whereas order of the reaction is changed with change the reaction conditions because order of the reaction is depends on the rate equation i.e. k and molecularity of the reaction is depends on the mechanism (mechanism of the reaction does not change with change in reaction conditions). 7. On the basis of molecularity, the reactions are classified as unimolecular (involving one reactant), bimolecular (involving two molecules of same or different reactants), trimolecular (involving three molecules of same or different reactants), etc reactions. 51

59 Simultaneous or Complex Reactions: Sometimes there are side reactions are occurred along with main chemical reaction. Such chemical reactions are called as complex reactions because it is not takes place in single step of reaction. The overall rate of complex reaction is decided from the stiochimetric equation of the complex reaction. Such reactions are grouped generally in following general reactions as- 1. Reversible or opposing reactions. 2. Parallel reactions. 3. Consecutive reactions. 1. Reversible or opposing reactions. We have predict all above rate equations by assuming that the chemical reaction can be proceeds in only one direction without any tendency of the reaction to reverse themselves i.e. point of equilibrium lies on the side of product is in greater extent. The product formed initiate the reaction opposite to the forward reaction and it s rate goes on increasing with time. The chemical reactions shows (exhibiting) the tendency to reverse themselves are called as reversible or opposing reaction. In reversible or opposing reactions, the products formed are also react and gives back the reactants. Initially rate of product formation (forward reaction) is very large and is goes on decreasing with time whereas initially rate of opposing reaction or backward reaction (reactant formation) is zero and is increasing with time. After some time t, a stage is reached when two rates are equals. It is called as equilibrium stage. It is dynamic in nature i.e. all the species are reacting at the rate at which they are being formed. At equilibrium stage, overall rate of reaction is zero i.e. dx/dt = 0. Consider following reversible reaction - A Where, k f and k b are the rate constants for the forward and backward reactions respectively. Initial concentration of A and B are [A] 0 = a mol and [B] 0 = 0 respectively. After time t, k f k b B 52

60 concentration of A and B are C A and C B respectively. The overall rate of the reaction = Rate of forward reaction rate of backward reaction... 1 Suppose, x moles of A is reacted after time t, C A = (a x) and C B = x mol. Therefore, equation (1) becomes;.. 2 But at equilibrium, overall rate of the reaction is zero i.e. = 0, therefore equation (2) becomes or.. 3 Where, is the concentration of A is converted into product B at the equilibrium state. From equation (3), equation (2) becomes 4 Integrating this equation with the limits at t= 0, x = 0 and at t = t, x = x. =. 5 53

61 From this equation, find the value of k f from the quantities a, x e and x at time t. From the value of k f the value of k b can be calculated by using the above equation (3). E.g. k 3 2NO + O 2 2 NO 2 k Below C the rate of forward reaction is third order and proceeds without and complications. But above this temperature, rate of decomposition of the nitrogen dioxide is noticeable and leads to decrease overall rate of the reaction. Suppose, a and b moles are the initial concentration of NO and O 2 respectively, x the amount of oxygen reacted after time t, then at time t, concentration of oxygen is (b x) and that of nitric oxide is (a 2x) while that of nitrogen oxide formed is 2x. Rate of forward reaction =.. 6 Rate of backward reaction =.. 7 Overall rate of reaction = 2 At equilibrium state, Where, x e is the value of x at equilibrium. By substituting the value of k 2 in equation (8), an expression is obtained involving only k 3 which is used for kinetic study of the chemical reaction. For this, the values of initial concentrations x at various time t and at equilibrium is calculated. 2. Consecutive reaction:- Consider a chemical reaction such ask1 k 2 A B C Which the conversion of reactants into product through one or more intermediate stages is called as consecutive reactions. Each stage having its own rate and rate constant; some rates and rates constants are experimentally determined. Out of these various stages, at least one stage is slowest 54

62 called as rate determining step which decides the rate of overall reaction. If we consider above conversion in whichi. k 1 >> k 2, then the conversion of B to C is slow step and determine the rate of formation of product. ii. On the other hand if k 2 >> k 1, the formation of B from A is slow step and decides the rate of overall reaction and as soon as B is formed from A is convert to product C. iii. When k 1 and k 2 are comparable in magnitude, the rate of reaction depends on both the constants k 1 and k 2 and situation becomes more complicated. e.g.- S N 2, S N 1 reaction mechanism. Let a be the initial concentration of A, x be the amount of it decomposed at time t and y be the concentration of product formed at the same instant. Therefore, at time t- C A = (a x); C B = (x y) and C C = (y). Rate of disappearance of A =. 10 Rate of decomposition of B = Rate of formation of C =. 11 To find out dependence of the concentration of A, B and C on times; we must solved the above rate equations. Integrating equation for first order reaction, finding the value of x, substitute it into equation (11) and then integrate it. On integrating equation (10) without limits gives concentration of A at time t is where, (similar to first order reaction) 12 It shows that concentration of A decreases exponentially with time t. Substitute the value of x obtained from equation (12) into equation (11), we obtain a simple linear differential equation of the first order which can be solved further gives value of y or concentration of B.. 13 In reaction sequence, there is no change in the total number of molecules. Since at every time, disappearance of A; B can be appearing and at every time a B disappearance a C appears. Therefore, C A + C B + C C = a and C z is calculated by using equation (12) and (13) and above equation

63 The equation (12), (13) and (14) indicates that, C A, C B and C C is function of time t. For a = 1 and k 1 = 2k 2, plot a graph of C A, C B and C C as function of time t. It will be observed that, concentration of A falls and that of C increases continuously. The concentration of B rises to a maximum and then decreases with time. This behavior of the concentration of the intermediate product is characteristic of consecutive reactions with comparable values of rate constants concentration * # *. * maximum #. # * # #.. * # time. *. *. Example: 1. Decomposition of sodium hypochlorite in alkaline solutions. The stoichiometric equation of the process. 3NaClO + 2 NaCl 56 NaClO 3 This equation suggests that, it is a third order reaction, but actually it is second order reaction. It indicates that decomposition will be takes places in two steps as- i. ii. 3NaClO + NaCl + + NaClO 2 NaClO 2 NaClO NaCl NaClO 3 Forster and Dolch shows that the decomposition of the sodium hypochlorite is slower than the reaction between sodium chlorite and sodium hypochlorite to form the chlorate (second reaction is 25 times faster than the first reaction). Therefore, rate of the first reaction is control the rate of overall reaction. 2. Thermal decomposition (pyrrolysis) of the acetone. i. ii. CH 3 -CO-CH 3 CH 2 =C=O CH 4 CH 2 =C=O 1/2 CH 4 CO + +

64 During this reaction, the intermediate ketene is formed, the concentration of ketene intermediate raise to maximum and then decreases with time. To deciding the order of the consecutive reaction, use bottle-neck principle. If one of the stages has specific rate much slower than of the other, then the overall rate of the reaction is controlled by rate constant of this particular reaction. For an above example- k 1 << k Decomposition of the ethylene oxide. k 1 k (CH O 3 CHO) * 2 CH 4 + CO 4. Any radioactive decay with emission of alpha and beta particals. 3. Parallel or Side reaction: In a parallel reaction, the reacting substances instead of proceeding along with one path to yield a given set of the products also followed one or more other paths to give different products. OR The reacting substance followed two or more paths to give two or more different products is called as parallel or side reactions. The preferential rate of such reaction is changed with change in physical conditions like pressure, temperature or catalyst. The chemical reactions in which maximum yield of the product are obtained is called a major or main reaction while other reactions or reaction is called as side or parallel reaction/s. Consider a schematic pair of parallel first order reactions. A In above reaction, the reactant A gives two products B and C separately in two different reactions with rate constants k 1 and k 2 respectively. If k 1 > k 2, the reaction A B will be a major reaction and A C is a parallel or side reaction. Let us assume that these reactions are of first order and a moles be the initial concentration of A at time t = 0. After time t = t, b moles of B and c moles of C is formed. Therefore, after time t, [A] = a b c. k 1 k 2 B C And 57

65 . 15 The total rate of disappearance of A is = = = = k (A) where, k = 16 Rearrange and integrate equation (16) with the limits (A) and and t = 0 to t = t, we get But (A) = a b c and (A * ) = a.. 17 Or. 18 When, t = 0, b = c = 0, solving these equation for the values of b and c is as Example 1: In the nitration of phenol p- and o-nitrophenol is formed as product simultaneously by using nitric acid by parallel reaction. NO 2 OH OH OH HNO 3 HNO 3 OH OH 2 k 2 k 1 O 2 N If a and b are the initial concentration of phenol and nitric acid and x mole of these are reacted after time t. Then rate of formation of o-nitrophenol and p-nitrophenol is The total rate of disappearance of reactants is

66 Take the ratio of equation (21) and (22) For the disappearance of reactants - Sum of the rate constants are obtained while for the formation of individual product, ratio of is obtained. From these sum and ratio, evaluate the individual constants. HO H3C CH 2 CH 3 H 3 C acid CH 3 H 3 C H 2 C + CH 3 C H 3 CH 3 CHAIN REACTIONS: A chemical reaction proceeding in a series of successive stages initiated by a suitable primary process is called as chain reaction. + e.g.:- H Br 2 HBr 2 During the studying kinetics of combination of hydrogen and bromine to form hydrogen bromide, it is found that the rate of process can not be represented by any simple equation. But it can be expressed by following chemical equations between C and C as Where, k and k are constants. The rate is inhibited by the product HBr. In initial stages of the combination, [HBr]/[Br 2 ] << k, then 2 Therefore, overall order of the reaction is 3/2. Then the problem can be solved independently and almost simultaneously by Christiansen, Herzfeld and Polanyl after 13 years. They proposed a chain of the reactions with following steps

67 chain initiation chain propagation chain termination chain breaking Br k 2 Br H HBr H.. H Br HBr. 2 Br k k k k HBr H 2. 2 Br Br 2 + H. Br. + + Br. (step-i) (step-ii) (step-iii) (step-iv) (step-v) The reaction is initiated by bromine atoms from the thermal dissociation of Br 2 as Br 2 2 Br.. The chain propagation forming two molecules of HBr and regenerate the bromine atom which is ready for another cycle. Therefore, very few bromine atoms are needed to causes an extensive reaction. Finally HBr inhibited (termination) the chain reaction. The inhibition is proportional to the ratio of [HBr]/[Br 2 ]. According to the mechanism, HBr is formed in step - II and step III and disappeared in step - IV. Therefore, rate of formation HBr is 3 Since the atoms H and Br are short lived intermediates, we can applied to them the steady state principle. Thus, we have 4 5 Simultaneous solution of equations (4) and (5) gives Which on substitution in equation (3), finally we have. 8 Comparing equation (1) and (8) 9 60

68 . 10 Also from the step I and step - V, we have k. 1 Br 2 Br 2 k 5 equilibrium constant = K = k1 / k 5 61

69 DEPENDANCE OF REACTION RATE ON TEMPERATURE: It has been found that, generally on increase on temperature, the rate of reaction also goes on increasing in gaseous or solution states. The reason behind this is that- As temperature increases, kinetic energy of the gas increases and molecules possesses sufficient amount of energy and easily undergoes a chemical change or reaction (kinetic energy is proportional to absolute temperature). As temperature increase by 10 0 C, rate of the reaction is doubled in most of the reactions. The dependence of rate of reaction on temperature can be quantitatively explained by using a new term called as temperature coefficient. It is defined as the ratio of the rate constants at two temperatures differing by 10 0 C. thus,. 1 The value of temperature coefficient is always positive except the chemical reaction as- 2 NO + O 2 2 NO 2. It having negative temperature coefficient therefore, its rate goes on decreasing with increase the temperature. In 1889, Arrhenius suggest a simple relationship between the rate constant for the reaction and the temperature of the reaction system as. 2 It is called as Arrhenius equation where k rate constant of the reaction, T is the absolute temperature, R is the ideal gas constant and E a is the energy or quantity which is characteristic of that reaction is called as energy of activation. It is a minimum amount of energy acquired by the molecules before they undergo any chemical change or reaction. It is different for the different reactions and hence rate of different reaction is different. Those chemical reactions has lower energy of activation are faster and vice-versa. The molecules having energy equal to or greater than energy of activation are called as activated molecules. Only these molecules are undergoes chemical reaction. As temperature increase, the number of activated molecules is also increased and therefore increases the rate of reaction. At any given temperature, some fraction of molecules is activated from the total number of molecules. It can be given by Maxwell- Boltzmann distribution law 3 a. Arrhenius equation is similar to Van t-hoff Isotherm that gives the variation of equilibrium constant of a reaction with temperature. Let us consider a reversible reaction as - 62

70 A + B C + D. It has equilibrium constant K, rate constant for forward and backward reaction is k f and k b respectively... 4 The Van t Hoff reaction isotherm gives relationship between equilibrium constant, change in internal energy E and temperature T as. 5 Where E = E 2 E 1, E 2 and E 1 are internal energies of the final and initial states of the system respectively. Therefore, equation (5) becomes It can be written in two individual equations as and. 6 Where, I is constant and its value is found to be zero. The above equation can be written in general form in which instead of k 1 and k 2 write k and instead of E 1 and E 2, write E act, therefore 2 It is called Arrhenius equation. b. The experimental form of the Arrhenius equation can be derived from the Maxwell- Boltzmann distribution law... 3 Here only n a molecules are capable for reaction at temperature T. Rate of the reaction = A n a 7 Where, A is proportionality constant, put equation (3) in equation (7) as Rate of the reaction = A n a 7 Rate of the reaction = A n 8 Since, n is total number of molecules per unit volume i.e. it is nothing but concentration of the reactant therefore equation (8) becomes - Rate of the reaction = A C 9 63

71 = k. C Where, k = A. 10 Where, A is called as frequency factor or per-exponentional factor. The equation (10) is the exponential form of Arrhenius equation. c. The Arrhenius equation can be used to calculate the energy of activation: There are two methods for the calculation of energy of activation. i. Graphical Method: Consider the equation (7) as = 11 Integrating equation (11) without limits as + = + Where, ln(a) is constant of integration. Assuming that E a is independent on the temperature therefore, above equation can be written as k = A Consider equation (12) as Dividing both side by as. 15 The equation (15) is that of straight line of the type - y = - mx + c. Plot a graph of log (k) against is a straight line with slope equal to E a /2.303R and the Y - intercept (c) is log (A). 64

72 slope = -(m) = -E /2.303R a log(k) log A 1/T From the slope of the straight line, energy of the activation can be calculated as Slope (-m) = - E a = (-m) x 2.303R E a = (-m) x (-2.303R) 16 During the calculation of E a, units of R are very important. If R is expressed in calories then E a is also expressed in calories. If R is expressed in joules then E a is also expressed in joules and so on. ii. Analytical Method: Consider equation (11), = 11 Integrating equation (11), assuming E a is independent on temperature T, between the limits at T = T 1, k = k 1 and at T = T 2, k = k 2. = =.. 17 The equation (17) is an integrated form of Arrhenius equation. The energy of activation can be calculated by putting the values of T 1, T 2, k 1, k 2 and R

73 The equation (18) indicates that molecule must acquired a certain critical energy E a (energy of activation) before they can react. The Boltzmann factor e -Ea/RT gives the fraction of molecules that having necessary energy E a before they react and when the temperature change, the fraction or factor e -Ea/RT goes on increasing, therefore increase the rate of reaction. THE ENERGY OF ACTIVATION (E a ): In a chemical reaction involving two or more molecules of reactants, they are come contact to each other before they react i.e. they are collide with each other. If collision is the sufficient condition for the chemical reaction, then rate of reaction must be equal to the rate of collision. But according to the kinetic theory (from mean velocity) of gases, the collision between the reacting molecules is many power of ten greater than the rate of reaction. Therefore, it is assume that the molecule having some special configuration at the collision or that must acquired sufficient high energy state before reaction or both. However configuration does play a part in some reactions. But in every reaction molecule must acquired sufficient energy before they undergoes change and Arrhenius denoted it by latter E a in it equation. It is called as energy of activation i.e. molecules must be activated before they react. According to the concept of activation, reactants do not directly passed into product but it acquired sufficient energy to pass over an activation energy barrier. It can be shown in following fig. Where, A - Denotes the average energy of the reactants. C - Denotes the average energy of the products. And B is the maximum amount of energy must possess the reacting molecules in order to react. B activated state B activated state Energy barrier Reactants A H E a1 E a2 C Products energy barrier H A Reactants E a1 Ea2 C Products reaction co-ordinates reaction co-ordinates 66

74 Molecules present in a state B are said to be activated or to be in activated state. Those reacting molecule having energy to overcome the activated state (i.e. E a ) was undergoes the chemical reaction i.e. the energy must proceeds from A to C not directly, but along with a path ABC. It is minimum amount of energy acquired by the reacting molecules before they react; it is denoted by latter E act. The reacting molecules at A absorb some energy (from surrounding or by energy exchange in collision) in order to in excited state or activated state and react is E a1 of the process A C. This energy is E a1 = E B E A i.e. difference in energy between excited state or activated state and that of corresponding to the average energy of the reactants. The energy of activation of reverse process C A is E a2 = E B E C. The heat of reaction is H or E. E = E a1 E a2 = (E B E A ) (E B E C ) = E C E A.. 1 At constant volume, = [Energy of products] [Energy of reactants] The concept of activation energy in no way violates the thermodynamics relations between the energies of reactants and products. 67

75 Unit II 2.1. Electrochemistry: It is branch of science used to study the interaction between electricity and chemical phenomena. Such interaction has been studied under three different heading as- (i) Electrical properties of the substances (mainly in solution state containing ions) that conducts electricity (electrolytic conductance), (ii) Conversion of electrical energy into chemical energy (electrolysis) and (iii) Conversion of chemical energy into electrical energy. Electronic and electrolytic conductors: The conductors (that carries electricity) in electrochemistry has been classified into two groups as- (i) Electronic or metallic conductors and (ii) Electrolytic conductors. The pure metals, metals in molten state, alloys, carbon, metal oxides, etc are corresponds to metallic conductors. They carries electricity by the flow of electrons. The atoms or ions does not have role to conduct electricity. But in case of electrolytic conductors, the movement of ions to the opposite charge electrodes in solution or molten state. This process is called as electrolysis. Direction of flow of current Direction of flow of electrons electronic conductor Anode Cation Anion Cathod Solution of electrolyte (electrolytic conductor) Conductance: The current flow through the conductor is directly proportional to the potential difference (voltage) applied across the two ends of the conductor (Ohm s law). Current α Potential difference (Voltage) 68

76 = Potential difference / Resistance I = 1 The resistance of the conductor is directly proportional to the length (l) and inversely proportional to area of cross section (A). R α R = or ρ = 2 A Conductor l Where ρ is called resistivity of the conductor. If R is in term of ohm, then ρ is in ohm.m or ohm.cm. But in case of electrolytic conductors, conductance is measured instead of resistance. Conductance is the reciprocal of the resistance. It is denoted by later C. C = 3 Units of C are Siemen or ohm -1 or mho. Specific conductance (κ kappa): It is conductance of 1 cm 3 or unit volume of electrolyte solution. OR It is reciprocal of resistivity or specific resistance (ρ). κ = = 4 Units: S/m or S/cm or mho/m or mho/cm. If, l = 1 cm and A = 1 cm 2 then κ = C i.e. conductance of the solution between two electrolytes, separated by distance 1 cm and having area of cross section 1 cm 2 is specific conductance. The ratio of l/a is called as cell constant and has unit m-1 or cm-1. Therefore, κ = C x cell constant 5 Equivalent Conductance (λ c ): It is the conductance of the electrolytic solution containing 1 gmequivalent of electrolyte placed between two electrodes which are separated by unit distance 69

77 from each others & having area of cross section 1 cm 2 OR It is specific conductance of 1 gmequivalent of electrolyte. λ c = Specific conductance x No. Of gm-equivalent in the solution If concentration of the solution is c gm-equivalent per lit, the volume that contains 1 gmequivalent will be 1/c lit or 1000/c cm 3. λ c = 6 Where c is the concentration in gm-equivalent per lit. Units of equivalent conductance are S.cm 2 per gm-equivalent, mho.cm 2 per gm-equivalent, mho.m 2 per gm-equivalent. Molar conductance (λ): It is the specific conductance of the 1 mole per lit of solution OR It is equivalent conductance of one mole per lit of solution OR It is the conductance of the electrolytic solution containing 1 mole of electrolyte placed between two electrodes which are separated by unit distance from each others & having area of cross section 1 cm 2. λ = 7 Where c is the concentration in moles per lit. Units of equivalent conductance are S.cm 2 per mole, mho.cm 2 per mole, mho.m 2 per mole. Determination molar conductance (λ): Different types of conductivity cells are used to measured the conductance are shown below- The solutions are placed between two platinised platinum plates (called electrodes) having area of cross section A cm 2 and separated by distance l cm. The cell constant (l/a) of the conductivity cell is determined by using 0.1 M KCl solution. The measured conductance is the specific conductance when A = 1 cm 2 and l = 1 cm. Therefore Cell constant =. Measured the conductance of any electrolyte solution under study. By using above calculated value of cell constant and measured value of conductance, calculate specific conductance, molar conductance and equivalent conductance of the solution at any given concentration c. During the 70

78 Molar conductane Ramesh Yamgar and Bapu Thorat Research Group conductance measurement, avoid the use of DC current to avoid the electrolysis of electrolytes. An AC current of 50 cycles per second to 1000 cycles per second is preferred Variation of molar conductance with concentrations: The conductance of the solution was depends on the amount of or number of ions present in the solution. Some electrolytes are dissolve and dissociated completely into ions are called as strong electrolytes. It has good conductance. E.g. NaCl, KCl, HCl, KNO 3, etc. There are some electrolytes which are dissolve but dissociate partially into ions and has low conductance are called as weak electrolytes. E.g. CH 3 COOH, NH 4 OH, LiOH, etc. For all electrolytes (weak and strong), molar conductance increases on dilution (decrease the concentration) as shown in following diagram. Limiting molar conductance Strong electrolytes Concentration Weak electrolytes In case of weak electrolytes, dissociation of the molecules into ions are increased on dilution. The molar conductance of the solution is depends on the number of ions therefore increased on dilution (because dissociation increase). The solution at particular dilution, almost all molecules of electrolyte get dissociated and therefore molecular conductance increases sharply. On further dilution, each ions moves freely in the solution therefore conductance is increases sharply. At infinite dilution, each ions moves independently, the molar conductance is approaching to a limiting value. Strong electrolytes are nearly dissociate completely into ions at all concentrations and has larger or higher molar conductance at any concentration. The variation of molar conductance with concentration is linear and is increasing slowly with dilution. The molar conductance decreases 71

79 on increasing the concentration (on increasing the number of ions) can be explain with help of Debey-Huckel Theory. This variation can be explain by using equation- λ = λ 0 - b c ( y = -mx + c type) Limiting value of λ (λ 0 ): Limiting molar conductance λ 0 of an electrolyte is the molar conductance of the electrolyte solution on infinite dilution or having zero concentration. For strong electrolyte, the value of λ 0 can be calculated by extrapolating the graph of λ Vs c to zero concentration. But λ 0 of weak electrolytes does not calculated by extrapolating the graph λ Vs c to zero concentration. 72

80 Arrhenius theory of electrolytic dissociation and its limitations: Savante Arrhenius studied the conduction of current through water solutions of electrolytes. He came to believe that the conductivity of solutions was due to the presence of ions. In 1884, he put forward his theory of ionization called Arrhenius theory of ionization, may be stated as: 1. When neutral electrolyte molecules dissolved in water, they are split up into two types of charged particles. These particles were called ions and the process was termed ionisation. The positively charged particles were called cations and those having negative charge were called anions. In its modern form, the theory assumes that the ions are already present in the solid electrolyte and these are held together by electrostatic force. When placed in water, these neutral molecules dissociate to form separate anions and cations. Thus, For that reason, this theory may be referred to as the theory of electrolytic dissociations. 2. The ions present in solution constantly reunite to form neutral molecules. Thus there is a state of equilibrium between the undissociated molecules and the ions. Applying the Law of Mass Action to the ionic equilibrium we have, where K is called the Dissociation constant. 3. The charged ions are free to move through the solution to the oppositely charged electrode. This movement of the ions constitutes the electric current through electrolytes. This explains the conductivity of electrolytes as well as the phenomenon of electrolysis. 4. The electrical conductivity of an electrolyte solution depends on the number of ions present in solution. Thus the degree of dissociation of an electrolyte determines whether it is a strong electrolyte or a weak electrolyte. Limitations of Arrhenius theory: 73

81 1. Ostwald's dilution law which is based on Arrhenius theory is not applicable to strong electrolytes. 2. Strong electrolytes conduct electricity infused state, i.e., in absence of water. This is in contradiction of Arrhenius theory according to which the presence of solvent is a must for ionization. 3. Arrhenius theory assumes independent existence of ions but fails to account for the factors which influence the mobility of the ions. 74

82 Debye-Huckel Theory of conductance of strong electrolyte: The molar conductance of strong electrolytes varies linearly with c, mathematically it can be represented by the equation asλ = λ 0 - b c Where λ 0 is the limiting conductance and b is constant. To explain the decrease in molar conductance of strong electrolytes with concentration (even it can be dissociated completely), Debey-Huckel introduced new concept called ionic atmosphere. Due to interionic attractions, each ion in the solution was surrounded by opposite charged ions. In absence of any external electric field, the ionic atmospheres are symmetric and spherical. As external potential is applied across the electrodes dipped in solution for conductance measurement, ions starts moves and therefore symmetric ionic atmosphere get disturbed. Electrolyte Anion Cation In absence of external electric field The decrease in conductance with concentration can be explain with the help of two theories. 1. Relaxation or asymmetric effect. 2. Electrophoretic effect. 1. Relaxation / asymmetric effect: In presence of external electric field, central ion will migrates towards the opposite charge electrode while ionic atmosphere will get migrates towards opposite direction to the central ion (towards opposite charged electrode). Due to this opposite movement of central ion & ionic atmosphere, symmetry of ionic atmosphere will get decay and new fresh ionic atmosphere is build up in the direction of motion of ion. The force exerted by the ionic atmosphere on central ion is not uniform; it is greater behind the ion and weaker in front of it. Such unbalanced forces 75

83 decrease the speed of ions and therefore molar conductance of the solution. This effect is called as asymmetric or relaxation effect In presence of external electric field 2. Electrophoretic effect: This is additional effect which decreases the velocity and therefore conductance of the electrolyte. Each ion in the solution is not free, but get hydrated with water molecules in aqueous medium. Such hydrated ions along with its water molecules moves through medium so that the medium does not remain stationary, it can moves in the opposite directions. The counter movement of the solvent molecules makes more difficult for the movement of ions through the solution and hence reduces its velocity or speed. This can be mathematically explain by Onsager [called Debey-Huckel-Onsager equation]. λ = λ 0 (A + Bλ 0 ) c Where λ - molar conductance of the electrolyte. λ 0 - Molar conductance of the electrolyte at infinite dilution. η Viscosity of the medium. D Dielectric constant of the medium. T Absolute temperature of the medium. c Concentration of the medium. 76

84 Kohlrausch s law of independent migration of the ion: Kohlrausch s law is used to calculate λ 0 of the weak electrolyte. When molar conductance of the strong electrolytes is plotted against c is a straight line of the type - λ = λ 0 b c. This line is extrapolated to conductance line (Y-axis) gives λ 0 of the strong electrolyte. But when graph of λ against c of weak electrolyte is not linear, therefore λ 0 of the weak electrolyte was not calculated from the graph. Statement: At infinite dilution, when dissociation of an electrolyte is completed and inter-ionic effects are absent, ions are migrates independently in the solution and contributes a definite and constant value of the molar of the electrolyte. λ 0 value of electrolyte = sum of λ 0 values of ions in the solution [same T & solvent] λ 0 = λ λ 0 - With the known values of λ 0 of the ions, λ 0 of any electrolyte can be calculated. According to this law, the difference between λ 0 values of two electrolytes containing a common ion should be a constant and equal to the difference in molar conductances of ions which are not in common. λ 0 AB - λ 0 CB = λ 0 A - λ 0 C λ 0 KBr - λ 0 KCl = λ 0 NaBr - λ 0 NaCl = λ 0 Br- - λ 0 Cl- = Applications: 1. Calculate λ 0 value of weak electrolyte: It is useful for the measurement of conductance of the electrolyte in the solution. The conductance (λ 0 ) of the solution is depends on the nature of the ion and is constant at infinite dilution. The limiting conductance (λ 0 ) of weak electrolyte cannot be obtained from the graph of λ against c; hence it can be determined by using Kohlrausch s law. Consider weak electrolyte HA- HA H + + A - According to the Kohlrausch s law- λ 0 HA = λ 0 H+ - λ 0 A- (1) 77

85 Suppose, NaA is the salt of acid & is strong electrolyte- NaA Na + + A - λ 0 NaA = λ 0 Na+ - λ 0 A- λ 0 A- = λ 0 NaA - λ 0 Na+ (2) HCl is strong acid, therefore- HCl H + + Cl - λ 0 HCl = λ 0 H+ - λ 0 Clλ 0 H+ = λ 0 HCl - λ 0 Cl- (3) Form equation (1), (2) and (3)- λ 0 HA = λ 0 HCl - λ 0 Cl- + λ 0 NaA - λ 0 Na+ = λ 0 HCl + λ 0 NaA - λ 0 Cl- - λ 0 Na+ = λ 0 HCl + λ 0 NaA - λ 0 NaCl (4) HCl, NaA and NaCl are strong electrolytes whose limiting molar conductance can be determined graphically and substitute in equation (4) to calculate λ 0 of weak electrolyte. 2. Determination of dissociation constant of a weak electrolyte: Consider weak electrolyte HA, HA H + + A - If degree of dissociation of electrolyte is α and molar conductance is c, then [H + ] = [A - ] = α. c and [HA] = (1 α). c And Dissociation constant = K a = [H + ]. [A - ]/[HA] = α 2. c/(1 α) (1) It is the equation of Ostwald s dilution law. The degree of dissociation (α) of electrolyte at the molar concentration c is- α = λ/λ 0 (2) Put value of α (equation 2) in equation (1) and calculate K a. Steps involved for the calculation: 1. Measure the conductance of the HA solution of concentration c mol per lit. 2. Cell constant of the same conductivity cell is calculated by measuring conductance of 0.1 mol per lit of KCl solution. Cell constant = (Specific conductance of KCl sol.)/conductance of same KCl sol.) 3. By using calculated cell constant, specific conductance of HA solution is calculated by using- κ = C x cell constant. 4. Calculate molar conductance as- λ = κ / c; c is concentration in mol per lit. 5. Since HA is weak electrolyte, λ 0 HA is calculated by using Kohlrausch law asλ 0 HA = λ 0 HCl + λ 0 NaA - λ 0 NaCl. 78

86 6. Degree of dissociation can be calculated asα = λ HA /λ 0 HA 7. Dissociation constant K a is calculated- K a = α 2. c/(1 α) = (λ HA /λ 0 HA) 2 c/1 (λ HA /λ 0 HA); Where c is concentration in mol per lit. 3. Determination of solubility of a sparingly soluble salt: Steps involved in the determination of solubility of sparingly soluble salts by conductometric determination are listed below- 1. Prepared standard solution of given salt at any given temperature. 2. Measure the conductance of the given solution by using conductivity cell whose cell constant value was exactly known or calculated. 3. Measured the conductance of the distilled water by using same conductivity cell. Steps involved during actual analysis: 1. Measure the conductance of water and salt solution under same experimental conditions and subtract the specific conductance of water from specific conductance of salt. 2. Calculate the cell constant of conductivity cell by measuring conductance of 0.1 M KCl solution. 3. Calculate the specific conductance of salt solution and water from conductance and cell constant & difference between them is specific conductance of salt. 4. Solubility of the salt solution (S) is calculated by using following equation- Concentration or solubility = S = κ/λ The saturated solution of sparingly soluble salt is dilute hence molar conductance of it is taken as molar conductance at infinite dilution. λ saturated = λ 0 salt = λ λ 0 -. S (solubility) = κ/(λ λ 0 -) From the solubility of salt, solubility product K sp can be calculated. 79

87 2.2. Titrimetric Analysis II Introduction: Titrimetric analysis is a quantitative method of analysis based on measurement of volume & finally concentration of component of sample present in solution. This is based on simple titration process. The volume of known concentration of one reagent was reacted with known volume of another reagent whose concentration is to be determined in presence or absence of indicator is called as titration. Term used in titrimetric analysis: Titrant: The solution added from burette (usually of known concentration) is known as titrant. Titrand: The solution that is being titrated is known as titrand. Titration: The process of addition (mixing) of the titrant to the titrand leading reaction between them is known as titration. Indicator: It is the substance added externally to the system during the titration shows color change when reaction between titrant and titrand is complete i.e. completion of titration. E.g. Phenolphthalein, methyl red, starch, ZnO paste, Muroxide, etc. Equivalence Point: It is the point during the titration where the reaction between titrant and titrand is complete. The volume of titrant corresponding to the equivalence point is Veq. End point of the titration: The point of titration at which completion of reaction between titrant and titrand is judged with the help of the change in color of indicator. It is point of titration at which indicator shows change in color. Titration error: Ideally the end point and equivalence point of the titration should coincide. Practically in most of cases they are different. The difference between these two points is known as titration error. It is always expressed in term of volume of titrant added. 80

88 Classification of titrimetric analysis: Depending on the type of the reaction involve between titrant and titrand, titrimetric analysis has been classified in two major groups: a. Reaction involving transfer of electrons. During the titration, reaction between titrant and titrand involving transfer of electrons is known as redox reaction or oxidation-reduction reaction and the titration as redox titration. e. g. 1. Fe(II) with potassium dichromate 2. Iodine with sodium thiosulphate. b. Reaction between ions/molecules with ions/molecules. 1. Reaction between ions: (Precipitation titration): During the titration, reaction between ions (titrant and titrand) leads to the formation of sparingly soluble salts is known as precipitation reaction & titration as precipitation titration. E.g. KCl vs. AgNO 3 ; BaCl 2 vs. KSO 4, etc. A solution of potassium chloride can be titrated against silver nitrate solution using suitable indicator such as KCr 2 O 4, adsorption indicator, by potentiometry, etc. 2. Reaction between ions & molecules: (Complexometric titrations) During titration, a reaction between metal ion and neutral complexing agent leads the formation of stable complex. E.g. Estimation of Ca/Mg ions by EDTA. 3. Reaction between molecules: (Acid-Base titration) The reaction between acid and base leads the formation of salt and water. It can may be come in category of reaction between ion & molecule or between two ions. E.g. HCl vs. NaOH; HCl vs. NH 4 OH; CH 3 COOH vs. NaOH; CH 3 COOH vs. NH 4 OH, etc. 81

89 Selection of indicator for acid base titration The one group organic dyes or their derivatives are weak acids and bases and such compounds have at least one conjugate acid base species that is highly colored. During the titration, they result change in both ph and color. This change in color can serve as a useful means for determining the end point of a titration, provided that it occurs at the titration s equivalence point. The ph at which an acid base indicator changes color is determined from its acid dissociation constant. For an indicator that is a monoprotic weak acid, HI n, the following dissociation reaction occurs For which the equilibrium constant is 1 Taking the negative log of each side of equation (1), and rearranging for ph gives a equation The two forms of the indicator, HIn and In, have different colors. The color of a solution containing an indicator, therefore, continuously changes as the concentration of HIn decreases and the concentration of In increases. If we assume that both HIn and In can be detected with equal ease, then the transition between the two colors reaches its midpoint when their concentrations are identical or when the ph is equal to the indicator s pk a. The equivalence point and the end point coincide; therefore, if an indicator is selected whose pk a is equal to the ph at the equivalence point, and the titration is continued until the indicator s color is exactly halfway between that for HIn and In. Unfortunately, the exact ph at the equivalence point is rarely known. In addition, detecting the point where the concentrations of HIn and In are equal may be difficult if the change in color is subtle. We can establish a range of phs over which the average analyst will observe a change in color, if we assume that a solution of the indicator is the color of HIn whenever its concentration is ten times more than that of In, and the color of In whenever the concentration of HIn is ten times less than that of In. Substituting these inequalities into equation (1) - 82

90 It shows that an indicator changes color over a ph range of ±1 units on either side of its pk a. Thus, the indicator will be the color of HIn when the ph is less than pka 1, and the color of In for phs greater than pka + 1. The ph range of an indicator does not have to be equally distributed on either side of the indicator s pka. For some indicators only the weak acid or weak base is colored. For other indicators both the weak acid and weak base are colored, but one form may be easier to see. A list of several common acid base indicators, along with their pka s, color changes, and ph ranges, is provided in the top portion of following table. In some cases, mixed indicators, which are a mixture of two or more acid base indicators, provide a narrower range of phs over which the color change occurs. The relatively broad range of phs over which any indicator changes color places additional limitations on the feasibility of a titration. To minimize a determinate titration error, an indicator s entire color transition must lie within the sharp transition in ph occurring near the equivalence point. E.g. phenolphthalein is an appropriate indicator for the titration of 0.1 M acetic acid with 0.1 M NaOH. Bromothymol blue, on the other hand, is an inappropriate indicator since its change in color begins before the initial sharp rise in ph and, as a result, spans a relatively large range of volumes. 83

91 Indicator Acid color Base color ph range pka Cresol red red yellow Thymol blue red yellow Bromophenol blue yellow blue Methyl orange red orange Congo red Blue Red Bromocresol green Yellow Blue Methyl red Red Yellow Bromocresol purple Yellow Purple Litmus Red Blue Bromthymol blue Yellow Blue Phenol red Yellow Red Cresol red Yellow Red

92 Thymol blue Yellow Blue Phenolphthalein Colorless Red Alizarin yellow R Yellow Orange/Red Mixed indicators Name of mixed indicator Acid color Base color ph range Bromocresol green & methyl orange Orange Blue-green Bromocresol green & chlorophenol red Yellow-green Blue-violet Bromothymol blue & phenol red Yellow Violet Screened indicator Dimethyl yellow & methylene blue Blue-violet Green Methyl red & methylene blue Red-violet Green Neutral red & methylene blue Violet-blue green Chose of the indicators for acid base titration: The acid-base titrations are based on the sharp change in the ph at equivalence point. The magnitude of ph change will primarily depends on the acid and base used for the titration. The indicator selected for the titration should therefore shows color change in this region i.e. indicator ph range should be same or near to the ph range at equivalence point. The improper selection of indicator shows appropriate error in titration. Strong acid against strong base: For the titration between strong acid HCl and strong base NaOH, the ph change at the equivalence point is from about 4 to 10. The indicator selected should have the ph range in between 4 to 10. Methyl orange ( ); Methyl red ( ); Phenol red ( ); Phenolphthalein (8.3-10); bromothymol blue ( ) could be used as indicator. The indicator shows acid color up to equivalence point and after that it shows basic color. Of the five indicators, then, only bromothymol blue provides a satisfactory end point with a minimal systematic error in the titration of M NaOH. 85

93 Weak acid against strong base: For the titration between weak acid CH 3 COOH and strong base NaOH, the ph change at the equivalence point is from about 7.7 to 10. The suitable indicator for such titration will be Phenol red ( ) or Phenolphthalein (8.3-10). The indicator shows acid color up to equivalence point and after that it shows basic color. Strong acid against weak base: For the titration between weak base NH 4 OH and Strong acid HCl, the ph change at the equivalence point is from about 6.6 to 4.0. The suitable indicator for such titration will be methyl orange ( ) or methyl red ( ). The indicator shows basic color up to equivalence point and after that it shows acidic color. Weak acid against weak base: ph curve of weak acid and weak base indicates that there is no vertical part and hence, no suitable indicator can be used for such a titration. Following figures show that the choice of indicator is more limited for the titration of a weak acid than for the titration of a strong acid. For example, first figure illustrates that bromocresol green is totally unsuited for titration of M acetic acid. Bromothymol blue does not work either because its full color change occurs over a range of titrant volume from about 47 ml to 50 ml of M base. On the other hand, an indicator exhibiting a color change in the basic region, such as phenolphthalein, provides a sharp end point with a minimal titration error. Figure: 1 Figure: 2 The end-point ph change associated with the titration of M acetic acid (curve B of first figure) is so small that there is likely to be a significant titration error regardless of indicator. 86

94 However, using an indicator with a transition range between that of phenolphthalein and that of bromothymol blue in conjunction with a suitable color comparison standard makes it possible to establish the end point in this titration with decent precision (a few percent relative standard deviation). Second figure illustrates that similar problems occur as the strength of the acid being titrated decreases. A precision on the order of 62 ppt can be achieved by titrating a M solution of an acid with a dissociation constant of 1028 if a suitable color comparison standard is available. With more concentrated solutions, weaker acids can be titrated with reasonable precision. Example 1: Titration of weak acid against strong base. Fill the strong base such as NaOH solution into burette (titrant) and pipette out weak acid solution into conical flask (called titrand or analyte). The weak acid taken into conical flask refers to a monobasic acid (gives one proton per molecule after dissociation) such as acetic acid, formic acid, etc. It will dissociate partially in its aqueous solution. Suppose weak acid is acetic acid and strong base is NaOH, then neutralization reaction is CH 3 COOH + Na + + HO - H 2 O + Na + + CH 3 COO - Initially, pipette out 0.1 N acetic acid into conical flask. The ph of acetic acid solution is calculated from concentration and dissociation constant of the acid. As soon as titration is proceed, some acetic acid is converted into sodium acetate and forming acetate buffer in which all salt get dissociated which suppress the dissociation of acetic acid. Therefore, ph of the solution increases slowly up to equivalence point, after equivalence point, ph shift from acidic region to basic region. The ph of solution at equivalence point is somewhat greater than 7 because of the hydrolysis of sodium acetate forming some acetic acid and free hydroxide ions. After equivalence point, the ph of solution increases is due to the excess NaOH solution. Consider the titration of 10 ml of 0.1 N acetic acid with 0.1 N NaOH solution. The ph of solution at various stages can be calculated as follows (K a of acetic acid is 1.8 x 10-5 ). a. At the beginning of the titration: Acetic acid is monobasic weak acid therefore it dissociate partially as CH 3 COOH H + + CH 3 COO - Suppose, α is the degree of dissociation and C is the molar concentration of acetic acid, then [CH 3 COO - ] = [H + ] = α x C and [CH 3 COOH] = (1 α) C 87

95 The value of dissociation constant of acetic acid is calculated by using following equation K a = =. 1 But, 1 α 1 and K a = 1.8 x = α = 2 and [H + ] = α x C = x C = = where C = 0.1 M Therefore, - log[h + ] = ph = 2.87 b. When 2.0 ml of NaOH solution has added: 2.0 ml of 0.1 N of NaOH added into acetic acid solution which neutralizes 2.0 ml of acetic acid forming sodium acetate and water. The total volume of solution becomes 12 ml in which 8 ml is un-neutralized acetic acid. The concentration of salt = [salt] = The concentration of un-neutralized acid = [acid] = The solution containing weak acid and its salt with strong base i.e. it is buffer solution. The ph of the buffer solution is calculated by using following equation ph ph = pk a + log = - log (1.8 x 10-5 ) + log ph = = 4.14 c. When 5.0 ml of NaOH solution has added: 5.0 ml of 0.1 N of NaOH added into acetic acid solution which neutralizes 5.0 ml of acetic acid forming sodium acetate and water. The total volume of solution becomes 15 ml in which 5 ml is un-neutralized acetic acid. The concentration of salt = [salt] = The concentration of un-neutralized acid = [acid] = The solution containing weak acid and its salt with strong base i.e. it is buffer solution. The ph of the buffer solution is calculated by using following equation 88

96 ph ph = pk a + log = - log (1.8 x 10-5 ) + log ph = 4.74 d. Vicinity of equivalence point: when 9.9 ml of NaOH is added: : 9.9 ml of 0.1 N of NaOH added into acetic acid solution which neutralizes 9.9 ml of acetic acid forming sodium acetate and water. The total volume of solution becomes 19.9 ml in which 0.1 ml is unneutralized acetic acid. The concentration of salt = [salt] = The concentration of un-neutralized acid = [acid] = The solution containing weak acid and its salt with strong base i.e. it is buffer solution. The ph of the buffer solution is calculated by using following equation ph ph = pk a + log = - log (1.8 x 10-5 ) + log ph = = 6.74 e. At the equivalence point: 10 ml of 0.1 N NaOH is added so that all acetic acid get neutralized, only salt will be present and its concentration is [Salt] = = 0.05 M The ph at the equivalence will be corresponds to the ph due to sodium acetate. At equivalence point, concentration of sodium acetate is 0.05 M. It is undergoes hydrolysis in some extent as CH 3 COONa + H 2 O NaOH + CH 3 COOH OR CH 3 COO - + H 2 O HO - + CH 3 COOH The hydrolysis constant K h is defined as K h =.. 3 In this solution there are also two equilibrium as dissociation of acetic acid and dissociation of water as (a) Dissociation of acetic acid: CH 3 COOH H + + CH 3 COO - K a = 89

97 (b) Dissociation of water: H 2 O H + + HO - K w = (Dissociation constant of water) Consider, we get = = K h. If h represent the degree of hydrolysis i.e. fraction of the total number of moles of salt undergoes hydrolysis at equilibrium and C is the concentration of the salt, then at equilibrium, = (1 h) C, = h C, then equation (3) become K h = But (1 h) 1, therefore above equation become K h = h = Hence, = h C =. C = But, K h, therefore - = and = = = 4 Taking negative logarithm base 10 of equation (4) and substituted the values of K a, K w and C. -log = -log ph = (pk w + pk a + logc) Where, pk w = 14 (for water); K a = 1.8 x 10-5 and pk a = 4.74 (for acetic acid), and C = 0.05 M, Therefore, ph = ( log0.05) =

98 f. When 10.1 ml of 0.1 N NaOH added: 10.1 ml of 0.1 N of NaOH added into acetic acid solution which neutralizes all 10 ml of acetic acid forming sodium acetate and water. The total volume of solution becomes 20.1 ml in which 0.1 ml NaOH remains un-neutralized form which decide the ph of solution. The concentration of un-neutralized base = [HO - ] = = x The poh of the solution is calculated by using following equation poh = - log (4.975 x 10-4 ) = ph = 14 - poh ph = = 10.7 g. When 11.0 ml of 0.1 N NaOH added: 11.0 ml of 0.1 N of NaOH added into acetic acid solution which neutralizes all 10 ml of acetic acid forming sodium acetate and water. The total volume of solution becomes 21.0 ml in which 1.0 ml NaOH remains un-neutralized form which decide the ph of solution. The concentration of un-neutralized base = [HO - ] = = 4.76 x The poh of the solution is calculated by using following equation poh = - log (4.76 x 10-3 ) = ph = 14 - poh ph = = Finally, plot the graph of ph against volume of 0.1 N NaOH solution added. For this titration, the ph at the equivalence point is 8.7 therefore it is necessary to use the indicator with a ph range (color change) or pk a value (indicator) on the slightly alkaline side like phenolphthalein, thymol blue, thymolphthalein. 91

99 For the weak acid with dissociation constant 10-7, the ph value at the equivalence point is 9.85 and hence, thymolphthalein would be better choice as indicator. The acids with dissociation constant less than 10-7 cannot be satisfactory titrated by using 0.1 M solution with simple indicator. Example 2: Titration of strong acid against weak base: Fill the strong acid such as HCl solution into burette (titrant) and pipette out weak base solution into conical flask (called titrand or analyte). The weak base taken into conical flask refers to a monoacidic base (gives one hydroxide ion or accept one proton per molecule) such as ammonium hydroxide or ammonia, aniline, etc. It will dissociate partially in its aqueous solution. Suppose weak base is ammonium hydroxide and strong acid is HCl, then neutralization reaction is NH 4 OH + H + + Cl - H 2 O + NH Cl - Initially, pipette out 0.1 N ammonium hydroxide solution into conical flask. The ph of ammonium hydroxide solution is calculated from concentration and dissociation constant of the base. As soon as titration is proceed, stoichiometric amount ammonium hydroxide is converted into ammonium chloride and forming ammonia-ammonium chloride buffer in which all salt get dissociated which suppress the dissociation of ammonium hydroxide. Therefore, ph of the solution decreases slowly up to equivalence point, after equivalence point, ph shift from basic region to acidic region. The ph of solution at equivalence point is somewhat less than 7 because of the hydrolysis of ammonium chloride forming some ammonium hydroxide and free hydrogen ions (HCl). After equivalence point, the ph of solution is decreases due to the excess addition of HCl solution. 92

100 Consider the titration of 10 ml of 0.1 N ammonium hydroxide with 0.1 N HCl solution. The ph of solution at various stages can be calculated as follows (K b of ammonium hydroxide is 1.8 x 10-5 ). a. At the beginning of the titration: Ammonium hydroxide is monoacidic weak base therefore it dissociate partially as NH 4 OH NH HO - Suppose, α is the degree of dissociation and C is the molar concentration of ammonium hydroxide, then [NH + 4 ] = [HO - ] = α x C and [NH 4 OH] = (1 α) C The value of dissociation constant of ammonium hydroxide is calculated by using following equation K b = =. 1 But, 1 α 1 and K b = 1.8 x = α = 2 And [HO - ] = α x C = x C = = where C = 0.1 M Therefore, - log[ho - ] = poh = 2.87 Hence, ph = 14 poh = = b. When 2.0 ml of HCl solution has added: 2.0 ml of 0.1 N of HCl is added into ammonium hydroxide solution which neutralizes 2.0 ml of ammonium hydroxide forming ammonium chloride and water. The total volume of solution becomes 12 ml in which 8 ml is unneutralized ammonium hydroxide. The concentration of salt = [salt] = The concentration of un-neutralized base = [base] = 93

101 The solution containing weak base and its salt with strong acid i.e. it is buffer solution. The ph of the buffer solution is calculated by using following equation ph ph = pk w - pk b - log = 14 + log (1.8 x 10-5 ) - log ph = = 9.86 c. When 5.0 ml of HCl solution has added: 5.0 ml of 0.1 N of HCl added into ammonium hydroxide solution which neutralizes 5.0 ml of ammonium hydroxide forming ammonium hydroxide and water. The total volume of solution becomes 15 ml in which 5 ml is unneutralized ammonium hydroxide. The concentration of salt = [salt] = The concentration of un-neutralized base = [base] = The solution containing weak base and its salt with strong acid i.e. it is buffer solution. The ph of the buffer solution is calculated by using following equation ph ph = pk w - pk b - log = 14 + log (1.8 x 10-5 ) - log ph = = 9.26 d. Vicinity of equivalence point: when 9.9 ml of HCl is added: : 9.9 ml of 0.1 N of HCl added into ammonium hydroxide solution which neutralizes 9.9 ml of ammonium hydroxide forming ammonium chloride and water. The total volume of solution becomes 19.9 ml in which 0.1 ml is un-neutralized ammonium hydroxide. The concentration of salt = [salt] = The concentration of un-neutralized base = [base] = The solution containing weak base and its salt with strong acid i.e. it is buffer solution. The ph of the buffer solution is calculated by using following equation ph ph = pk w - pk b - log = 14 + log (1.8 x 10-5 ) - log ph = =

102 e. At the equivalence point: 10 ml of 0.1 N HCl is added so that all ammonium hydroxide get neutralized, only salt will be present and its concentration is [Salt] = = 0.05 M The ph at the equivalence will be corresponds to the ph due to ammonium chloride. At equivalence point, concentration of ammonium chloride is 0.05 M. It is undergoes hydrolysis in some extent as NH 4 Cl + H 2 O NH 4 OH + HCl OR NH H 2 O H + + NH 4 OH The hydrolysis constant K h is defined as K h =.. 3 In this solution there are also two equilibrium as dissociation of weak base ammonium hydroxide and dissociation of water as a. Dissociation of ammonium hydroxide: NH 4 OH NH HO - K b = b. Dissociation of water: H 2 O H + + HO - K w = (Dissociation constant of water) Consider, we get = = K h. If h represent the degree of hydrolysis i.e. fraction of the total number of moles of salt undergoes hydrolysis at equilibrium and C is the concentration of the salt, then at equilibrium, = (1 h) C, = h C, then equation (3) become K h = But (1 h) 1, therefore above equation become K h 95

103 h = Hence, = h C =. C = But, K h, therefore - = 4 Taking negative logarithm base 10 of equation (4) and substituted the values of K a, K w and C. -log = -log ph = (pk w pk b - logc) Where, pk w = 14 (for water); K b = 1.8 x 10-5 and pk b = 4.74 (for ammonium hydroxide), and C = 0.05 M, Therefore, ph = ( log0.05) = 5.28 f. When 10.1 ml of 0.1 N HCl added: 10.1 ml of 0.1 N of HCl added into ammonium hydroxide solution which neutralizes all 10 ml of ammonium hydroxide forming ammonium chloride and water. The total volume of solution becomes 20.1 ml in which 0.1 ml HCl remains in un-neutralized form which decide the ph of solution. The concentration of un-neutralized acid = [H + ] = The ph of the solution is calculated by using following equation ph = - log (4.975 x 10-4 ) = = x g. When 11.0 ml of 0.1 N HCl added: 11.0 ml of 0.1 N of HCl added into ammonium hydroxide solution which neutralizes all 10 ml of ammonium hydroxide forming ammonium chloride and water. The total volume of solution becomes 21.0 ml in which 1.0 ml HCl remains in un-neutralized form which decide the ph of solution. The concentration of un-neutralized acid = [H + ] = The ph of the solution is calculated by using following equation ph = - log (4.76 x 10-3 ) = = 4.76 x Finally, plot the graph of ph against volume of 0.1 N HCl solution added. 96

104 For this titration, the ph at the equivalence point is 5.28 therefore it is necessary to use the indicator with a ph range (color change) or pk a value (indicator) on the slightly acidic side like methyl orange, bromocresol green, methyl red, etc. For the weak bases with dissociation constant 10-7, the ph value at the equivalence point is 4.15 and hence, methyl orange or bromocresol green would be better choice as indicator. The bases with dissociation constant less than 10-7 cannot be satisfactory titrated by using 0.1 M solution with simple indicator. Example 3: Titration of weak acid against weak base: A typical example of this class of titration is the titration of acetic acid (K b = 1.78 x 10-5 ) against ammonium hydroxide (K b = 1.8 x 10-5 ). Fill the weak base such as 0.1 M ammonium hydroxide solution into burette (titrant) and pipette out weak acid such as 0.1 M acetic acid solution into conical flask (called titrand or analyte). The weak acid taken into conical flask refers to a monobasic acid (gives one proton per molecule). It will dissociate partially in its aqueous solution. The neutralization reaction is NH 4 OH + CH 3 COOH H 2 O + NH CH 3 COO - Initially, pipette out 0.1 M acetic acid solution into conical flask. The ph of acetic acid solution is calculated from concentration and dissociation constant of the acid. As soon as titration is proceed, stoichiometric amount acetic acid is converted into ammonium acetate and a buffer system is formed in which all salt get dissociated which suppress the dissociation of acetic acid. Therefore, ph of the solution increases slowly up to equivalence point, after equivalence point, ph shift from acidic region to basic region. The ph of solution at equivalence point is depends 97

105 on the dissociation constants of acid and base. After equivalence point, the ph of solution is increases due to addition of excess of ammonium hydroxide solution. Consider the titration of 10 ml of 0.1 N acetic acid with 0.1 N ammonium hydroxide solution. The ph of solution at various stages can be calculated as follows (K b of ammonium hydroxide is 1.8 x 10-5 and K a of acetic acid is 1.78 x 10-5 ). The ph values upto the equivalence point will be identical for acetic acid sodium hydroxide titration i.e. 0.0 ml of ammonium hydroxide added ph of the solution ml of ammonium hydroxide added ph of the solution ml of ammonium hydroxide added ph of the solution ml of ammonium hydroxide added ph of the solution 6.74 At the equivalence point: 10 ml of 0.1 N ammonium hydroide is added so that all acetic acid get neutralized, only salt will be present and its concentration is [Salt] = = 0.05 M The ph at the equivalence will be corresponds to the ph due to ammonium acetate. At equivalence point, concentration of ammonium chloride is 0.05 M. It is undergoes hydrolysis in some extent as CH 3 COONH 4 + H 2 O NH 4 OH + CH 3 COOH OR CH 3 COO - + NH H 2 O CH 3 COOH + NH 4 OH The hydrolysis constant K h is defined as K h =.. 1 Multiplying and dividing of right hand side of equation (1) by, we have - K h = a. Dissociation of ammonium hydroxide: NH 4 OH NH HO - K b =. 2 b. Dissociation of acetic acid: CH 3 COOH H + + CH 3 COO - K a =.. 3 c. Dissociation of water: 98

106 H 2 O H + + HO - From equation (1), (2), (3) and (4), we get K w = (Dissociation constant of water) 4 K h = = If h represent the degree of hydrolysis i.e. fraction of the total number of moles of salt undergoes hydrolysis at equilibrium and C is the concentration of the salt, then at equilibrium, = = (1 h) C, = h C, then equation (1) become K h = But (1 h) 1, therefore above equation become K h h = The expression for the ph of the solution can be derived by considering dissociation of acetic acid i.e. CH 3 COOH H + + CH 3 COO - K a =.. 3 = K a = K a Since, K h = = h K a = = = = 5 Taking negative logarithm base 10 of equation (5) and substituted the values of K a, K w and K b. -log = -log ph = (pk w + pk a - pk b ) 99

107 Where, pk w = 14 (for water); K b = 1.8 x 10-5, K a = 1.78 x 10-5 and pk a = pk b = 4.74 (for acetic acid and ammonium hydroxide), and C = 0.05 M, Therefore, ph = ( ) = 7.0 The solution is neutral because, K b = K a. If K b < K a, then ph < 7, solution is acidic but if K b > K a, then ph > 7 and solution will be alkaline at equivalence point. After equivalence point: Addition of excess 0.1 M ammonium hydroxide solution to the salt (ammonium acetate) solution forming buffer. When 10.1 ml of 0.1 M of ammonium hydroxide added into acetic acid solution which neutralizes all 10 ml of acetic acid forming ammonium acetate and water. The total volume of solution becomes 20.1 ml in which 0.1 ml ammonium hydroide remains in un-neutralized form which decide the ph of solution. The concentration of un-neutralized base = [base] = = x The concentration of salt is 0.05M which is nearly remains constant after equivalence point. The ph of the buffer solution is calculated by using following equation ph = pk w - pk b - log = log = 7.24 When 11.0 ml of 0.1 N ammonium hydroxide is added: When 11.0 ml of 0.1 M ammonium hydroxide is added, 1.0 ml of ammonium hydroxide will be excess. The concentration of un-neutralized base = [base] = The concentration of salt = 0.05M = 4.76 x The ph of the buffer solution is calculated by using following equation ph = pk w - pk b - log = log = 8.24 Finally, plot the graph of ph against volume of 0.1 N ammonium acetate solution added. For this titration, the ph at the equivalence point is 7.0 therefore it is necessary to use the indicator with a ph range (color change) or pk a value (indicator) near to equivalence point. 100

108 Example 4: Titration of polybasic acid against strong base: Polybasic acid undergoes dissociation into water forming hydrogen ion or proton, more specifically hydronium ion (H 3 O + ). Such substances are not strong electrolytes so that extent of dissociation is always less than 100% and is suppressed after primary dissociation (by hydroniun ions). Thus every step of dissociation of polybasic acid represents the dissociation of weak acid. Therefore it is possible to titrate polybasic acids under proper conditions and number of titration steps depends on the nature of polybasic acid; two steps and two equivalence point for dibasic acid; three steps and three equivalence point for tribasic acid; and so on. The dissociation of dibasic acid H 2 B is represented as H 2 B + H 2 O H 3 O + + HA - HA - + H 2 O H 3 O + + A 2- When the ratio of 10 4, the solution behaves as a mixture of two weak acids. Consider the titration of maleic acid against sodium hydroxide solution. 1. To obtain the initial ph of maleic acid, we consider the solution containing maleic acid (weak acid) which donates one proton with dissociation constant Ka = 1.30 x For the calculation of ph before equivalence point, we will consider the buffer solution containing unreacted maleic acid and its conjugate base (as NaHM). 3. At the first equivalence point, there is only salt NaHM (salt of weak acid and strong base) is present which is undergoes hydrolysis. The following equation is used to calculate ph of the solution. ph = 101

109 4. After the first equivalence point, second buffer solution is formed which consist of weak acid NaHM and its conjugate salt as Na 2 M. 5. At the second equivalence point, the solution containing only Na 2 M salt i.e. conjugate base of weak acid NaHM with a dissociation constant of 5.9 x Consideration of hydrolysis of A 2- will enable calculation of ph. ph = (pk w + + logc) 6. After second equivalence point, the ph of the solution is determined from the excess of NaOH solution. Based on these considerations, the ph values during the titration of 25 ml of 0.1 M maleic acid with 0.1 M NaOH solution are calculated and tabulated in the following table. Volume of 0.1 M NaOH added ph Volume of 0.1 M NaOH added ph 0.0 ml ml ml ml First equivalence point Second equivalence point From the above data, it is found that the first equivalent point is observed at ph Thus methyl orange ( ) and bromocresol green ( ) would found suitable indicators for the first equivalent point detection. The second equivalent point is observed at ph 9.38 therefore the indicator suitable for second equivalent point detection are phenolphthalein ( ) and thymolphthalein ( ). It is observed for this titration that second equivalence point can be detected more accurately than the first equivalent point. An example for the tribasic acid is orthophosphoric acid. The dissociation steps & dissociation constants of phosphoric acid are given below H 3 PO 4 + H 2 O H 3 O + + = 7.5 x H 2 O H 3 O + + = 6.5 x H 2 O H 3 O + + = 5.0 x

110 In phosphoric acid, / = 1.2 x 10 5 and / = 1.2 x 10 5 and hence the acid will behaves as a mixture of three monobasic acids with the respective dissociation constants. The first equivalence point is obtained when primary stage (first dissociation) is completely neutralized; and during this second or third stage does not affect or interferes. The second equivalence point is obtained when the second stage is completely neutralized and again during this third stage is not affected and interferes. The third equivalence point corresponds to the complete neutralization of the acid. During the titration, there is formation of three different buffer solutions before the each equivalent point. The ph at the first equivalence point is given approximately as ph = = = 4.6 And ph = = = 9.7 For the third stage of titration, the acid is very weak and the ph at equivalence point can be calculated by considering hydrolysis of salt, namely sodium phosphate, Na 3 PO 4. Since the salt is of a weak acid and strong base, its ph can be calculated by using following equation ph = (pk w + pk a + log C) If 50 ml of 0.1 M H 3 PO 4 is being titrated against 0.1 M NaOH solution, the third equivalence point will obtain at 150 ml addition of NaOH solution. Concentration of salt is = [salt] = = 2.5 x Therefore, ph = [14 + (-log 5 x ) + (-log 2.5 x 10-2 )] 103

111 = [ ] = For the first step (primary step) of titration, the ph at equivalence point is 4.6, hence methyl orange (pk is 3.46) or bromocresol green (pk is 4.90) can be used as indicators. The ph at second equivalence point is 9.7 and only the simple indicator used for this step is thymolphthalein (pk is 9.7). Phenolphthalein indicator gives titration error. In practice, a mixed indicator of 3 parts of phenolphthalein and 1 part -naptholphthalein is the most suitable indicator system for the determination of end point of phosphoric acid as a dibasic acid. In tertiary stage, disodium phosphoric acid is an extremely weak acid; the titration curve is almost flat and no suitable indicator available for the determination of third equivalence point Complexometric Titrations Introduction: In coordination compounds, the central metal species acts as electron acceptor (lewis acid) and negative / neutral / positive molecule (ligand) with lone pair of electrons or 104

112 anions acts as electron donor (lewis base). A metal atom or ion when bonded directly to fixed number of anions or molecules explain coordination entity. E.g. For [Pt(NH 3 ) 2 Cl 2 ] coordination entity in which Pt(II) is surrounded by two ammonia and two chloride ions. The metal atom or ion present in complex is called central metal atom or ion and the charged ions or neutral molecules with lone pair of electrons bounded to the central atom in the coordination entity are called ligands. The number of ligand donor atoms directly attached to central atom is defined as the coordination number. The central atom and the ligands bonded to it are enclosed in square bracket and is collectively called as the coordination sphere. The special arrangement of ligands around the central atom is termed as coordination polyhedron. The most common coordination polyhedrons are octahedral, tetrahedral and square planar. The ligands are bonded to the central metal atom or ion through donor atom. According to the number of donor atoms present in ligand, they are classified as mondentate, bidentate, tridentate, polydentate ligands. The ligands having more than one donor atoms are called chelating agents. e.g. NH 3, CN -, Ph 3 P, - SCN, OH 2, ox (C 2 O 2-4 ), acac acetylacetato, en ethylenediamine, phen 1,10-phenonthrolene, dien (H 2 NCH 2 CH 2 NHCH 2 CH 2 NH 2 ); terpy, EDTA, etc. The bidentate or polydentate bonded to central metal atom or ion through two or more atoms, due to which a ring structure is formed. Such ring structure formed by bidentate or polydentate ligands are known as chelates. EDTA is important chelating agent which binds the metal atom through two nitrogen and four oxygen atoms and hence acts as a hexadentate ligand and forms five rings. Principle of complexometric Titrations: Titrations based on complex formation, sometimes called complexometric titrations, have been used for more than a century. The truly remarkable growth in their analytical application, based on a particular class of coordination compounds called chelates, began in the 1940s. A chelate is produced when a metal ion coordinates with two or more donor groups of a single ligand to form a five- or six-membered heterocyclic ring. The copper complex of glycine, mentioned in the previous paragraph, is an example. Many principles of acid-base titrations are used in complexometric titration. In complexometric titration, the free metal ions are changed into complex ions. In acid-base titrations, the end point is marked by sudden change in ph. Similarly, in EDTA titration, if we plot pm (negative log of metal ion concentration) v/s volume of titrant, we will find that at the end point, the pm rapidly 105

113 increases. Any method, which can determine this disappearance of free metal ions, can be used to detect end point in complexometric titrations. End point can be detected usually with an indicator or instrumentally by potentiometric or conductometric (electrometric) method. There are number parameters affect the end point of complexometric titration, some of them are listed below. 1. The stability of complex formed: The greater the stability constant for complex formed, larger the charge in free metal concentration (pm) at equivalent point and more clear would be the end point. 2. The number of steps involved in complex formation: Fewer the number of steps required in the formation of complex, greater would be the break in titration curve at equivalent point and clear would be the end point. 3. Effect of ph: During a complexometric titration, the ph must be constant by use of a buffer solution. Control of ph is important since the H + ion plays an important role in chelation. Most ligands are basic and bind to H + ions throughout a wide range of ph. Some of these H + ions are frequently displaced from the ligands (chelating agents) by the metal during chelate formation. Only metals that form very stable complexes can be titrated in acidic solution, and metals forming weak complexes can only be effectively titrated in alkaline solution. EDTA as a chelating agent: EDTA (ethylenediaminetetraacetic acid) has complexation property and therefore has wide applicability as chelating agent in various branches of analytical chemistry and industries. EDTA was patented in Germany in EDTA is polydentate ligand and forming stable complex with metal ions called as chelate and the EDTA is called as chelating agent. Chelation is a process in which a metal ion co-ordinates with two or more donor atoms of same ligand resulting in the formation of one or more rings. The word ligand comes from the latin word ligare, to bind and chelate word first proposed in 1920 by the Morgan and Drew, is derived from the Greek word chele means claw. The chelate are more stable than complex, five or six membered chelate rings are usually more stable. The stability of chelate can be explained by considering following examples: 1. The ligands approaches to central metal ions are repelled to each others, but in case of chelating agents such repulsion is less (because both donor atoms are of same molecule, chelating agent). 106

114 2. Some distortion of the ideal bond angles with in ligand almost always occurs in chelate formation. This can be unfavorable as compared with monodentate complex formation if distances of the donor atom are not ideally suited to the metal atom. Bond distortions are generally lowest in five and six member rings and these rings sizes are usually favored. 3. A chelating agent generates a larger crystal field spitting than do otherwise similar monodentate ligands and this enables the formation of stronger complexes. The chelate effect can be seen by comparing the reaction of a chelating agent (having more than one donor atom) and metal ion with corresponding reaction involving comparable monodentate ligands. By keeping coordination number same, the complex resulting from coordination with chelating agent is much more thermodynamically stable as compared to that formed with monodentate ligand. This can be explaining with help of instability constant or dissociation constant or formation constant. Disodium salt of EDTA is a water soluble chelating agent and is always preferred. It is nonhydroscopic and very stable sequestering agent (ligand which forms water soluble chelates are called sequestering agents). EDTA has wider general applications in analysis because of following important properties. 1. It has low price. 2. The special structure of its anion which has six donor atoms. 3. It forms strainless five membered rings. There are number of factors affecting EDTA reactions, some of them are listed below. 1. Nature and activity of metal ion. 2. The ph at which the titration is carried out. 3. The presence of interfering ions such as CN -, citrate, tartrate, F - and other complex forming agents (see masking and demasking agents). 4. Organic solvents also increase the stability of complex. 1. Nature and activity of metal ion: Disodium salt of EDTA forms complexes with most of metal ions in a 1:1 ratio; irrespective of the valency of the ion. M 2+ + [H 2 X] 2- [MX] H + or [MXH 2 ] M 3+ + [H 2 X] 2- [MX] H + or [MXH 2 ] + M 4+ + [H 2 X] 2- [MX] + 2 H + or [MXH 2 ]

115 Where M is a metal and [H 2 X] 2- is the anion of disodium salt of EDTA which is most frequently used for the analysis. The possible structures of these complexes with di-, tri-, and tetravalent metals contain three, four and five rings respectively. O O - O - N O O O - N N O N M M O O O O O O O O O O O O N N M O O O O O The transition metals and their ions have much higher tendency to form coordination compounds as compared to the S and P-block elements. It is because of their relatively smaller sizes, higher ionic charges and the availability of d-orbitals for the bond formation. The coordination compounds unlike normal compounds retain their identity even when dissolved in water or any other suitable solvent. The properties of these compounds are totally different from those of their constituents. 2. Effect of ph on complex formation of EDTA: Ethylenediaminetetraacetic acid (EDTA) ionizes in four stages, pk 1 = 2.0; pk 2 = 2.67; pk 3 = 6.16 and pk 4 = and since the actual complexing species is X 4-, complexes will form more efficiently and be more stable in alkaline conditions. If the solubility product of metal hydroxide is low, it may be precipitate if ph increases. On the other hand, at lower ph values the concentration of X 4- is low, and therefore the stability constant of the complexes will not be so high. The complexes of most divalent metals are stable in ammonical solution such as complexes of alkaline earth metals. Those of the transition metals such as copper, lead and nickel are stable down to ph = 3 and hence can be titrate selectively in the presence of alkaline earth metals. The trivalent metal complexes are usually still more firmly bound and stable in strongly acidic solutions. E.g. Co(III)-EDTA complex is stable in concentrated HCl. Although most complexes are stable over a fair range of ph, solutions are usually buffered at a ph at which the complex is stable and at which the color change of the indicator is most distinct. The Scope and limitations of EDTA Titrations: Complexometric titrations with EDTA have been applied to the determination of virtually every metal cation with the exception of the alkali 108

116 metal ions. Because EDTA complexes most cations, the reagent might appear at first glance to be totally lacking in selectivity. In fact, however, considerable control over interferences can be realized by ph regulation. For example, trivalent cations can usually be titrated without interference from divalent species by maintaining the solution at a ph of about 1. At this ph, the less stable divalent chelates do not form to any significant extent, but trivalent ions are quantitatively complexed. Similarly, ions such as cadmium and zinc, which form more stable EDTA chelates than does magnesium, can be determined in the presence of the magnesium by buffering the mixture to ph 7 before titration. Eriochrome Black T serves as an indicator for the cadmium or zinc end points without interference from magnesium because the indicator chelate with magnesium is not formed at this ph. Water hardness is usually determined by an EDTA titration after the sample has been buffered to ph 10. Finally, interference from a particular cation can sometimes be eliminated by adding a suitable masking agent, an auxiliary ligand that preferentially forms highly stable complexes with the potential interfering ion. Thus, cyanide ion is often used as a masking agent to permit the titration of magnesium and calcium ions in the presence of ions such as cadmium, cobalt, copper, nickel, zinc, and palladium. All of these ions form sufficiently stable cyanide complexes to prevent reaction with EDTA. The masking and demasking reagents are used to improve the selectivity of EDTA reactions. Construction of titration curves: Acidic properties of ligand: The dissociation constants for the acidic groups in EDTA are K 1 = 1.02 x 10-2, K 2 = 2.14 x 10-3, K 3 = 6.92 x 10-7, and K 4 = 5.50 x Note that the first two constants are of the same order of magnitude. This similarity suggests that the two protons involved dissociate from opposite ends of the rather long molecule. Because the protons are several atoms apart, the negative charge resulting from the first dissociation does not greatly influence the removal of the second proton. Note, however, that the dissociation constants of the other two protons are much smaller and different from one another. These protons are closer to the negatively charged carboxylate ions resulting from the dissociations of the first two protons, and they are more difficult to remove from the ion (zwitter ion) because of electrostatic attraction. The various EDTA species are often abbreviated H 4 Y, H 3 Y -, H 2 Y 2-, HY 3-, and Y 4-, the relative amounts of these five species vary as a function of ph. Note that the species H 2 Y 2 109

117 predominates from ph 3 to 6. The free acid H 4 Y and the dihydrate of the sodium salt, Na 2 H 2 Y.2H 2 O, are commercially available in reagent quality. The free acid can serve as a primary standard after it has been dried for several hours at C to C. However, the free acid is not very soluble in water and must be dissolved in a small amount of base for complete solution. More commonly, the dihydrate, Na 2 H 2 Y.2H 2 O, is used to prepare standard solutions. Alternatively, an approximate concentration can be prepared and then standardized against primary standard CaCO 3. Solutions of EDTA are particularly valuable as titrants because the EDTA combines with metal ions in a 1:1 ratio regardless of the charge on the cation. M 2+ + [H 2 X] 2- [MX] H + or [MXH 2 ] M 3+ + [H 2 X] 2- [MX] H + or [MXH 2 ] + M 4+ + [H 2 X] 2- [MX] + 2 H + or [MXH 2 ] 2+ EDTA is a remarkable reagent not only because it forms chelates with all cations but also because most of these chelates are sufficiently stable for titrations. This great stability undoubtedly results from the several complexing sites within the molecule that give rise to a cage-like structure in which the cation is effectively surrounded and isolated from solvent molecules. O O - O - N O O O - N N O N M M O O O O O O O O O O O O N N M O O O O O The ability of EDTA to form complexes with metals is responsible for its widespread use as a preservative in foods and in biological samples. At any ph a mass balance requires that the total concentration of unbound EDTA equal the combined concentrations of each of its forms. Total concentration of EDTA in un-complexed form is + Note that the constant refers to the equilibrium involving the fully unprotonated species for the complex formation with M n+ metal ion is formation constant K T 110

118 1 A titration curve for the reaction of a cation with EDTA consists of a plot of pm (pm = - log[ ]) versus reagent volume. In the early stage of a titration, values for pm are readily computed by assuming that the equilibrium concentration of is equal to its analytical concentration, which is found from stoichiometric data. Calculation of [ ] at and beyond the equivalence point requires the use of above equation for. In this region of the titration curve, it is difficult and time consuming to apply above equation if the ph is unknown and variable because both [ ] and [ ] are ph dependent. Fortunately, EDTA titrations are always performed in solutions that are buffered to a known ph to avoid interferences by other cations or to ensure satisfactory indicator behavior. Calculating [ ] in a buffered solution containing EDTA is a relatively straightforward procedure provided the ph is known. In this computation, we use the alpha value for H 4 Y,. (alpha-4 value of EDTA): alpha values are useful in visualizing the changes in the concentration of various species that occur in a titration of a monoprotic weak acid. Alpha values provide an excellent way of thinking about the properties of polyfunctional acids and bases. For example, if we get be the sum of the molar concentrations of the EDTA-containing species in the solution throughout the titration, the alpha value for the free acid is defined as. 2 Where, is the total molar concentration of uncomplexed EDTA. + Note that, at a given ph,, the fraction of total EDTA in the unprotonated form, is constant. The value of is - Where, are the four dissociation constants of H 4 Y (EDTA). Substitute the equation (2) in equation (1) 3 Combining the two constants, and yields the new constant called conditional formation constant which is constant only at the ph for which is applicable. 111

119 4 Conditional constants are easily computed once the ph is known. They may be used to calculate the equilibrium concentration of the metal ion and the complex at the equivalence point and where there is an excess of reactant. Note that replacement of with in the equilibriumconstant expression greatly simplifies calculations because is easily determined from the reaction stoichiometry whereas is not. In an EDTA titration, we are interested in finding the cation concentration as a function of the amount of titrant (EDTA) added. Prior to the equivalence point, the cation is in excess, and its concentration can be found from the reaction stoichiometry. At the equivalence point and in the post equivalence-point region, however, the conditional formation constant of the complex must be used to calculate the cation concentration. A titration curve for the reaction of a cation with EDTA consists of a plot of pm (pm = - log[ ]) versus reagent volume. From the concentration of metal ion, calculate the pm by using above equations. The following example demonstrates how above formulae and spreadsheet can be used to construct the titration curve. Example: Use a spreadsheet to construct the titration curve of pca versus volume of EDTA for 50.0 ml of M titrated with M EDTA in a solution buffered to ph Given -. Solution: Initial conc. of = M; conc. of EDTA = M;. Make spreadsheet or table having entries in the row: first - volume of EDTA added, second -, third [ ], fourth -, fifth pca. The initial pca is calculated from the initial [ ] by taking the negative logarithm. For the other entries (third and fourth row) prior to the equivalence point, the equilibrium concentration of is equal to the untitrated excess of the cation plus any resulting from dissociation of the complex. The latter concentration is equal to. Usually, is small relative to the analytical concentration of the uncomplexed calcium ion. For example, after 5.00 ml of EDTA has been added, 112

120 Calculated [ ] is entered in second column and corresponding pca is entered in the fifth column. Similarly, do the addition and calculate [ ] and pca till the equivalence point. The Equivalence-Point pca: At the equivalence point (25.00 ml of EDTA), first compute the analytical concentration of CaY 2 : The only source of ions is the dissociation of the complex. It also follows that the concentration must be equal to the sum of the concentrations of the uncomplexed EDTA,. Therefore [ ] = and [CaY 2 ] = - [ ] for To obtain [ ], we substitute into the expression for, [ ] = for Beyond the equivalence point, analytical concentrations of CaY 2 and EDTA are obtained directly from the stoichiometry. After the addition of 26.0 ml of EDTA, we can write (because after equivalence point, CaY 2 not formed) To calculate [ ], we then substitute this approximation for in the conditional formationconstant expression, and obtain [ ] = Calculate the [ ], and for further additions. Finally plot the titration curve of pca against volume of EDTA added. 113

121 Types of EDTA titrations: Several different types of titration methods that can be used with EDTA. 1. Direct Titration: Many of the metals in the periodic table can be determined by titration with standard EDTA solutions. Some methods are based on indicators that respond to the analyte itself, while others are based on an added metal ion. 2. Methods Based on Indicators for the Analyte. Nearly 40 metal ions that can be determined by direct titration with EDTA using metal-ion indicators. Indicators that respond to the metal directly cannot be used in all cases either because an indicator with an appropriate transition range is not available or because the reaction between the metal ion and EDTA is so slow as to make titration impractical. 3. Methods Based on Indicators for an Added Metal ion: In cases where a good, direct indicator for the analyte is unavailable, a small amount of a metal ion for which a good indicator is available can be added. The metal ion must form a complex that is less stable than the analyte complex. For example, indicators for calcium ion are generally less satisfactory than those we have described for magnesium ion. Consequently, a small amount of magnesium chloride is often added to an EDTA solution that is to be used for the determination of calcium. In this case, Eriochrome Black T can be used as indicator. In the initial stages of the titration, magnesium ions are displaced from the EDTA complex by calcium ions and are free to combine with the Eriochrome Black T, therefore imparting a red color to the solution. When all of the calcium ions have been complexed, however, the 114

122 liberated magnesium ions again combine with the EDTA until the end point is observed. This procedure requires standardization of the EDTA solution against primary-standard calcium carbonate. Structures of some important indicators used in complexometric titrations are given below. Sr. No. Name of the Indicator Colour change ph range Metals detected Mordant black II 1 Eriochrome black T Solochrome black T Red to Blue 6-7 Ca, Ba, Mg, Zn, Cd, Mn, Pb, Hg Murexide 2 or Ammonium purpurate Violet to Blue 12 Ca, Cu, Co 3 Catechol-violet Violet to Red 8-10 Mn, Mg, Fe, Co, Pb 4 Methyl Blue Blue to Yellow 4-5 Thymol Blue Blue to Grey Pb, Zn, Cd, Hg 5 Alizarin Red to Yellow 4.3 Pb, Zn, Co, Mg, Cu 6 Sodium Alizarin sulphonate Blue to Red 4 Al, Thorium 7 Xylenol range Lemon to Yellow 1-3 Bi, Thorium 4-5 Pb, Zn 5-6 Cd, Hg 4. Potentiometric Methods: Potential measurements can be used for end-point detection in the EDTA titration of those metal ions for which specific ion electrodes are available. 5. Spectrophotometric Methods: Measurement of UV/visible absorption can also be used to determine the end points of titrations. In these cases, a spectrophotometer responds to the color change in the titration rather than relying on a visual determination of the end point. 6. Back-Titration Methods: Back-titrations are useful for the determination of cations that form stable EDTA complexes and for which a satisfactory indicator is not available. The 115

123 method is also useful for cations such as Cr(III) and Co(III) that react slowly with EDTA. A measured excess of standard EDTA solution is added to the analyte solution. After the reaction is judged complete, the excess EDTA is back-titrated with a standard magnesium or zinc ion solution to an Eriochrome Black T or Calmagite end point. For this procedure to be successful, it is necessary that the magnesium or zinc ions form an EDTA complex that is less stable than the corresponding analyte complex. Back-titration is also useful for analyzing samples that contain anions that could form precipitates with the analyte under the analytical conditions. The excess EDTA complexes of the analyte prevents precipitate formation. 7. Displacement Methods: In displacement titrations, an unmeasured excess of a solution containing the magnesium or zinc complex of EDTA is introduced into the analyte solution. If the analyte forms a more stable complex than that of magnesium or zinc, the following displacement reaction occurs: Where, represents the analyte cation. The liberated or, in some cases, is then titrated with a standard EDTA solution. Methods of increasing the selectivity of EDTA as a titrant: EDTA is a very unselective reagent because it complexes with numerous doubly, triply and quadruply charged cations. When a solution containing two cations which complex with EDTA is titrated without the addition of a complex-forming indicator, and if a titration error of 0.1% is permissible, then the ratio of the stability constants of the EDTA complexes of the two metals M and N must be such that K M /K N 10 6 if N is not to interfere with the titration of M. strictly, of course, the constants K M and K N considered in the above expression should be the apparent stability constants of the complexes. If the complex-forming indicators are used, then for a similar titration error K M /K N The following procedures will help to increase the selectivity: A. Use of masking and demasking agents B. ph control. C. Use of selective metal indicators. D. Classical separation 116

124 E. Solvent extraction F. Removal of anions G. Kinetic masking A. Use of masking and demasking agents: Masking agents act either by precipitation or by formation of complexes more stable than the interfering ion-edta complex. a) Masking by Precipitation: Many heavy metals e.g.- Co, Cu and Pb, can be separated either in the form of insoluble sulphides using Sodium sulphide, or as insoluble complexes using thioacetamide. These are filtered, decomposed and titrated with disodium EDTA. Other common precipitating agents are sulphate for Pb and Ba, oxalate for Ca and Pb, fluoride for Ca, Mg and Pb, ferrocyanide for Zn and Cu, and 8-hydroxy quinoline for many heavy metals. Thioglycerol (CH 2 SH.CHOH.CH 2 OH) is used to mask Cu by precipitation in the assay of lotions containing Cu and Zn. b) Masking by Complex formation: Masking agents form more stable complexes with the interfering metal ions. The most important aspect is that the masking agent must not form complexes with the metal ion under analysis. The different masking agents used are enlisted below: i. Ammonium fluoride will mask aluminium, iron and titanium by complex formation. ii. Ascorbic acid is a convenient reducing agent for iron(iii) which is then masked by complexing as the very stable hexacyanoferrate(ii) complex. This latter is more stable and less intensely colored than the hexacyanoferrate(iii) complex. iii. Dimercaprol (2,3-Dimercaptopropanol); (CH SH.CHSH.CH OH). Cations of mercury, 2 2 cadmium, zinc, arsenic, tin, lead and bismuth react with dimercaprol in weakly acidic solution to form precipitates which are soluble in alkaline solution. All these complexes are stronger than the corresponding edetate complexes and are almost colorless. Cobalt, copper and nickel form intense yellowish-green complexes with the reagent under the above conditions. Cobalt and copper, but not nickel, are displaced from their edetate complexes by dimercaprol. iv. Potassium cyanide reacts with silver, copper, mercury, iron, zinc, cadmium, cobalt and nickel ions to form complexes in alkaline solution which are more stable than the corresponding edetate complexes, so that other ions, such as lead, magnesium, manganese and the alkaline earth metals can be determined in their presence of the metals in the first 117

125 group mentioned, zinc and cadmium can be demasked from their cyanide complexes by aldehydes, such as formaldehyde or chloral hydrate (due to the preferential formation of a cyanohydrins), and selectively titrated. v. Potassium iodide is used to mask the mercury(ii) ion as (HgI 4 ) 2- and is specific for mercury. It can be used in the assay of mercury(ii) chloride. vi. Tiron (disodium catechol-3,5-disulphonate) will mask aluminium and titanium as colorless complexes. Iron forms highly colored complexes and is best masked as its hexacyanoferrate(ii) complex. vii. Triethanolamine [N(CH 2.CH 2.OH) 3 ] forms a colorless complex with aluminium, a yellow complex with iron(iii), the color of which is almost discharged by adding sodium hydroxide solution, and a green manganese(iii) complex which oxidizes mordant black II. For these reasons, if murexide is used in the presence of iron and manganese, it is best to mask them with triethanolamine; similarly, mordant black II can be used in the presence of triethanolamine-aluminium complex. c) Demasking: It is the process in which the masked substance regains its ability to enter into a particular reaction. This enables to determine a series of metal ions in one solution containing many cations. Example of using masking and demasking agents in complexometry is the analysis of 3 metals, Cu, Cd and Ca. the following method of analysis is followed: 1. Direct titration of the mixture with the EDTA gives the sum of the 3 metals. 2. Cu and Cd may be masked with the addition of cyanide to the solution, leaving only Ca ion. 3. When formaldehyde or chloral hydrate is added to the cyanide containing mixture, only Cd is demasked and the EDTA titrates the sum of Ca and Cd. In this manner, the concentration of three ions is determined by 3 individual titrations. Step I: All three metal ions are titrated Ca Cd Cu + EDTA Ca - EDTA Cd - EDTA Cu - EDTA Step II: Only Ca is titrated Cu Cd Ca Cyanide ions Cyanide ions Cyanide ions Cu - Cyanide complex Cd - Cyanide complex No reaction EDTA Ca - EDTA complex 118

126 Step III: Ca and Cd are titrated Cu - Cyanide complex Cd - Cyanide complex Ca Cd + EDTA + EDTA + + HCOH HCOH Ca - EDTA complex Cd - EDTA complex No reaction Cd ions free B. ph control Method: The formation of a metal chelate is dependent on the ph of the reaction medium. In weakly acid solution, the chelates of many metals are completely dissociated such as alkaline earth metals, whereas chelates of Bi, Fe 3+ or Cr are readily formed at this ph. Thus, in acidic solution, Bi can be effectively titrated with a chelating agent in the presence of alkaline earth metals. This method is based upon the differences in stability of the chelates formed between the metal ions and the chelating agent. C. Use of selective metal indicators: These indicators are the metal complexing agents which react with different metal ions under various conditions. Several selective metal indicators have been used and they are specific for a particular ion. D. Classical separation: These may be applied if they are not tedious; thus the following precipitates may not be used for separations in which, after being re-dissolved, the cations can be determined complexometrically: CaC 2 O 4, nickel dimethylglyoximate, Mg(NH 4 )PO 4, 6H 2 O, and CuSCN. E. Solvent extraction: It is one of the best techniquie for separation. Example, Zinc can be separated from copper and lead by adding excess of ammonium thiocyanate solution and extracting the resulting zinc thiocyanate with 4-methylpentan-2-one (isobutyl methyl ketone); the extract is diluted with water and the zinc content determined with EDTA solution. F. Removal of Anions: Anions, such as orthophosphate, which can interfere in complexometric titrations, may be removed using ion exchange resins. G. Kinetic masking: This is a special case in which a metal ion does not effectively enter into the complexation reaction because of its kinetic inertness. Thus the slow reaction of chromium (III) with EDTA makes it possible to titrate other metal ions which react rapidly, without interference from Cr (III); this is illustrated by the determination of iron (III) and chromium (III) in a mixture. 119

127 Metallochromic indicators Complexometric indicators: The action of indicators in visual complexometric titrations is based on changing a particular optical property (absorption, fluorescence etc.) of the solution titrated in the conditions. The mechanism of the indicator reactions are based on several principles: 1. The indicator forms a colored complex with the metal ion to be titrated. The uncomplexed indicator may be colorless (one-colour indicators) or colored in its various protonated form (two-colour indicators). Such indicators are sometimes called metallochromic indicators. 2. When the complexation reaction of interest proceeds in another liquid phase (usually organic solvent) in equilibrium with the solution being titrated the indicators are described as extraction indicators. 3. When the indicator is influenced by a redox system, whose equilibrium is controlled by removal of the metal ions being titrated, the indicators are called redox indicators; they are usually one-colour indicators. The most typical complexometric indicators are metallochromic indicators. Because the change (or appearance) of colour is based on complex formation reactions the behavior is usually reversible, unless kinetic factors, mainly connected with the nature of the metal ions are significant. The reactions in complexometric titrations are mainly based on chelate formation. The most common and favorable case is when the titrant - analyte reaction proceeds in a stoichiometric ratio of 1:1. Formation of complexes with stepwise ligand attachment may give diffuse end points, unless the formation of the intermediate complexes is well separated. The same considerations apply when more than one metal ion may be bound by a multidentate ligand. The spectral characteristics of the indicator used in visual titrations should include the observed colors, wavelengths of absorption maxima and molar absorptivities of all relevant species, i.e. of the protonated species of the indicator and that of its complexes with the metal being titrated. These data are of concern to the visible range only. 1. Purity of indicator: The indicators may be contaminated by the substances formed or remaining from the synthesis. Other sources of contamination are decomposition or 120

128 transformation products of the indicator itself, as well as the various isomers formed as byproducts in the reagent preparation, added diluents or surfactants. 2. Preparation of indicator should be described whether as a solution or solid mixture in the case when the indicator solution is unstable. Depending on the preparation and concentration, the amount of indicator used for titration should be given. The indicator error for a complexometric titration is due to the following factors: 1. The end point error: The systematic error occurring because under the given conditions of the titration the metal ion concentration at the equivalence point differs from that at the end point, determined from the colour change of the indicator. 2. The indicator consumption error: The indicator consumption error is a systematic error occurring because at the end point a fraction of the metal is not bound by the titrant but is present as metal-indicator complex(es). This error has a negative value and depends on the amount of indicator present. For indicators exhibiting high colour intensities, which may be used in smaller concentrations, this error decreases. A significant compensation of this error normally takes place because the standardization of the titrant is carried out in similar conditions to the analysis titration. Characteristics of metallochromic indicators: 1. Colored organic compounds which form complexes with metal ions. 2. Free indicator must have a different colour to the chelate (indicator/metal ion complex) 3. Work by combining with excess metal ion and releasing when excess EDTA is present 4. Indicator must release the metal ion to the EDTA as close as possible to the endpoint i.e. the indicator metal ion chelate must be less stable than the EDTA/metal/ion chelate Example: Erichrome Black T (EBT) a. Useful in any titration were ph range is between 7 and 10, including calcium, magnesium and zinc. b. EBT is triprotic and has a different structure at varying ph values. c. Between ph 7 and 10 it exists as the dianion (Hin 2- ) and is blue in colour. d. It forms a red-purple complex with metals. 121

129 Limitation: When used with only calcium present an error is caused as the Ca-EBT complex is relatively unstable, releasing the indicator prior to the endpoint. Small amount of Mg-EBT complex is added to overcome this error as the Mg-EBT complex is much more stable and releases at the endpoint. Other examples of metallochromic indicators: Indicator ph range Colour change (complexed to free) applications Erichrome Black T Alkaline Red to Blue Many metals Calagmite Alkaline Red to Blue Better than EBT Xylenol orange Acid neutral Red to Yellow Zn, Sn, Pb Methylthymol blue Very alkaline Blue to Yellow Ca, Sr Some common applications: Water Hardness: Determination of Ca and Mg in water provides a measure of the hardness of water. Hardness in water causes normal soaps to fail to lather, causes scaling in boilers clogging pipes. Titration is done at ph 10 where calcium and magnesium are titrated, with EBT (or Calagmite). The result is reported as calcium carbonate. Aluminium: Uses a back titration method as aluminium reacts very slowly with EDTA. A known excess amount of EDTA is added to the aluminium solution, the sample heated and then the excess EDTA titrated with a standard solution of magnesium, calcium or zinc. Indirect Analysis of Anions: EDTA is used to titrate the metal ions that may be used to precipitate anions such as sulfate. Barium ions are used to precipitate out sulfate which is filtered and transferred to titration flask. A known excess of EDTA is added, the solution made alkaline and boiled to dissolve the barium sulfate and force the barium to complex the EDTA. Excess EDTA is back titrated with a standard calcium or magnesium solution. 122

130 Precipitation: The basic principle of precipitation is the solubility and solubility product of the given electrolyte in suitable solvent. As solvent change, solubility and solubility product of the electrolyte change. For the sparingly soluble salts (compounds with the solubility is less than 0.01 mol/lit), it is an experimental fact that the product of the total molecular concentrations of the ions is a constant at constant temperature. This product Ks is termed the solubility product. For binary electrolyte: AB A + + B - K s = [A + ] [B - ] In general for the electrolyte A p B q which ionizes into p A q+ and q B p- ions; A p B q p A q+ + q B p- K s = [A q+ ] p [B p- ] q When excess of the sparingly soluble salt or electrolyte is shaken up with water, some of it passes into the solution to form saturated solution and remaining solid is in equilibrium with the ions present in the solution. For the dilute solutions, the concentration of ions is equal to activities. The solubility product relation applies for the quantitative analysis. In the presence of moderate concentrations of salts, the ionic concentration and therefore ionic strength of the solution will increases, the activity coefficient of both ions will be decreased and consequently the ionic concentration (solubility) must increase in order to maintain the solubility product constant. This effect is most marked when the added electrolytes does not possess an ion in common with sparingly soluble salt. It is also called as salt effect. The great importance of the solubility product concept is it is used to explain the precipitation from solution in quantitative analysis. Solubility product is the product of ionic concentration (in saturated solution of sparingly soluble salt) at equilibrium between solid phase of the difficultly soluble salt and the solution. If the experimental conditions are such that the ionic concentration product is different from the solubility product, then system will attempt to adjust itself in such manner that the ionic and solubility products are equal in value. If the ionic product of the salt is higher than solubility product, precipitation of the solid salt occurs at saturated conditions. The important application of solubility product is to the calculation of solubility of sparingly soluble salts in solutions of salts with a common ion. 123

131 The solubility product principle is also used for the analysis when two slightly soluble salts are formed. For example, addition of the precipitating agent in the solution containing two anions, both of which formed slightly soluble salts with same cation. When silver nitrate is added to solution containing both chloride and iodide then question is arises that which salt will be precipitated first and how completely will the first salt be precipitated before the second ion begins to react with reagent? The solubility product of AgCl and AgI are 1.2 x (mol/lit) 2 and 1.7 x (mol/lit) 2 indicates that AgI is less soluble and will precipitate first than AgCl. K s(agcl) = [Ag + ] [Cl - ] = 1.2 x = K s(agcl) /[Ag + ] = [Cl - ] K s(agi) = [Ag + ] [I - ] = 1.7 x = K s(agi) /[Ag + ] = [I - ] The silver ions are in equilibrium with both salts. The above equation indicates that, when concentration of the iodide ion is about one millionth part of the chloride ion concentration, silver chloride starts precipitated. For the concentration of both chloride and iodide ions is 0.1 M, the silver chloride will be precipitated when, [I - ] = 0.1 x 1.4 x 10-6 = 1.4 x 10-7 M = 1.8 x 10-5 g/lit The solubility of the precipitate can be increases due to excess addition of the precipitating agent is frequently due to complex ion formation. 124

132 3.2. Separation Techniques Filtration Filtration of a mixture after completion of a reaction will often be necessary either to isolate a solid product which has separated out or to remove insoluble impurities or reactants, in which case the desired product remains in solution. When substantial quantities of a solid are to be filtered from suspension in a liquid, a Buchner funnel of convenient size is employed. The use of suction pump for rapid filtration using Buchner funnel which results more complete removal of the mother-liquor than filtration under atmospheric pressure. Distillation: If a liquid is kept in a sealed container, equilibrium is eventually established between the liquid and gaseous molecules. The pressure exerted by these gaseous molecules is called the vapor pressure and it increases with increasing temperature of the liquid. The boiling point of a liquid is defined as the temperature at which the vapor pressure of the liquid equals the external pressure (usually 1 atmosphere). It is also defined as the temperature at which vapor and liquid are in equilibrium at a given pressure. The effect of any solute, A, on the boiling point of a liquid B, will depend on the nature of A. If A is less volatile than B, then the total vapor pressure of the solution is lower at any given temperature, and its boiling point is higher than that of pure B (e.g., a solution of sugar in water). If, on other hand, solute A is more volatile than B, then the total vapor pressure of the solution, at any given temperature, is higher and its boiling point is lower than that of pure B (e.g., a solution of acetone and water). The behavior of a solution of two miscible liquids, A and B, is best explained by referring to Raoult's law which states that the partial pressure of liquid A ( ) in a mixture is equal to the vapor pressure of pure liquid A ( ) multiplied by the mole fraction of A in the mixture (X A ). The same applies to liquid B. From Dalton's law, the total vapor pressures of the solution ( ) is the sum of the partial pressures of A and B. A solution of A and B will boil when the total vapor 125

133 pressure ( ) equals the external pressure. This occurs at a temperature which is intermediate between the boiling points of the two pure liquids. In order to understand the separation of a pair of miscible liquids A and B by simple and fractional distillation, a following boiling point diagram is helpful This diagram shows the temperature at which mixtures of A and B of various compositions boil (lower curve). The composition of the vapor in equilibrium with the liquid is given by the tie line connecting the liquid and vapor curves. It is clear from above Figure that the vapor will always be richer than the liquid in the more volatile component. This makes sense, since the molecules of the component with the higher vapor pressure (more volatile) will escape more readily, and thus be in higher proportion in the vapor phase. Distillation is the process of heating a liquid to its boiling point, condensing the vapor by cooling, and collecting the liquid distillate. It is a technique for the purification of liquids and for the separation of liquid mixtures. If a liquid mixture of A and B with composition C 1 (X A = 0.2) is heated to boiling (L 1 ), then the vapor in equilibrium with it (V 1 ) will have the composition C 2 (X A = 0.4), i.e., the vapor will contain more of the volatile component A, than the original liquid. If this vapor is condensed (L 2 ) and redistilled, the distillate (V 2 L 3 ) will be much richer in A (composition C 3 ). As the distillation progresses, the mixture will gradually have less of the more volatile component and its boiling point will gradually rise. Consequently the distillate will contain a continually decreasing proportion of the more volatile component until finally all has been collected and the less volatile component is left as a residue. In practice, separation of a liquid mixture into its components by a single distillation (simple distillation) is possible only when the boiling points of the components are 80 degrees or more apart. For mixtures of liquids having boiling points much less than 80 degrees apart, separation 126

134 can be achieved only by fractional distillation. Such a distillation is equivalent to several repeated simple distillations. It uses a fractionating column which provides a large surface area for continuous heat exchange between the hot ascending vapor and the cooler descending liquid, thus resulting in a series of evaporations and condensations leading to separation of the two components. Vacuum distillation is a technique for the distillation of high boiling liquids, and for compounds that decompose at atmospheric pressure. At the low pressures employed, those compounds distil at much lower temperatures. Solvent extraction: Extraction is the separation of a substance from a mixture by means of a solvent that preferentially dissolves that substance. If the substance is extracted from a solid phase, the process is called solid-liquid extraction, as in the isolation of caffeine from tea leaves by means of hot water. Extraction of a substance from a liquid phase is called liquid-liquid extraction. The most common applications of this latter technique are: a. The recovery of an organic product from a reaction mixture containing excess unreacted materials and by-products. b. Isolation of an organic substance from its natural source, such as a plant. Liquid-Liquid Extraction is the most common type of extraction. It involves shaking the liquid mixture with an immiscible solvent which preferentially dissolves the desired compound. On standing, the two immiscible phases (usually organic and aqueous) form two separate layers (upper and lower) that can be separated by means of a separatory funnel. The various solutes in the mixture distribute themselves between the organic and aqueous phases according to their relative solubilities in each solvent. At equilibrium, the ratio of the concentration (C) or solubility (S) of the substance in the organic phase, (C 0 or S 0 ) to that in the aqueous phase (C w or S w ) is called the distribution coefficient (K D ). A large distribution coefficient implies that the compound is much more soluble in the organic phase than in the aqueous one and, in this case, a single extraction suffices to remove the desired compound from the mixture. When K D is small, it means that the compound distributes itself more evenly in both phases, so that repeated extractions are required to recover such a compound 127

135 from the aqueous mixture. In general, it is more efficient to divide the total volume of extracting solvent over several extractions than to use the whole volume in a single extraction. Choice of Solvent: A solvent used for extraction should have the following characteristics: 1. Immiscible with the liquid in which the solute is present. 2. Readily dissolve the solute to be extracted. 3. Extract little or none of the impurities and other compounds present in the mixture. 4. Non-flammable, non toxic, cheap and easily removable from the solute after extraction (i.e., volatile). Salting-out: Extraction of organic compounds from aqueous mixtures is usually improved by saturating the aqueous phase with a salt such as NaCl or Na 2 CO 3. This phenomenon is called salting-out and has the following effects: 1. Decreases the solubility of organic compounds in the saturated aqueous phase. 2. Decreases the solubility of the organic and aqueous phases in each other, thus improving their separation. This is particularly useful in breaking up emulsions. Emulsions: In certain cases, the two immiscible phases do not separate cleanly into two distinct layers; instead, they form an emulsion which, once formed, is usually difficult to break. It is therefore advisable to prevent the formation of emulsions during extraction. This is best achieved by avoiding vigorous shaking of the layers whenever an emulsion is expected to form (e.g., when alkaline aqueous solutions are extracted with chloroform or dichloromethane). If an emulsion still forms one can often break it by: 1. Stirring the emulsified layer gently with a glass rod. 2. Saturating the aqueous layer with a salt. 3. Centrifugation. Drying Agents: The organic phase often shows turbidity due to the presence of traces of water from the aqueous phase. Anhydrous CaCl 2, MgSO 4, or Na 2 SO 4 may be used as drying agents which absorb the traces of water present in the organic phase. When dry, the organic phase becomes clear. Chromatography: Chromatography is a technique that may be used to separate the components of a mixture as well as to identify organic substances and examine their purity. Chromatography encompasses several techniques such as column, thin-layer, paper, gas, liquid, etc. 128

136 chromatography. Two principles are basically involved in chromatography: adsorption (as in thin layer chromatography) and partition (as in paper chromatography), and certain terms are common to both types of chromatography. In adsorption chromatography, separation depends on the selective desorption of the components of a mixture by the eluent (mobile phase) from the surface of a solid adsorbent (stationary phase). The adsorbent may be packed in a column (column chromatography) or spread as a thin layer on a glass plate as in thin-layer chromatography. In partition chromatography, separation depends on partition of the components of a mixture between the stationary and mobile phases. The mobile phase may be a liquid (liquid-liquid partition chromatography) or a gas (gas-liquid partition chromatography). Analysis of chromatograms: In thin layer and paper chromatography, substances are characterized by their R f values (retardation factor). The R f value is a number (less than one) which is characteristic of a compound for a given adsorbent and developing solvent. It is defined as: In gas-liquid chromatography, compounds are characterized by their retention times. Thin Layer Chromatography (TLC): It is one application of adsorption chromatography in which an adsorbent, usually silica gel or alumina, is spread out as a thin layer on an inert surface, such as a glass plate or microscope slide. The mixture is applied at one end of the coated plate and, as the mobile phase (a liquid) moves up the solid adsorbent by capillary action, the adsorbed components of the mixture get desorbed and carried along at different rates by the moving solvent. Adsorption of the components of the mixture, on the surface of the adsorbent, occurs to differing extents depending on their structural features and polarity. The more strongly adsorbed a given compound is, the slower it is transported by the mobile phase, and conversely, the more weakly adsorbed the compound is, the faster it is transported up the stationary phase. The result is that the components of the mixture are separated into different zones or spots. Separation by thin-layer chromatography depends on the kind and activity of the adsorbent (stationary phase), the polarity of the eluent (mobile phase) and on the chemical nature of the components of the mixture. The most common adsorbents employed in TLC are silica (SiO 2. xh 2 O) and alumina (Al 2 O 3. xh 2 O), and the activity of these adsorbents is largely determined by 129

137 their water content. For a given adsorbent and compound, greater the polarity of the eluent, greater is its ability to dislodge a compound from the surface of the adsorbent, and therefore the higher the R f value. Eluting power of solvents: Acetic acid > Ethyl alcohol > Acetone > Diethyl ether > Dichloromethane > Hexane. Preparation of TLC Plates: Large glass plates (20 x 20 cm) are commonly used for quantitative separations, while microscope slides are usually used for qualitative purposes. Homogeneous slurry of the adsorbent in a volatile organic solvent (chloroform or dichloromethane) is poured over the glass plates and allowed to air-dry at room temperature. Microscope slides can be coated, two at a time, by dipping them into the slurry for sometime then holding them vertically to air-dry. The jar of adsorbent must be shaken thoroughly before each use to homogenize the slurry. Spotting: The mixture to be analyzed is dissolved in a suitable solvent (1% solution). With a drawn capillary tube, a small amount of this solution is spotted on the TLC plate about 1 cm from the bottom. The spots should have a diameter not larger than 1-2 mm, since larger spots result in "tailing" and overlapping of close spots. Once the solvent evaporates from the spots, the plate is ready for developing. Development of the Chromatogram: The eluent, also called developing solvent, is chosen on the basis of the nature and polarity of the compounds being studied. It is best to choose the solvent that will give a satisfactory separation within the range of R f values. The plate is placed in a developing chamber (e.g. a covered beaker) containing the solvent and lined with filter paper soaked in the solvent to help saturate the atmosphere with solvent vapors. When the solvent front reaches the finish line, the plate is removed from the beaker and placed on the bench top to air-dry. Visualization of Spots: Compounds on the plate are located according to their characteristics: a. If the spots are colored, they can be observed in ordinary light. b. If the compounds are colorless, they can be seen under UV-light where they appear as dark spots on a white background. c. Colorless spots may also be located with an indicator. Most organic compounds form complexes with iodine giving dark brown spots when the plate is exposed to iodine vapor. Sulfuric acid may also be used to make colorless spots visible. Most organic compounds turn black when sprayed with sulfuric acid. 130

138 Solvent extraction: It is one of the most frequent method that is used for the separation of a neutral organic compound (or compounds) from a solution or suspension (as either a solid or liquid) in an aqueous medium, by shaking with an organic solvent in which the compound is soluble and which is immiscible (or nearly immiscible) with water. The solvents generally employed for extraction are diethyl ether or di-isopropyl ether, toluene, dichloromethane and light petroleum. The solvent selected will depend upon the solubility of the substance to be extracted in that solvent and upon the ease with which the solvent can be separated from the solute. Diethyl ether, owing to its powerful solvent properties and its low boiling point (35 0 C) thus rendering its removal extremely facile, is very widely used; its chief disadvantage lies in the great fire hazard. If extraction with diethyl ether proves unsatisfactory the experiment is repeated with a fresh sample of reaction mixture using dichloromethane (b.p C) as the extraction solvent. If necessary, the other solvents are tried similarly until a suitable solvent has been selected. In the isolation of organic compounds from aqueous solutions, use is frequently made of the fact that the solubility of many organic substances in water is considerably decreased by the presence of dissolved inorganic salts (sodium chloride, calcium chloride, ammonium sulphate, etc.). This is the so-called salting-out effect. A further advantage is that the solubility of partially miscible organic solvents, such as ether, is considerably less in the salt solution, thus reducing the loss of solvent in extractions. Partition coefficient and distribution ratio (Nernst Distribution law): This law gives relationship between the concentrations of given molecular species (solute) in two different immiscible solvents (phases) which are in equilibrium to each other. When any solute X is shaken with two immiscible solvents A and B, it get distributed in between two solvents 131

139 according to it solubility and experimental conditions and exist equilibrium in both phases. The ratio of concentration of X in both phases is constant at constant temperature. Where, K is constant and is called as the distribution or the partition coefficient. It is independent on amount of solute added and solvent also. This relationship is called as the distribution or the partition law. In 1891, Nernst studied this phenomenon and generalized it, is called as Nernst distribution law or distribution or partition law. It is stated as- A solute X is distributes in between two immiscible solvents A and B, at equilibrium and at constant temperature (if X is in the same molecular condition in both solvents), the ratio of concentration of X in the two solvents is constant. Where, K D is constant and is called as the distribution or the partition coefficient. Let C A be the concentration of X in solvent A and, C B is the concentration of X in solvent B, then. 1 Example 1: Distribution of iodine in two solvents such as carbon tetrachloride and water (both are immiscible solvents). Iodine is dissolve partly in both solvents itself according to the solubility of iodine in it. The concentration of the iodine is different but their ratio is fixed at given temperature. K is the ratio of iodine in organic layer and water or aqueous layer. Example 2: When succinic acid in varying amount is added in two immiscible solvents such as ether and water. It get distributes in two solvent in such way that, it cannot affect ratio of K D value. 132

140 Distribution constants are useful because they permit us to calculate the concentration of an analyte remaining in a solution after a certain number of extractions. They also provide guidance as to the most efficient way to perform an extractive separation. The concentration of A remaining in an aqueous solution after n-extractions with an organic solvent ([A] n ) is given by the equation... 2 Where, [A] n is the concentration of A remaining in the aqueous solution after extracting V aq ml of the solution with an original concentration of [A] 0 with n-portions of the organic solvent, each with a volume of V org. Limitations of Distribution law: Nernst s distribution law is applicable only when it satisfied following conditions as - 1. Constant temperature: Temperature does not change throughout the experiment because solubility of solute is function of temperature. 2. Non miscibility of solvent: The two solvents are immiscible or very slightly miscible to each others. The addition of solute does not change mutual solubility of solvents. There also no chemical reaction between solute and any solvent. 3. Same molecular state: Molecular state of solute remains same in both solvents. The distribution coefficient ratio C 1 /C 2 is only constant when there is no dissociation or association of solute molecules on either solvent. 4. Dilute solutions: The concentration of solute in both solvents should be low because law does not give good result for higher concentrations. 5. Equilibrium conditions: The concentration of the solute in each liquid phase has been accurately measured only after the system is in equilibrium. 6. Purity of solvents: The solvent should be free from soluble impurities. These are may react with solute. 133

141 In most of cases, the solute molecules undergoes dissociation, association and salvation therefore the distribution law has been modified as - a. Solute undergoes association in one of the solvent: Let solute undergoes association in solvent 2 and remains unchanged in solvent 1. Let C 1 is the concentration of solute in phase (solvent) 1. In solvent (phase) 2, the solute molecules undergoes association therefore there are two species normal and associated solute molecules. Let C 2 and C 3 is the concentration of associated and normal solute molecules. X Normal molecule (C 1 ) Solvent (1) (organic phase) Association nx Xn (C 2 ) (C 3 ) Solvent (2) (aqueous phase) Then from the law, we can write as - C 1 = K C 1 by distribution law 3 Two equilibrium exist in the system can be written as - X nx Xn Normal Normal Associated molecules molecules molecules in solvent 1 in solvent 2 in solvent 2 C 1 C C 3 2 Where n be the normal molecules present in solvent 2 which are undergoes association, therefore according to the law of mass action - 134

142 But, according to distribution law,, Where, C 1 is the concentration of solute in solvent 1, C 2 is the total concentration of associated solute molecules (if all solute molecules undergo association). The above equation can be used when solute undergoes association in one of the solvent. It does not give good result when association is small. The value of n can be calculated by carrying experiment either by trial and error method or by graphical method. Plot a graph of log C 1 against log C 2 is straight line having slope and Y-intercept log K. Taking log on both side,, plot the graph of against. log C 1 slope = 1/n log K log C 2 b. Solute undergoes dissociation in one of the solvent: Suppose the solute molecules dissociated into fragments A + B in solvent 2, and remains undissociated in solvent

143 X C 1 Solvent 1 normal molecules X (1-a) C 2 A + B Dissociation Solvent 2 Let C 1 be the concentration of X in solvent 1 and C 2 is the total (dissociated + undissociated) concentration of solute in solvent 2. If α be the degree of dissociation of solute X in solvent 2, then- X A + B (1 α) α α Hence, the concentration of undissociated molecule or normal molecule in solvent 2 is C 2 (1 α). According to the distribution law This is modified equation of distribution law, when solute undergoes dissociation in solvent 2. If solute undergoes dissociation in solvent 1, then c. Some solute dissociate in both the solvents: Consider the solute X is distributed between the two immiscible solvents solvent 1 and solvent 2. Let the initial concentrations of the solute is C 1 and C 2 in solvent 1 and solvent 2 respectively. The solute undergoes dissociation in both the solvents. Let 1 and 2 be the degree of dissociation of solute in the two solvents. Hence, concentration of normal undissociated molecules are C 1 (1-1 ) and C 2 (1-2 ) and hence distribution coefficient is- 136

144 Applications of distribution law: Distribution law has been used in following area - 1. Solvent extraction. 2. Desilverisation of argeniferrous leads (Parke s process). 3. Investigation of association/dissociation/complex formation by the solute molecules in different solvent systems. 4. Quantitative conformation of bromine and iodine. 5. Liquid-liquid chromatography. 6. Determination of equilibrium constant. Types of solvent extraction Batch and continuous process: Organic compounds are usually relatively more soluble in organic solvents than in water, hence they may be extracted from aqueous solutions. If electrolytes, e.g. sodium chloride, are added to the aqueous solution, the solubility of the organic substance is lowered, i.e. it will be salted out: this will assist the extraction of the organic compound. The problem that arises in extraction is the following. Given a limited quantity of the solvent, should this be used in one operation (batch extraction) or divided into several portions for repeated extractions (continuous extraction) in order to secure the best result? A general solution may be derived as follows. The simplest extraction procedure possible and the technique most employed in the laboratory for analytical separations involves the bringing of a given volume of solution into contact with a given volume of solvent until equilibrium has been attained, followed by separation of the liquid layers. If necessary, the procedure may be repeated after the addition of fresh solvent. This batch extraction process provides rapid, simple, and clean separations, and is more beneficial when the distribution ratio of the solute of interest is large. Continuous extractions are particularly applicable when the distribution ratio is relatively small, so that a large number of batch extractions would normally be necessary for quantitative separation. Let the volume v ml of the aqueous solution containing grams of the dissolved substance be repeatedly extracted with fresh portions of s ml of the organic solvent, which is immiscible with water. If grams is the weight of the solute remaining in the aqueous phase after the first extraction, then the concentrations are g per ml in the aqueous phase and g per ml in the organic solvent layer. The partition coefficient K is given by: 137

145 1. 2 Let grams remain in the aqueous layer after the second extraction, then:. 3 Or 4 Similarly if grams remain in the aqueous layer after the nth extraction: 5 Amount of analyte get extracted after n-extraction in organic solvent = g. We desire to make as small as possible for a given weight of solvent, i.e. the product of n and s is constant, hence n should be large and s small; in other words, the best results are obtained by dividing the extraction solvent into several portions rather than by making a single extraction with the whole quantity. The extraction efficiency can be explained in percentage. It is the amount of analyte gets extracted in organic solvent from total dissolved in given aqueous solution. The more commonly used term for expressing the extraction efficiency by analytical chemist is the percent extraction E, which is related to D as- Where V represent solvent volume and the other quantities remain as previously defined. The percent extraction may be seen to vary with the volume ratio of the two phases as well as with D. The greater efficiency of continuous extraction over the batch extraction is explained with the help of following example. 138

146 The extraction of a solution of 4.0 g of butanoic acid in 100 ml of water at 15 0 C with 100 ml of benzene at 15 0 C. The partition coefficient of the acid between benzene and water may be taken as 3 (or between water and benzene) at 15 0 C. For a single extraction with benzene, we have: s = 100 ml, v = 100 ml, K =, and = 4.0 g. = 1.0 g The 3.0 g of butanoic acid butanoic acid get extracted in 100 ml of benzene. Therefore, the extraction efficiency is 75%. For three extractions with 33.3 m1 portions of fresh benzene i.e. n = 3 and s = 33.3 ml. = 0.5 g The 3.5 g of butanoic acid butanoic acid get extracted in total 100 ml of benzene after 3 extractions. Therefore, the extraction efficiency is 87%. This clearly shows the greater efficiency of extraction obtainable with several extractions when the total volume of solvent is the same. Moreover, the smaller the distribution coefficient between the organic solvent and the water, the larger the number of extractions that will be necessary. The extraction efficiency of each extraction in continuous or batch extraction can be explain with help of following general example. Consider W g of solute dissolved in 1 liter of water and is extracted by 1 liter of organic solvent. The distribution coefficient of solute for this organic solvent water solvent pair is 2 i.e. K = 2. Case I: Extraction in one lot: Let x g be the amount of solute get extracted in 1000 ml of organic solvent, then concentration of solute of organic layer = g per ml, and that of aqueous layer is = g per ml. 2 W 2x = x g It indicate that, in single extraction process, 2/3 or % of solute can be extracted. 139

147 Case II: Extraction in two lot: Let g be the amount of solute get extracted in 500 ml of organic solvent in first extraction, then concentration of solute of organic layer = g per ml, and that of aqueous layer is = g per ml. g It indicates that, in first extraction process, 1/2 or 50.0 % of solute can be extracted. The amount of solute remain unextracted after first extraction = W - = g Now g be the amount of solute get extracted in 500 ml of organic solvent in second extraction, then concentration of solute of organic layer = g per ml, and that of aqueous layer is = = g per ml. It indicates that, in second extraction process, 1/4 or 25.0 % of solute can be extracted. The overall extraction efficiency after two extraction = = 75.0% which is more than the one time extraction. Similarly when extraction is carried out in four lots with 250 ml solvent for each extraction, efficiency is 80.25%. While if extraction is carried out in 10 lots, each of volume 100 ml then almost 84% solute get extracted. Separation factor (γ): Since solvent extraction is used for the separation of different elements and species from each other, it becomes necessary to introduce a term to describe the effectiveness of separation of two solutes. The separation factor γ is related to the individual distribution ratios as follows: = = Where, A and B represent the respective solutes. 140

148 In those systems where one of the distribution ratios is very small and the other relatively large, complete separations can be quickly and easily achieved. If the separation factor is large but the smaller distribution ratio is sufficiently large then less separation of both components occurs. It is then necessary to apply various techniques to suppress the extraction of the undesired component. Classification of solvent extraction systems: Extraction can be classified on the basis of - Nature of extracted species and Process of extraction. A. On the basis of nature of extracted species there are two types 1. Chelate extraction 2. Ion association B. Classification based on the basis of process of extraction 1. Extraction by chelation or Chelate formation 2. Extraction by Ion pair formation 3. Extraction by solvation 4. Synergistic extraction Extraction by chelation or Chelate formation: An extraction is often more attractive than a precipitation method for separating inorganic species. Many organic chelating agents are weak bases (neutral chelates) or weak bases (anionic chelates) that react with metal ions to give uncharged complexes that are highly soluble in organic solvents such as ethers, hydrocarbons, ketones, and chlorinated species (including chloroform and carbon tetrachloride). Chelating ligand may play an important role in extraction of metal. The substance which brings about chelation is called as chelating agent. Metal ion + chelating agent Metal chelate The chelates are classified according to the type of basic group present. If both the basic groups are uncharged it results into a positively charged metal chelate. However, if the reagent has one anionic group, a neutral chelate is formed while multiple negative charges on chelating agent results in negative charged chelates. Neutral chelates are easily extracted in organic solvent. 141

149 Most uncharged metal chelates, on the other hand, are nearly insoluble in water. Similarly, the chelating agents themselves are often quite soluble in organic solvents but of limited solubility in water. The above figure shows the equilibrium that develop when an aqueous solution of a divalent cation, such as zinc(ii), is extracted with an organic solution containing a large excess of 8- hydroxyquinoline. Four equilibrium are shown. In the first, 8-hydroxyquinoline, HQ, is distributed between the organic and aqueous layers. The second is the acid dissociation of the HQ to give H + and Q - ions in the aqueous layer. The third equilibrium is the complex-formation reaction giving MQ 2. Fourth is distribution of the chelate between the two solvents. If it were not for the fourth equilibrium, MQ 2 would precipitate out of the aqueous solution. The overall equilibrium is the sum of these four reactions or The equilibrium constant for this reaction is Usually, HQ is present in the organic layer in large excess with respect to M 2+ in the aqueous phase so that [HQ] org remains essentially constant during the extraction. The equilibriumconstant expression can then be simplified to Or Thus, we see that the ratio of concentration of the metal species in the two layers is inversely proportional to the square of the hydrogen ion concentration of the aqueous layer. Equilibrium 142

150 constants K vary widely from metal ion to metal ion, and these differences often make it possible to selectively extract one cation from another by buffering the aqueous solution at a level where one is extracted nearly completely and the second remains largely in the aqueous phase. Chelates have relatively large stability constants, so their formation greatly lowers the concentration of hydrated metal ion. Those chelating agents such as acetylacetone, cupferron, dithizone, and 8-quinolinol form uncharged, essentially covalent compounds, which are readily soluble in organic solvents. Chelating agents such as dipyridyl or ethylene diamine tetra acid (EDTA) which form charged chelates are useful as metal masking agents. Extraction by Ion pair formation: Ion association complexes are uncharged species formed by the association of ions because of purely electrostatic attraction. The extent of such association increases sharply as the dielectric constant of the solvent decreases below 40 to 50. This condition not only exists in all of the commonly used organic solvents but also in highly concentrated aqueous solutions of strong electrolytes. Two categories of ion association complexes may be recognized. The first includes those ionpair formed from a reagent having large organic ion such as tetraphenylarsonium ion, tribenzylammonium ion or perfluorobutyrate ion. These reagents combine with a suitable metalcontaining ion to give a large organic solvent-like ion-pair. The second type of ion-pair is essentially like that of the first with the exception that solvent molecules are directly involved in its formation. Thus in the extraction of uranyl nitrate with isobutyl alcohol, the extractable complex is probably UO 2 (BuOH) 6.(NO 3 ) 2 in which the coordinated solvent molecules contribute both to the size of cation and the resemblance of the complex to the solvent. The extraction will proceed with formation of a neutral uncharged species which interns is extracted into organic phase. Most of the high molecular weight amines or so called liquid ion exchanger comes under this group. The mechanism of extraction by ion pair formation can be described as follows 143

151 Best separations are possible with good diluents. The control of temperature and activity is most important in accomplishing quantitative separations. In ion pair extraction the metal may be incorporated with by co-ordination in either the cation or anion of the extractable ion pair. Extraction by solvation: Solute molecules are associated with the solvent molecules this is known as solvation. In extraction by solvation, solvent molecules are directly involved in formation of the ion association complex. The value of ion pair formation constant, K is related to dielectric constant, and temperature. Where, N = Avogadro s number = Boltzmann s constant Q(b) = Calculable function a = emperical parameter = dielectric constant In case of solvent extraction, the solvent itself participates in extraction of complex. E.g. Extraction of Fe 3+ from 5.5 M HCl by diethyl ester In case of extraction by salvation the extracted species is solvated with a definite number of solvent molecules and provided that the solvent must be inert. Synergistic extraction: This extraction involves two extractants i.e. chelating ligand and solvating solvent. Conditions for Extractions - a. The chelating ligand HX should neutralize the metal charge by chelation. b. The solvent should co-ordinates less strongly than chelating ligand. c. The solvent should displace any residual co-ordinated water from the neutral metal complex, rendering it less hydrophilic. d. The maximum co-ordination number of the metal and geometry of the ligand should be favorable. 144

152 E.g. Extraction of uranyl ion by tributyl phosphate(tbp) and thinly trifluoroacetate (HTTA). Due to adduct formation the extraction efficiency of uranyl ion by HTTA in presence of TBP increases this is called as synergism. Important Questions Unit I 1. Define Gibbs free energy. Explain physical significance of G. 2. Define Helmholtz free energy. Explain its physical significance. 3. Define free energy. Give the relationship between A and G. 4. Define Helmholtz free energy. Derive mathematical equation for variation of A with V and T. 5. Define Helmholtz free energy. Derive alternative equation for the variation of A with T. 6. Define Gibbs free energy. Derive mathematical equation for variation of A with P and T. 7. Derive Gibb s-helmholtz equation. Explain its physical significance. 8. Define partial molar quantity. Derive equation for chemical potential. 9. Define partial molar quantity, partial molar volume, partial molar entropy, partial molar volume, partial molar Helmholtz energy, chemical potential, activity, activity coefficient, fugacity, reversible reaction, dynamic equilibrium, equilibrium constant 10. Define partial molar quantity. Derive Gibb s-duhem equation. 11. Define partial molar quantity. Show that partial molar quantity is intensive property. 12. Define K c of reversible reaction. Explain characteristics of K c. 13. Define K p of reversible reaction. Explain characteristics of K p. 14. Define equilibrium constant. Derive relationship between K p and K c. 15. Define Reaction isotherm. Show that net work done of the reaction = 2.303RT ln Kp. 16. Define Reaction isotherm. Derive 17. Define Reaction isotherm. Derive 145

153 18. Define quantum yield, Einstein, singlet state, triplet state, fluorescence, phosphorescence, photoluminescence, bioluminescence, photochemistry, quantum efficiency, photochemical reactions. 19. Define thermal reaction. Distinguish between thermochemical reaction and photochemical reaction. 20. Define photochemical reaction. Explain the features of photochemical reactions. 21. State and explain Grotthus-Draper law or the first law of photochemistry. 22. State and explain Stark-Einstein law or the second law of photochemistry. 23. Explain the term Einstein energy. 24. Define quantum efficiency. Explain the determination of quantum efficiency by using Chemical actinometer. 25. Define quantum efficiency. Explain the causes of high quantum yield of photochemical reaction. 26. Explain the causes of lo quantum yield of photochemical reactions. Give the examples of lo quantum yield photochemical reactions. 27. Define rate of reaction, rate constant, law of mass action, order of reaction, molecularity of reaction, reversible or opposing reaction, consecutive reactions, parallel reactions, chain reactions, temperature coefficient of reaction. 28. Define energy of activation. Derive Arrhenius equation. 29. Define energy of activation. Derive Arrhenius equation from the Maxwell- Boltzmann distribution law. 30. Define energy of activation. Explain the importance of Arrhenius equation. Examples: 1. What is the total volume of a mixture of 50.0 g of ethanol and 50.0 g of water at 25 C? 2. What is the change in free energy of a chemical process whose change in enthalpy at 373K is kj and the entropy change is -220 JK -1? 3. For the reaction A 2(g) + B 2(g) 2AB, the equilibrium constant is doubled when the temperature increases from 298 K to 308 K. Calculate H for the reaction. 4. At 298K, for the reaction, 6C (s) + 6H 2(g) C 6 H 12(l), H = kj, S = J/K, calculate the free energy of formation of C 6 H 12 at 298K. 146

154 5. For the reaction, C (s) + H 2 O (g) CO (g) + H 2(g) H = kj, S = kj/k, Will the reaction will be spontaneous at 1000K. 6. Calculate the energy of a photon and an Einstein of wavelength 982 nm. 7. A system absorbs 2 x quanta of light per second. At the end of 10 minutes, it is observed that mole of the irradiated substance has reduced. What is the quantum efficiency of the reaction? 8. In a photochemical decomposition of gas, 0.66 x 10-2 mole decomposed due to the absorption of 3.95 kj of λ = 202 nm. Calculate the quantum efficiency of the gaseous reaction. 9. The energy of activation of gaseous reaction is kj/mol. Calculate the rate constant at 50 0 C if it is 4 x 10-3 sec -1 at 30 0 C. (R = J/K,mol). Unit II 1. Define electrochemistry, ohms law, conductance, specific conductance, cell constant, equivalence conductance, molar conductance, electrolyte, limiting conductance, dissociation constant, degree of dissociation, ionic atmosphere of electrolyte, 2. Explain variation of molar conductance with dilution of strong and weak electrolytes. 3. State and explain Arrhenius theory of ionization. Give its limitations. 4. Explain factor or effect affecting conductance of strong electrolyte with concentration. 5. State and explain Kohlrausch s law of independent migration of the ion. Give its application. 6. State Kohlrausch s law of independent migration of the ion. How it will used to determining limiting conductance of weak electrolyte. 7. State Kohlrausch s law of independent migration of the ion. How it will used to determining dissociation constant of a weak electrolyte. 8. State Kohlrausch s law of independent migration of the ion. How it will used to determining solubility of a sparingly soluble salt. 9. Define titration, titrant, titrand, indicator, equivalence point, end point, titration error. 10. Define titration. Give the classification of titrimetric analysis on the basis of type of reaction. 147

155 11. Explain the criteria for the selection of indicator in acid base titration with the help of examples. 12. Derive equation which shows relationship between ph and pka of indicator. 13. Explain the titration and titration curve of weak acid against strong base. 14. Explain the titration and titration curve of strong acid against weak base. 15. Explain the titration and titration curve of weak acid against weak base. Examples: 1. A 2 x 10-2 mol/lit solution of sodium chloride has a specific conductance of S/m. Calculate molar and equivalence conductance of sodium chloride. 2. The molar conductance for HCl, NaCl and sodium acetate at infinite dilution are , and x 10-2 Sm 2.m 2.gm eq -1 respectively. Calculate molar conductance of acetic acid at infinite dilution at the same temperature. 3. The specific conductance of a saturated silver chloride solution at 298K is 3.37 x 10-4 m - 1, whereas that of distilled water is 2 x 10-4 S/m. The limiting conductance values for potassium chloride, silver nitrate and potassium nitrate are , and respectively. Calculate the solubility and solubility product of silver chloride. 4. Calculate the ph of 10 ml 0.1 M HCl and 5 ml 0.1 N NaOH solution. 5. Calculate the ph of 10 ml 0.1 M acetic acid and 5 ml 0.1 N NaOH solution. 6. Sketch the titration curve of 20 ml of 0.05 M acetic acid against 0.05M NaOH solution. 7. Sketch the titration curve of 20 ml of 0.1 M ammonia against 0.05M HCl solution. Unit III 1. Explain the principle of complexometric titration with the help of suitable example. 2. Define complexometric titration. Explain the parameter affecting the end point of complexometric titration. 3. Explain importance of EDTA in complexometric titration. 4. Write structure of EDTA. Explain the factor affecting EDTA titration with the help of suitable examples. 5. Explain the scope and limitations of EDTA titration. 148

156 6. Define formation constant of EDTA. Construct the titration curve of pca versus volume of EDTA for 50.0 ml of M calcium ion titrated with M EDTA in a solution buffered to ph Given K T = 1.75E Explain the type of EDTA titration. 8. Explain the methods used to increase the selectivity of EDTA titration. 9. Explain the role of masking and demasking agents in complexometric titration. 10. Explain importance of Metallochromic indicators in complexometric titration. 11. Explain characterization and indicator error of Metallochromic indicators. 12. Explain structure, importance and limitations of Erichrome Black T (EBT). 13. Explain the estimation of total hardness of water by complexometric titration. 14. Explain the principle of precipitation, filteration, TLC, chromatography, and solvent extraction. 15. Explain principle of liquid-liquid extraction. Give criteria for the selection of solvent for solvent extraction. 16. Define Nernst distribution law with the help of suitable example. 17. Define Nernst distribution law. Give the limitations of Nernst distribution law. 18. Explain the types of solvent extraction. 19. Explain the importance of extraction efficiency in solvent extraction. 20. Explain separation factor of solute in solvent extraction. 21. Explain - the extraction of metal ion by using chelation or chelate formation. 22. Explain extraction of uranyl nitrate with isobutyl alcohol by ion pair formation method. Examples: 1. 90% of an organic substance is extracted from its aqueous solution by using equal volumes of aqueous and organic solvents in single extraction. What will be the percentage of extraction if the quantity of organic solvent is doubled? ml of an aqueous solution of 0.1 M La(III) was extracted three times with an organic solvent. Calculate the minimum volume of the solvent required per unit extraction so as to reduce the concentration of La(III) in aqueous solution to 10-5 M (Given distribution ration = 370). 149

157 3. When 0.5 liter of an aqueous solution was extracted twice with 0.2 liter of an organic solvent. 99% of solute was extracted. Calculate the value of distribution ratio in favor of organic solvent. 4. The distribution ratio D is 10 in favor of the organic solvent for a particular system. Calculate the % extraction for a volume ratio V 0 /V w of (1) 1 and (ii) 10 for a single extraction % of the metal chloride is extracted when equal volumes of aqueous and organic phases are used, what will be the percent extraction if the volume of the organic phase is doubled. 6. When an aqueous solution of FeCl 3 in concentrated HCl is shaken with twice its volume of ether, 99% of the iron is extracted. Calculate the distribution ratio (organic/aqueous) of the compound Electrochemistry II Transport Number of ions: The current flow through the solution due to migration of ions of electrolyte. The cations are migrates towards cathode while anions are migrates towards anode. If I is total current flowing through the solution, then contribution to it by cations is I + and that of anions is I -. I = I + + I

158 e.g. NaCl solution, I NaCl = I Na+ + I Cl-. NaCl + CuSO 4 solution, I solution = I Na+ + I Cl- + ICu 2+ + ISO4 2-. The fraction of the total current carried by the cation/anion isf + = I + / I & f - = I - / I f + and f - are the fraction of total current carries by cation and anion respectively. The fraction of the current carries by ion from total current is also called as transport number (t) of ion. Transport number of cation = t + = f + = I + / I t + = I + / I i. i - total number of ions Transport number of anion = t - = f - = I - / I t - = I - / I i. i - total number of ions Dependence of transport number on the velocity of the ion: The transport number of the ion will be depends on its velocity in the solution. This can be explain as follows- Suppose d is the distance between two electrodes LMNO and ABCD in between solution of electrolyte is placed. n + & n - are the number of cations & anions present in the solution between two electrodes. Z + & Z - are the charges on cations and anions, u + & u - are the velocities of cations and anions respectively. M Q F B L Cathode N P E q + n + are cations q - u + R u - G n - are anions A Anode C O S d H D The total current (I) is the quantity of charges transferred per unit time (number of ions deposited in unit time) which will be depends on the charge carried by individual ion & total number of ions present in the solution. As velocity of cation is u + & distance covered by cation in one second is q +, it means that all cations from the distance q + from LMNO get deposited on the cathode in one second. 151

159 Total charge transferred by cation = = [Total cation deposited on cathode in 1 sec.] [charge carried by cation] = [Total cation deposited on cathode in 1 sec.] [Z + ] 1 The number of cations deposited on cathode in one second will be the number of cations present in the solution between LMNO & PQRS. [Total cation deposited on cathode in 1 sec.] = [Total cations in between LMNO & PQRS] = [total number of cations present in total volume of solution] = 2 Put equation (2) in equation (1) as- I + = = 3 Similarly, current carries by the anions will be the total charge due to anions present in the volume of solution enclosed between ABCD and EFGH. I - = = 4 The total current (I) passes through the solution = I = I + + I - 5 From the equation (3), (4) & (5), I = 6 The solution of any electrolyte is always electrically neutral, therefore - [Total charges due to cation] = [Total charges due to anions] Z + n + = Z - n - 7 From equation (6) & (7) - I = = 8 Therefore transport number of cation = t + = = 9 Similarly, for anions is- = t - = = 10 And = 11 Conclusions: 1. Transport number of ions are directly proportional to its velocity, t α u. 2. Transport number is also depends on the velocity of co-ions moves in the solution. 3. If u - = u +, then t - = t

160 4. t - + t + = = 1; sum of transport number is one. Hittorf Rule: Definition of the transport number involved I - or I + and I. The total current can be measured directly, but I - or I + cannot be determined directly from the experiment. Hence some methods are used for the indirect measurement of either I - or I + which are based on the consequences of the migration of the ions in presence of electric field. When current passage through the solution causes following changes- 1. Ions of the electrolytes are migrates towards opposite charge electrolytes and thus carry the current through the solution. 2. Ions get discharged on the opposite charged electrodes is called electrolysis of the solution. Due to the electrolysis and the migration of the ions in an unstirred solution, a net change in concentration of the electrolyte around the electrodes was observed experimentally. This change in concentration was related to the velocity of the ions and its co-ions i.e. related to the transport number of the ions. Therefore, change in concentration around the electrodes can be used to determined transport number. This can be explain by considering following two cases. Case I: Cations and anions are moving with equal speed [u - = u + ] The electrolyte cell can be divided into three components, the cathode, the anode and middle compartment. In absence of external electric field, the concentration of ions in each compartment is same. 153

161 + A B - Anode Cathode a In absence of external electric field By applying external electric field b c Anode compartment A' middle compartment B' Cathode compartment Balancing the charges or concentration After electrolysis Let each compartment (cathode, anode and middle) contains five equivalents of the electrolyte before electrolysis. Suppose four faraday of electricity be passed through the solution, causes the electrolysis of four equivalent of cations form cathode compartment and four equivalents of anions form the anode compartment. To balance ionic neutrality, ions are moving with equal speed and hence will carry the same magnitude of the current [if each having +/- one equivalent charge]. Therefore out of four faraday of current passed through the solution of electrolyte, two faraday will be carried by the cation and two faraday by the anions. This will leads the migration of two cations from anode to middle and from middle to cathode compartment. Similarly, two equivalents of anions will get migrated from the cathode to the middle and from middle to anode compartment. At the end, the concentration of the middle compartment does not change, while that of the anode and cathode compartment is changed but remains same, because cations and anions are moving with equal speed. Case II: Cations and anions are moving with unequal speed (u + = 3u - ) (u + u - ) Suppose each compartment (cathode, anode and middle) contains five equivalent of electrolyte and speed of the cation is three times to the speed of anions i.e. u + = 3u -. Suppose four faraday of electricity be passed through the solution, causes the electrolysis of four equivalent of cations form cathode compartment and four equivalents of anions form the anode 154

162 compartment. The ions are moving with unequal speed, therefore unequal fraction of current carries by cations & anions i.e. I + / I - = u + /u - = 3. The velocity of cations is three times to the velocity of anions; therefore, current carries by the cation will be three times to the current carries by the anions. Hence, out of four faradays of electricity passed through the solution, three faraday of electricity was conducted by cations and only one fraction was by the anions. This will be results the migration of three equivalents of cations from anode compartment to the middle compartment and from middle compartment to cathode compartment while one equivalent of anion from cathode to middle and from middle to anode compartment. + A B - Anode Cathode a In absence of external electric field By applying external electric field b c Anode compartment A' middle compartment B' Cathode compartment Balancing the charges or concentration After electrolysis As a result, concentration of the middle compartment does not change, but that of the cathode and anode compartments decreases unequally. The decrease in concentration of cathode and anode compartment is equal to the ratio of velocities of the cations and anions. [Lose in equivalent of electrolyte in cathode compartment] [Lose in equivalent of electrolyte in anode compartment] From these two observations, Hittorf s rule states that- u + 1 = = u - 3 The loss in equivalents of an electrolyte in a given compartment due to migration is proportional to the velocity of the ion migrating away from the compartment. 155

163 The moving boundary method to determine transport number: Principle: The method used to determine the distance covered by a boundary generated and maintained between two electrolyte solutions during electrolysis. From that distance covered in given time interval, transport number of the ion can be determined. Construction: It consists of vertical glass tube fitted with two metal electrodes, one at the top and second at the bottom. The electrode in the bottom portion of the tube is of the same metal as the cation of the electrolyte M A which is filled at the lower portion of the tube. This electrode is worked as anode. Pt electrode Source R MA' Direction of movement of cation & boundary C B B' MA C' M'A Transport number is to be determined (boundary) following electrolyte A Anode (M') D The electrode at the top is made up of platinum and act as cathode which is surrounded by electrolyte MA. The rest portion of the tube is filled with electrolyte MA for which the transport number is to be determined. The cation M + has less velocity than M + hence the solution M A is called as following electrolyte. The boundary BB between two electrolytes solution M A and MA can be made visible by using dye or indicator. The position of boundary can also be determined by using refractive index measurement (two solutions have different refractive index). Working: Complete the circuit as shows in above diagram. As current passage, both M + and M + will be moves in the upwards direction; with M + following M + due to lesser velocity. So that boundary BB will move in same direction. For the given time interval, measure the distance covered by the boundary BB during electrolysis. 156

164 Calculation: 1. If l is the distance covered by the boundary & A is cross section of the tube, then volume swept by the boundary will be- V = A x l cm 3 (ml) 2. If c is the concentration of electrolyte in gm-equivalents per lit, then V ml of solution will contain ml equivalents. 3. The quantity of the charge transported by the cations in ml of the solution. I + = ; where F stands for Faraday = coulombs. 4. If Q is the total quantity of electricity passed through solution, thent + = = FVC/1000I.t; Where I stand for total current passed through solution & t is time in seconds. 157

165 Factor affecting transport number of electrolytes: Transport number of ions depends on- 1. Concentration. 2. Temperature. 3. Nature of the co-ion. 4. Size of the ion. 5. Complex formation. 1. Concentration: Transport number of the ion increases with decreases in the concentration of the electrolyte similar to the variation of equivalent conductance with concentration. The variation of transport number with concentration can be expressed mathematically ast = t 0 - A c. Where, t is the transport number at the concentration c, t 0 is the transport number at infinite dilution. 2. Temperature: As temperature increases, transport number of all ions increases and reaches to the limiting value as 0.5. As temperature increases, velocity of the ions increases and therefore transports number. This behavior is observed in both cations and anions. At elevated temperature, both cations and anions are migrates with equal speed and shows same contribution in the transport number (each by 0.5). 3. Nature of co-ion: The transport number of the ions will be depends on the velocity with which the ion moves in the solution and velocity of the co-ions. At any given temperature, a given ion will move with same velocity in all of its salt solutions, but velocity of the co-ions is different in each case. But at same temperature, transport numbers of anions are different in different salt solutions of the same cation. 4. Size of the ion: Transport number of ion depends on its velocity in the solution with which it can moves in solution. The velocity of the ion will be depends on size. As size of ion decreases, velocity of it increases and vice-versa. Hence transport number of the ions of same group is used to determine their size. Sc < Ti < V < Cr < Mn < Fe < Co < Ni < Cu < Zn Size decreases 158

166 Transport number increases 5. Complex formation: Transport number of the ion will be also affected by the complex formation and in some cases, it will be negative. e.g. In concentrated solution of cadmium iodide, cadmium exist in anionic complex [CdI 4 ] 2-, hence it migrates towards anode. But actually cadmium ion (Cd 2+ ) must migrates towards cathode. As the ions are actually migrates toward opposite direction than expected, the transport number of the cadmium is negative under such conditions. 159

167 Relationship between transport number, ionic mobility and λ of electrolyte: The velocity with which the ions moves in the solution is called as ionic mobility. The ionic mobility will be depends on the applied potential gradient and nature of the ion. It is expressed in m/sec. The ionic mobility of an ion with applied potential gradient at 1 V/m is called absolute ionic mobility. Its unit m 2 /V.sec. 1. Relationship between ionic mobility, ionic conductance & transport number: Ionic conductance is directly proportional to ionic mobility. λ 0 = 1 And ionic conductance of the ions is depends on the mobility or velocity of the ion. α and α 2 From equation (1) & (2)- λ 0 α ( + ) = k ( + ) where k is the proportionality constant = k ( + ) 3 = k. And = k. 4 Transport number of the ions at infinite dilution can be defined as- = = = Or = x λ 0 5 Similarly, = x λ Relationship between ionic conductance & ionic mobility: Consider one mole of A z B y electrolyte and placed between two electrodes separated by distance d cm. It is dissociated into x number of cations and y number of anions. A x B y x A z+ + ya z-. Where, z+ and z- are the charges on cation and anion respectively. The number of cations in solution = n + = x. N And the number of anions in solution = n - = y. N (N is Avogadro s number) 1 The fraction of the current carries by cations and anions are- 160

168 I + =, where e is charge on electron = 1 faraday. = = 2 But- N. e = F. I + = 3 Similarly, I - = 4 Therefore total current passed through the solution- I = I + + I -. I = + But overall solution is electrically neutral i.e. x. z + = y. z - Therefore, I = 5 If A is area of cross section of electrolytes, then volume of solution between two electrodes will be - V m = A x d 6 If the concentration of the electrolyte solution is c gm-equivalent per lit, then the volume of the solution that contain 1 gm-equivalent of the electrolyte is cm 3. One molecule of the electrolyte gives x number of cation having z + charge, then the total number of cations in the volume of solution containing one mole of the electrolyte is (x. z +. V) (Where, V is the volume containing one equivalent of electrolyte). V m = = 7 From equation (6) & (7)- A x d = Or = 8 But conductance of the solution is C - C = κ ( ) and λ = 1000 (molar conductance) Therefore, C = = 9 From equation (8) & (9) C = 10 According to Ohm s law - I = = E. C (where - C = ) From equation (10)- I =

169 Compared equation (5) & (11) - F = ( ) λ 12 Where, is the potential gradient that is operative when definite voltage is applied between two electrodes separated by the distance d cm. When = 1, then- F = λ For infinite dilute solution - F = λ 0 According to the Kohlrausch s law - λ 0 = F = = / F & = / F 13 But =. λ 0 & =. λ 0 14 Put equation (14) in (13) - =. λ 0 / F & =. λ 0 / F

170 4.2. Nuclear chemistry II Introduction: Atoms contains three subatomic particles namely electrons, protons and neutrons. The protons and neutrons are present in the nucleus and electrons are present in extra nuclear region of the atom (i.e. revolved around the nucleus). The ordinary chemistry of the elements is based on the electronic structure of it i.e. both physical and chemical properties of atoms, ions and molecules are related to the intermolecular forces which is derived from its electronic structure. The masses of atoms and molecules are due to its atomic nuclei. The major role of atomic nuclei is to keep the electrons in its positions. Chemical transformation involves the change in the valence electrons of the participating atoms without change in its atomic nuclei. In chemical transformation, the atoms retain their identities and rates are markly affected by the change in temperature. But in 20 th century another kind of the transformations are observed which involved change in the atomic nucleus is called as nuclear reactions. The energy evolved in the nuclear reactions is very very large as compared to chemical transformation. Such reactions are not affected by temperature. The radioactive nucleus (unstable nucleus) emits the radiations such as- α-, β-, and γ-radiations. In 1932, Chadwick discovered other subatomic particles in addition to the proton and electron is called as neutron. It is chargeless particle. Therefore, it is believed that nucleus contains two types of fundamental particles protons and neutrons. These particles are collectively called as nucleons. Classification on the basis of stability: A. Stable nuclides: These nuclei are permanently stable. In such nuclides, the proton and neutron content remains unchanged for ever and is not affected by the change in location or in number of electrons in their outer sphere. The nuclei can be change only by bombarding them with external radiations or particles with high energy or by nucleons capture. About 274 naturally occurring nuclides are stable. e.g. 1 H, 2 H, 16 O, 17 O, 19 F, 23 Na, 27 Al, 31 P, 35 Cl, 37 Cl, 63 Cu, 65 Cu, etc. Nuclei containing 2, 8, 20, 28, 50, 82, or 126 protons or neutrons are generally more stable than nuclei that do not possess these magic numbers. Atomic nuclei consisting of such a magic number of nucleons have a higher average binding energy per 163

171 nucleon than one would expect based upon predictions such as the semi-empirical mass formula and are hence more stable against nuclear decay. The stability of such nucleus are explain by shell model. B. Radioactive or unstable nuclides: These nuclei are internally unstable and undergo spontaneous change with time. New nuclei are formed by such changes which may be accompanied by rearrangement or loss of their some protons and or neutrons. They continuously emit the radiations of high energy. The emitted radiations are α-, β-, and γ- radiations. About 2000 nuclides are radioactive (natural and man-made). e.g. 32 P, 226 Ra, 55 Fe, 60m Co, etc. 164

172 Factors affecting stability of nucleus The stability of the nuclei are discussed in terms of following factors - 1) Odd-even combination of protons and neutrons. 2) Neutron to proton ratio of the nucleus, and 3) Binding energy and average binding energy. Even-odd nature of the number of protons and neutrons: The 274 stable nucleides are distributed according to the stability of the nuclei and odd-even combination of protons and neutrons as- Z N Z+N=A Total number of nucleides examples Even Even Even He, 24 Mg, 208 Pb Even Odd Odd O, 25 Mg, 57 Fe Odd Even Odd 50 7 Li, 19 F, 63 Cu Odd Odd Even 4 2 H, 6 Li, 10 B, 14 N only Some conclusions are drawn from the above table - i) The number of nucleides is maximum when both N and Z are even numbers suggesting a tendency to form P-P and N-N pairs for the nuclear stability accorded. The stability accorded to the nucleus on pairing of spins of protons and neutrons shows that there are strong interactions between the two protons and two neutrons which are formed a shell and shows a weak interaction between the other pairs. the earth crust about 85% is consist of even Z and even N nucleides and about 13% of odd Z and even N nuclides. ii) The number of stable nucleides which having either Z or N is odd is about one third of those having both even numbers. The number of stable nucleides of odd A is about same whether the odd number of protons (50) or of neutrons (55). This suggests that protons and neutrons behave similarly even though they having different charge value. iii) Only four stable isotopes are existing in nature with odd-odd combination of protons and neutrons. Each isotope contains only one proton and one neutron more than the quartet of two protons ant two neutrons. The extra proton and extra neutron are interacting with each other and provide the stability to these nuclei. 165

173 The tendency of proton to pair up with a proton and of a neutron with a neutron is explain by using following rules - For the elements between oxygen and chlorine, the stable nuclides are obtained by adding two neutrons one at a time in the nucleus which is followed by the addition of two protons again at a one time. The addition of two neutrons results the formation of three isotopes of elements of even Z as A, (A+1) and (A+2) but only one isotope of elements of odd Z. For progressive formation of stable nuclides from 16 O to 35 Cl, the horizontal arrow indicates the addition of a neutron giving an isotope and vertical arrow indicates the addition of proton giving a new element O O O 18 [ F] F [ F] Ne Ne Ne 22 [ Na ] Na [ Na ] Mg Mg Mg 27 Al Si Si Si P [ P ] 32 S S S [ S ] For such nuclei which have odd Z-value, it is observed that only one stable isotope is formed e.g. 19 F and 23 Na, etc. other isotopes are unstable, radioactive nuclides. The nuclides having even Z value, it exist in three stable isotopes forms. The same hold is true up to chlorine. Beyond chlorine, in case of nucleides with odd Z addition of two neutrons together results the formation of a pair of stable isotopes e.g. 35 Cl- 37 Cl, 39 K- 41 K, 63 Cu-6 5 Cu, 79 Br- 81 Br, 85 Rb- 87 Rb, 107 Ag- 109 Ag, etc. The middle isotopes as - 36 Cl, 40 K, 64 Cu, 80 Br, 86 Rb, 108 Ag, etc is invariably radioactive. Out of some twenty mono-isotopic elements, 19-elements (nuclei) have odd Z-value, only one named 35Cl 166

174 9 B has even Z, but it has odd number of neutrons. Addition of n horizontal and addition of p vertical [ ]* indicates formation of radioactive nuclei. Stability on the basis of neutron to proton (N/Z) ratio: All the nuclei except 1 H consist of protons and neutrons. Both are present in the nucleus for its stability. The protons and neutrons give rise to three types interactions; all except p-p interactions are of attractive type however the p-p interactions are partly attractive and partly repulsive. Therefore total number of protons and the neutrons in the nucleus decides overall attractive and repulsive interactions with in the nucleus and hence its stability. These stability of the nucleus is explain in term of neutron to proton ratio (N/Z) for a given Z. the stability of the nucleides can be considered by plotting the graph of number of neutrons against number of protons as - N/P>1.536 n N/P = 1.00 to (stability strip) N/P=1 (valid upto Z=20) Number of neutrons (N) p + B - electron emission X N/P<1 this graph is called as Segre chart Y p n + B + (positron emmision) Number of protons (Z) 1) The stable nucleides shows the ratio N/Z in them 1. The ratio is equal to one (N/Z) = 1 in all the light stable nucleides up to Z = 20. 2) The number of neutrons in their nucleus exceeds the number of protons which makes N/Z > 1. In case of stable isotopes of heavy elements such as 208 Pb or 209 Pb, the N/Z ratio is slightly greater than The reason for this is that with increase the atomic number, the repulsive forces increases rapidly and become greater than attractive forces. e. g. For heavy nuclei 208 Pb the repulsive force is ten times greater than that in 40 Ca. Therefore additional number of neutrons gives additional n-p and n-n attractive forces which overcome the excess repulsive force and provide the stability to nucleus. 167

175 3) Since many elements have more than one isotope and therefore the graph N against Z is not a straight line, it is strip. The strip becomes broader as increases the value of Z. all the nuclei in the strip are stable while those are lie outside the trip are unstable (radioactive). The nucleides of given Z lie above the strip contains more neutrons and undergoes emission of β - particles (electrons) for the stability. On the other hand, the nucleides of a given Z lie below the strip contains less number of neutrons than those required for the stability. Therefore, nucleides either emits positrons β + particles or capture extranuclear electron depending on their energy. This conversion will be continuous till the stable nucleus is formed. 4) The most of stable isotopes of any given elements are usually found near the center of the stability strip. Consider the nucleides with Z =11 (sodium), the only stable nucleide is 23 Na. replacing proton by neutron result in 23 Ne which is radioactive similarly when neutron is replaced by proton result 23 Mg which is also radioactive. Again keeping Z-constant and remove the neutron 22 Na and add the neutron gives 24 Na; both are radioactive. Binding Energy: Binding energy is another important characteristic property of each nuclide. It measures the stability of the nucleus and explains how long the nucleus is held together in the nucleus. The binding energy of a nucleus originates from the mass that is lost during the formation of the nucleus from constituents neutrons and protons and the remaining lost mass is converted to energy which can be explain by using Einstein theory. The relationship between mass and energy is E = mc 2 where c is velocity of light i.e. mass and energy are inter convertable to each other. These can be explaining as follows. Let us consider a nucleus A X Z with atomic mass m amu having Z - protons and (A - Z) neutrons. From the mass of protons and neutrons, the theoretical mass of A X Z nucleus is calculated as- = theoretical mass of A X Z = Z x m p + (A-Z) x m N 1 168

176 The difference between m and m is calculated as Δm = m is called as mass defect of the nucleus and which is possible for all nucleus. Δm = m = [Z x m p + (A-Z) x m N ] m 2 The mass defect Δm is the characteristic of the given nucleus which is converting to energy. Therefore according to the Einstein s principle- E = Δm c 2 erg. 3 = {[Z x m p + (A-Z) x m N ] m} x c 2 erg. Let us consider the reverse process, if one breaks the nucleus A X Z into Z-protons and (A - Z) neutrons; the same energy E has to be supplied to the nucleus. The supplied energy is called as binding energy. The binding energy is the energy which must be given to the nucleus to break it completely into its protons and neutrons. Total binding energy of the nucleus is the energy with which all the nucleons are hold together in the nucleus. Bonding energy is the total energy of the particles inside the nucleus and is made up by potential and kinetic energy. Binding energy = Potential energy + Kinetic energy Binding energy and potential energies are generally taken as positive even though they are negative quantities. Potential energy = Binding energy + Kinetic energy Or Total Potential energy = Σ Binding energy + Σ Kinetic energy The binding energy is expressed in ev, kev or MeV. Suppose one amu of mass is lost, the energy librated is calculated as follows- E = Δm c 2 = x x (3 x ) 2 erg. But 1eV = x erg. E (in ev) = = x 10 6 ev Also 1MeV = 10 6 ev, 169

177 E = MeV. Therefore one amu of mass is equivalent to MeV of energy. If mass defect is Δm then - E = x Δm MeV. 4 The magnitude of binding energy E can be calculated by using equation (4) from the known values of m H = amu and m N = amu and the actual value of m( A X Z ) from the table. It is observed that, the binding energy of a nucleus is directly proportional to its mass number. The heavy nucleus having higher binding energy and are expected to be more stable whereas light elements having low binding energy and are expected to be less stable. But actually it is observed that, the heavy elements like uranium, thorium etc are radioactive and are continuously transferred into other elements and the light elements such as nitrogen, oxygen, etc are stable. Therefore the stability of the nucleus can be explained by using new concept is called average binding energy. Average Binding energy: Average binding energy ( ) is defined as a ratio of binding energy (E) of a nucleus to its mass number (A). 5 It is an average amount of energy required to remove a nucleons from the nucleus and to take away it from the nucleus. It is then expected that if higher the average binding energy, more is the stability of the nucleus and vice-versa. To explain the stability of nucleus, plot a graph of average binding energy against A of the nucleus. 170

178 10 light elements medium maximum stability heavy nucleides unstable heavy nucleides radioactive nuclei E f d a g c b e Fe Co Ni maximum E Zr Sn Sb Bi stable heavy element U Th mass number a = He, b = Li, c = B, d = C, e = N, f = O, g = O The above fig of average binding energy against mass number shows following features- 1) Light Nucleides : [A<30] The nuclei which A can be expressed in multiple of four e.g. 4 He, 12 C, 16 O, 20 Ne, 28 Si have maximum stability except 8 B. It does not have a ground state and get cleaved into two alpha particles. Also the nucleides having even A are more stable than the nucleides having odd A. the high stability of helium indicates, the sun s radiant energy arises due to the formation of helium nuclei by nuclear fusion of hydrogen and its isotopes. 2) Medium nucleides: [30<A<90] It has mean binding energy around 8.3 to 8.7. the average binding energy increases along with atomic mass number (A) and it become maximum around A=60 (nickel and iron) and then slowly decreases. The maximum nuclear stability of iron makes its occurrence in the nature and abundant. 3) Heavy nucleides: [A>90] For nucleides A>90, the mean binding energy decreases continuously from the maximum 8.7 to 7.7 for A=210. The most stable heaviest nucleus is 209 Bi. Beyond this nucleides are unstable and radioactive, mainly emits alpha particles. e.g. 238 U has average binding energy 7.3 MeV therefore it can be fission (split) into two medium nucleides because of its stability. Packing fraction: 171

179 It is a new term introduced by F. W. Aston in it is defined by using following equation - Packing fraction = Atomic mass - mass number mass number x 10,000 Packing fraction decreases rapidly with A, passes through minimum and then slowly increases. Negative packing fraction means that atomic mass is less than the mass number and conversion of mass into energy. The nucleus having negative packing fraction is more stable and that of have positive packing fraction are unstable and radioactive. The graph of packing fraction against mass number is exactly opposite to the graph average binding energy against mass number and is shown below- +ve light element mediu maximum C Z S F S heavy B stable heavy unstable heavy nucleides U Th packing 0 fraction -ve packing fraction negagative having maximum stability packing fraction positive unstable nuclei radioactive mass 172

180 Radioactivity: The radioactive elements spontaneously emit the radiations of high energy and it gets transferred to other elements which may or may not be radioactive. The original radioactive element is called as parent and the new element that is formed called as daughter. The elements like uranium, thorium, radium, etc are occurs in nature and disintegrates spontaneously with emission of nuclear particles and/or an electromagnetic radiation is called as natural radioactivity. Some elements after the uranium are not occurs in the nature (are called as transuranic compounds) because they are short lived, therefore its radioactive isotopes are prepared in laboratory. Nature of radioactive radiations: Ernest Rutherford shows that radiations emitted by the radioactive element are of three types according to the mass and charge present on it. He performed an experiment by taking a piece of radioactive element and placed in a cavity of lead metal. Rays emitted from the substance are passed through the slit and then between the two metallic plates connected to the two opposite pole of the battery. When rays passed through the two charged plates, it divided themselves into three groups. A similar situation is observed when magnetic field is applied. i) The rays those deflected towards the negative charged plates are called as α-particles which possess positive charge. ii) The rays those deflected towards the positive charged plates are called as β-particles which possess negative charge. iii) Those which are undeflected by the electric and magnetic field are called as γ-rays which are electromagnetic radiations. 173

181 alphaparticles - gamma rays beta-particles + charged plates photographic plate slits + radioactive element lead block α-rays/α-decay: It consists of α-particles which are positively charged nuclei of helium 4 He. During emission of α-particle, mass and atomic number of the parent nuclei decreases by four and two units respectively. It carries a charge equal to 2 x x e.s.u. which is the same as the charge of helium nucleus. The e/m ratio of the α-particle has been found to be x 10 4 coulombs per gram. e.g. A Z A-4 4 X Y + He or Z Ra 86 Rn + He or 2 alpha particle alpha particle Z-2 Z-1 A Z X parent A-4 Y Z-2 daughter Properties: The α-particles having velocity 1/10 th of the velocity of light. Actually velocity of these particles will depend on the nature of the radioactive elements from which they are emitted. They having very small penetrating power i.e. about 1/100 th of that of β-particles. They are having large ionizing power (is about 100 times as compaired to the β-particles). The α-particles are ionizing the gas through which they are passed due to collision of it with gas molecules or atoms. They mildly affect the photographic plate and produces fluorescence when they are fall on the ZnS plate, diamond. They produce dangerous biological effects or changes in environment. α-particles emitted by the Radium have a range of 3.5 cm in air at NTP. After traveling this distance, they lose their ionizing power and power of exciting fluorescence. Geiger 174

182 in 1910 shows that the range (R) of α-particles depends on the velocity (v) with which they emerged from the source. R α v 2 or R = a v 2 where, a is a constant. β-rays/β-decay: They consist of negatively charged particles known as β-particles (β - ) which are the electrons having same e/m value. In the nucleus, during conversion of neutron into proton, electron is ejected out. Along with a electrons, a particles called as antineutrino which having negligible mass but having spin is also emitted. n p + B + v A it is represented as- X Y + B + v Z A Z+1 e.g A Z X Ra Ac + B + v B- Z+1 A Z+1Y parent daughter During emission of β - -particles, daughter nuclei will shift right in periodic table having same mass A. Many artificially synthesized radioactive isotopes are emits positrons which are similar to electrons in all respect except charge. They carry positive charge with same magnitude as the negative charge present on an electron. During this emission positron and neutrino, proton is converted to neutron in the nucleus. p n + B + + v A A it is represented as- X Y + B + + v Z Z-1 e.g Z-1 A Z-1Y + P Si + B + v B + A Z X parent daughter The atomic number of the parent is greater than by one unit than the daughter, both having same mass number. The positron emission is possible when the radioactive nucleide contains more 175

183 number of protons than those required for its stability. Also the energy of the parent nuclei should be greater than the daughter by at least 1.02 MeV. If this is not a case, then the parent nuclei absorb one of the extranuclears usually from K-shell. This phenomenon is called as K- capture which is occurred with emission of neutrino as- p + e - n + v A it is represented as- X + e - Y + v Z A Z-1 55 e.g. Fe + e Mn Ba + e v Cs v Z-1 A Z X parent A Z-1Y K-capture daughter Properties: The β-particles are moves with high velocity and is ranges between 33% to 99% of the velocity of light. Because of this variations of the velocity β-particles are not homogeneous. Its energy ranges from the MeV. The ionizing power of the β-particles is 1/100 th of that of α-particles. They having 100 times more penetrating power and effect on the photographic plate are more than the α-particles. They show very low effect on ZnS plate. They are more dangerous biologically than the α-particles. γ-rays: These radiations are very similar to electromagnetic radiations possessing very short wavelength. The daughter nuclei formed due to α- or β-emission are exist in excited state. It emits excess energy in the form of γ-rays photon and returns to the ground state. In such case, the atomic number and mass number of the daughter nuclei remains same as the parent. 176

184 A Z X B- Z+ A Z+ paren daughte * Y (excited state) A-4 Y* Z-2 Z-1 A Z X Y- emission Y - emission Z-2 A z+1 Y daughter ground state A-4 Y Z He e.g. Ra Rn* Rn Y 60m 60 Co Co + Y Properties: They are electrically neutral particles and having very short wave length (10 ppm). They moves same velocity as that of light and having energy range is MeV. It has maximum penetrating power but having least ionization power. They show small effect on the photographic plate and practically no effect on the ZnS plate. They diffracted by the crystal like X-rays and are biologically more dangerous as compaired to α-rays and β-rays. Mechanism of radioactive decay: During emission of α-particles from the nucleus, a bundle of four nucleons (two protons and two neutrons) are ejected from the nucleus and forming more stable other nucleus. The α- emission is limited for the nucleides with Z > 82, though there are few α-emitters are present in lanthanide group. The emission of γ rays causes rearrangement of the nucleons with release of the energy as a electromagnetic radiations. The emission of β +, β - and electron capture are difficult to realized as- B+ emission B p n e + +1 (positron) emission n p + e -1 (electron) 1 electron capture p + e n 1-1 The n/p ratio is very high then a neutron is converted to a proton and β - particle is emitted. In case of nucleides which having very low n/p ratio, either a proton is converted into neutron followed by β + emission or electron capture is occurred

185 Units of Radioactivity: The SI unit of radioactivity is Becquerel (Bq). It is defined as- one disintegration per second. Curie (C i ) is earlier used as a unit for radioactivity. The activity of one gram of Ra-226 is considered as the unit of radioactivity called as Curie (C i ). Since one gram of Ra-226 contains x /226 atoms having decay constant λ = 1.38 x sec -1 (t 1/2 = 1600 years) i.e x atoms disintegrates or decay per second. The disintegration rate of 1 gm of Ra-226 is- = [1.38 x x x ] / 226 = 3.7 x disintegration per second. 1 curie (Ci) = 3.7 x disintegration per second. 1 curie (Ci) = 3.7 x Becquerel (Bq). The strength in curies gives information about the absolute number of atoms of parent element decaying per second which will be fraction of disintegration per second and is depends on the efficiency of detector and the geometry used. The curie is large unit so smaller units are - 1 curie (C i ) = 10 3 mc i =10 6 μc i. Another unit is also used for radioactivity measurement called as Rutherford and is defined asthe amount of radioactive substance which undergoes 10 6 disintegration per second. The units of radiation doses: i) Curie: It is the amount of radioactive material decaying at same rate as 1 gm of radium-226 (3.7 x disintegration per second). ii) Rad: It is a dosage of radiation that can be deposited 1 x joule of energy per kilogram of mater. iii) Rem: It is a unit related to rad but taking in account the differing effects of various types of radiations of same energy on biological matter. This relationship is though a quality factor. The quality factor is one for X-rays, γ-rays and β-particles. It is five for protons and slow neutrons and 10 for the α-particles i.e. 1 rad = 1 rem for X-rays, 1 rad = 10 rem for α-particles. Unit of exposure: The interaction of nuclear radiation with matter leads to ionization; in fact, nuclear radiation (as well as uv and x-ray photons) is sometimes also referred to as ionizing radiation. Because 178

186 energies of only tens of electron volts are sufficient to ionize atoms,, β, and γ particles, with energies of MeV, are each able to ionize many thousands of atoms before losing their energy. It is this ionization that makes nuclear radiation dangerous to living organisms. Here we introduce various units to measure exposure, and discuss those doses and the relative biological effects of radiation. A unit of exposure, the roentgen (R), was first introduced to define the extent of ionization produced by x-rays, but is also used for gamma radiation. Defined as the total number of ion pairs produced in a volume of 1 cm 3 of dry air under standard conditions (0 C and 1 atmosphere of pressure), one roentgen is given by 1 R = 2.58 x 10-4 C/kg air. This is a unit of exposure, giving the ionization level in air, but it does not give any information about absorption of radiation by living tissue or its effects on that tissue. Absorbed dose of radiation: A measure of the absorbed dose of radiation, the absorbed energy per unit mass, is the gray (Gy), where 1 Gy = 1 J/kg. An older unit, still commonly used today, is the rad, where 1 rad = 0.01 Gy. For a given exposure, the absorbed dose will vary greatly depending on the absorption characteristics of the material and the type of radiation. Furthermore, the amount of damage produced by a constant absorbed dose will also vary depending on the type of radiation. To account for these, another type of quantity is introduced, the biological dose equivalent, measured in sieverts (Sv), and given by Biological dose equivalent (in Sv) = absorbed dose (in Gy) x RBE. Where RBE is a dimensionless weighting factor, named for relative biological effectiveness that depends on the type of radiation. Another unit commonly used for biological dose equivalent is the rem, where 1 rem = 0.01 Sv (note that the rem is commonly used when the absorbed dose is measured in rads, so that the biological dose equivalent (in rem) = absorbed dose (in rad) x RBE). Equivalent dose is a dose quantity used in radiological protection to represent the stochastic health effects (probability of cancer induction and genetic damage) of low levels of ionizing radiation on the human body. It is based on the physical quantity absorbed dose, but takes into account the biological effectiveness of the radiation, which is dependent on the radiation type and energy. Equivalent dose H T is calculated using the mean absorbed dose deposited in body tissue or organ T, multiplied by the radiation weighting factor W R which is dependent on the type and energy of the radiation R. The radiation weighting factor represents the relative biological 179

187 effectiveness of the radiation and modifies the absorbed dose to take account of the different biological effects of various types of radiation. Where, H T is the equivalent dose absorbed by tissue T, D T,R is the absorbed dose in tissue T by radiation type R, W R is the radiation weighting factor defined by regulation. The SI unit of measure for equivalent dose is the sievert, defined as one Joule per kg. In the United States the roentgen equivalent man (rem), equal to 0.01 sievert. Thus for example, an absorbed dose of 1 Gy by alpha particles will lead to an equivalent dose of 20 Sv, and an equivalent dose of radiation is estimated to have the same biological effect as an equal amount of absorbed dose of gamma rays, which is given a weighting factor of 1. To obtain the equivalent dose for a mix of radiation types and energies, a sum is taken over all types of radiation energy doses. External dose due to natural sources: When a beam of radiation falls on the surface of matter, some amount of energy is absorbed in the target which leads to ionization and excitation of some of its atoms and molecules. In the case of living matter, these processes initiate a complex chain of radiochemical and biochemical events in the cells which may ultimately lead to biological damage. Particularly vulnerable is DNA (genetic material) in the nucleus of the cell. The cell, however, has a tremendous capacity to repair the damage. Biological effects are broadly classified into two types: stochastic (those without a threshold, i.e., the probability of an effect depend on the dose) and deterministic, earlier called non-stochastic (those with a threshold, i.e., no effect at dose below the threshold value). Radiation can result in either cell death or a damaged cell which may be partially or fully corrected by repair processes. In case of a partially repaired cell, it may lead on subsequent multiplication to the manifestation of leukaemia or other types of cancers. Man is being continuously exposed to radiations, both ionizing as well as non-ionizing, right from his origin. The major sources of exposure are of two types: natural and manmade. Natural radiations are universal in the sense that the entire population, in all parts of the world, is 180

188 exposed to them to a larger or smaller extent throughout life, while the artificial exposure affects only a small part of the population only for apart of their life. Natural Sources: They are of three types: atmospheric, terrestrial and internal emitters in the body. Atmospheric Exposures: The major radiation exposure comes from the cosmic rays and their interaction products. Cosmic radiations are of primary as well as secondary origin. The primary cosmic rays originate in outer space (galactic) and have high energy protons as their major component along with some alpha particles, other atomic nuclei, and high energy electrons and photons. The intensity of galactic radiations is reduced very much during their journey to earth, and they, therefore, contribute very little to human exposure. Secondary cosmic rays are produced by the interactions of the primary cosmic rays with the atomic nuclei in the earth's atmosphere. These radiations are highly penetrating and are responsible for a substantial part of the natural background radiations on earth. The intensity of these radiations decreases with decreasing altitudes. Thus the dose rate at sea level will be much less than that on the top of a mountain. The average dose rate at sea level is estimated to be about 0.3 msv per year and becomes approximately double with every 1500 metres increase in altitude for the first few kilometres, beyond which it increases more rapidly with altitude. Similarly, the intensity at the poles will be greater than at the equator, because the stronger earth's magnetic field near the equator prevents. In addition to these radiations, interaction of cosmic neutrons with stable elements in the atmosphere produces radioactive elements, which also contribute to man's radioactive environment. The major contributors are 14 C (carbon), 3 H (tritium) and 81 Kr (krypton), mainly as internal sources. Terrestrial Radiations: They arise in the earth's crust and include the naturally occurring radioisotopes of the heavy elements, which are deposited in the earth. Major contribution comes from the uranium, thorium and actinium deposits as well as radioactive potassium (40K), which occurs as a contaminant of natural potassium ( 39 K). The intensity of terrestrial background radiations depends on the geographical location, e.g., vicinity to the mines, and also the composition of the soil, etc. Igneous rocks have higher intrinsic radioactivity than sedimentary rocks. For example, some parts of coastal Kerala and Tamil Nadu in South India have radioactivity levels 5-10 times higher than in the other parts of the country. This is due to the presence of thorium deposits in the sand containing the monazite mineral. 181

189 Based on its survey of terrestrial radiations in our country, Bhabha Atomic Research Centre (BARC), India has found that the highest levels of terrestrial radiations (leaving the monazite areas) were recorded in Andhra Pradesh and Sikkim, and the lowest in Andaman-Nicobar islands and Lakshadweep. The average dose for the entire country from this source comes out to 0.44 msv/y. Internal Emitters: Individual exposures also depend on the intake of radioactive elements through inhalation and ingestion. A significant dose is received from 40 K, a naturally occurring radioactive isotope of potassium, which emits both beta and gamma radiations, and contributes about 0.15 msv/y. The other isotopes, 14 C and H, both beta emitters produced in the atmosphere, enter the body as constituents of organic materials, 14 C \SIC giving an annual dose of 0.01 msv and 3 H about 0.01 msv. Man-made Sources: During the second half of this century, increase in the use of radiations and radioactivity by man in the medical and industrial fields as well as for power production, has enhanced the risk of exposure of human populations. Since the presence of low levels of radioactivity in the atmosphere is not easily detected, it may take years before any untoward effect is manifested. So, radiation pollution from nuclear tests and reactor accidents has become a subject of great concern among the scientists and common man alike, more than that of any other industrial pollutants in the world. Therefore, the health impacts of nuclear radiations have been more thoroughly studied as compared to any other potentially harmful occupational environmental agent. Artificial radiations in the background are determined by the type of human activity, e.g. reactor siting, industry, hospitals, nuclear testing, etc. Medical Exposures: Artificial radiation sources are mostly used for medical exposures, of which diagnostic radiations contribute about 80% of the population exposure. The doses received by the patients are extremely variable, ranging from very small, as in diagnostic examinations, to very high in therapeutic exposures. E.g. X-ray, fluoroscopy and Computed Tomography (CT), radioactive medicine for diagnostic, etc. Other sources for exposures are Nuclear Explosions, Nuclear Power Production, Radioactive Waste, consumer products such as luminous dials containing radium or tritium, colour television sets, static eliminators, smoke detectors, ceramics (dental porcelain) and tobacco products. 182

190 4.3. Liquid State Surface tension Surface tension is a fundamental property by which the gas liquid interfaces are characterized. The zone between a gaseous phase and a liquid phase looks like a surface of zero thickness. The surface acts like a membrane under tension. It is well surface phenomena. Let us consider a liquid in contact with its vapor. A molecule in the bulk liquid is subjected to attractive forces from all directions by the surrounding molecules. It is practically in a uniform field of force. But for the molecule at the surface of the liquid, the net attraction towards the bulk of the liquid is much greater than the attraction towards the vapor phase, because the molecules in the vapor phase are more widely dispersed. This indicates that the molecules at the surface are pulled inwards. This causes the 183

191 liquid surfaces to contract to minimum areas, which should be compatible with the total mass of the liquid. The droplets of liquids or gas bubbles assume spherical shape, because for a given volume, the sphere has the least surface area. If the area of the surface is to be extended, one has to bring more molecules from the bulk of the liquid to its surface. This requires expenditure of some energy because work has to be done in bringing the molecules from the bulk against the inward attractive forces. The amount of work done in increasing the area by unity is known as the surface energy. If the molecules of a liquid exert large force of attraction, the inward pull will be large. Therefore, the amount of work done will be large. Surface energy is the amount of work done per unit area extended. Its unit is J/m 2 (which is equivalent to N/m). For example, the amount of work required to create 1 m 2 surface is about 72.8 x 10-3 J for water. Surface tension is defined as the force at right angle to any line of unit length in the surface. Therefore, surface tension = force/distance. It is expressed in N/m. Therefore, it is apparent that the units of surface energy and surface tension are identical. Surface energy can be determined by measuring the surface tension. = When the temperature of liquid increases, inter molecular forces of attraction decreases which result decrease in the inward pull functioning. Hence, surface tension decreases with increase in temperature. Theoretically, the value of surface tension should become zero at the critical temperature, since at this temperature; the surface of separation between a liquid and its vapor disappears. However, it has been observed that the meniscus disappears a few degrees below the critical temperature for some liquids. Surface tension also responsible for rise and fall of liquids in the capillary tube. The greater surface tension of the liquid, higher is its capillary rise. Hence capillary rise is used to measure the surface tension of liquid. E.g. Water has natural tendency to be attracted to the surface of glass. The attraction between water and glass (adhesive force) causes water to spread into a concave film on the surface of the glass, thus increase in the surface area of water. In a capillary tube in order to reduce its surface area, water rises in the tube. In case of mercury, molecules are strongly attracted by each other (cohesive force) than the glass (adhesive force), therefore 184

192 mercury does not spread on the glass, and it has little contact with glass surface, consequently mercury level in the capillary falls down. Surface tension of liquid was changes when other substances are dissolved in it. E.g. Soaps and detergents lower the surface tension of water which improves the spreading property of these substances. Even in the preparations of tooth pastes, mouth washes, toilet creams and medical emulsions, detergents are added to improve spreading property. Surface tension (in mn/m) of some liquids at 293 K is Acetic acid 27.4, acetone 23.3, aniline 42.9, benzene 28.9, chloroform 27.2, ethyl acetate 23.8, ethanol 22.3, methanol 22.6, water 72.8, mercury 476.0, etc. Method of determination of surface tension: The surface tension of liquid can be experimentally measured by several methods. The dropweight method, du Noüy ring method, Wilhelmy plate method and the maximum bubble pressure method, etc. Parachor method: Sugden (1924) proposed the following equation to calculate surface tension from the physical properties of the compound. Where, and are the densities of the liquid and vapor, respectively, and M is the molecular weight. is known as parachor, which means comparative volume. If we neglect the density of vapor in comparison with the density of the liquid, then Where, is the molar volume of the liquid. A comparison of the parachors of different liquids is equivalent to the comparison of their molar volumes under the condition of equal surface tension. is a weak function of temperature for a variety of liquids over wide ranges of temperature, and generally assumed to be a constant. Additive procedures exist for calculating. The above equation suggests that surface tension is very sensitive to the value of parachor and the liquid density. Estimation of surface tension using the parachor data usually gives good results. Its simplicity makes it a popular method for calculating surface tension. Escobedo and Mansoori (1996) have 185

193 suggested that is a function of temperature. They proposed the following temperaturedependence for. Where, is independent of temperature, but depends on the physical properties of the compound, such as its critical temperature, pressure, normal boiling point and molar refraction. Drop-weight method: The stalagmometric method is one of the most common methods used for the surface tension determination. In this method, a drop is allowed to form slowly at the end of a tube having a fine capillary inside it. Then it is slowly released and collected in a container. Several drops (e.g., 100 drops, at the rate of one drop in about 200 s) are collected in the same manner and the weight of the liquid is measured. From this weight, the average weight of a drop is calculated. The classical instrument for carrying out this measurement in the laboratory is Stalagmometer. Now days, computer-controlled instruments can form precise drops. The principle behind the drop-weight method is as follows. As the size of the drop at the tip of the tube grows, its weight goes on increasing. It remains attached to the tube due to surface tension, which acts around the circumference of the tube in the upward direction. When the downward force due to gravity acting on the drop becomes slightly greater than the surface tension force, the drop detaches from the tube. Therefore, Upward force =.. 1 Downward force = mg 2 Where, is the outer radius of the tip of the tube, m is the average weight of a drop. At the point of detachment, = mg. 3 The equation (3) is known as Tate s law. The use of this equation requires the value of ro. To avoid this, a relative method is usually used. A liquid whose surface tension is known is used as a reference liquid. Highly-purified water or an ultrapure organic liquid may be used for this purpose. The surface tension is calculated from the following equation... 4 Where, liquid is ref is the surface tension of the reference liquid, and the weight of a drop of this. The equation (4) does not gives good result, therefore it can be modified. 186

194 .. 5 When equation (3) is used to measure surface tension, corrections need to be applied because only a portion of the drop (the larger portion) falls from the tube. A significant amount of liquid (up to 40%) may remain attached to the tip of the tube. A correction factor,, known as Harkins- Brown factor, is used to correct the surface tension obtained from equation (3).. 6 Where, is a function of (V = volume of the drop), which has been verified experimentally using different liquids and tips of different radii. The radius of the tip should be chosen such that is least sensitive on the variation of. The correction factor can be quite large. Since the value of V can differ from liquid to liquid, may differ from one liquid to another, even when the same tip is used. Therefore, the ratio of correction factors in the relative method may not be unity. The following precautions should be taken during the experiment 1. The liquid should either completely wet the tip or do not wet it at all. In the latter case, the internal radius of the tip should be used as. 2. The tip must be very clean. The presence of a very small amount surface active substance can cause significant error in the measurement. Applications of dynamic surface tension: 1. Flow in capillaries and porous media is affected by DST. This finds importance in enhanced oil recovery where aqueous foams are often used to increase the sweepefficiency in carbon dioxide flooding. 2. In bioprocessing systems, DST affects the rate of water-oxygenation by influencing the mass transfer coefficient. 3. DST is also important in metal and textile processing, pulp and paper production, and pharmaceutical formulations. 4. An important application of dynamic surface tension is for lung surfactants, where the dynamic tension under constant or pulsating area conditions controls the health and stability of the alveoli. 187

195 5. In the formulation of pesticides, if the aqueous spray has a low DST, it can be dispersed into smaller droplets, which will spread more easily on the leaves. For these reasons, surfactants are used as pesticide spraying aids known as adjuvants Viscosity: The word "viscosity" derives from the Latin word "viscum alba" for mistletoe. A viscous glue called birdlime was made from mistletoe berries and used for lime-twigs to catch birds. The behavior of a fluid in flow is very much related to two intrinsic properties of the fluid: density and viscosity. Viscosity implies resistance to flow. It is a measure of the resistance of a fluid which is being deformed by either shear stress or tensile stress. In everyday terms (and for fluids only), viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity. Put simply, the less viscous the fluid is, the greater its ease of movement (fluidity). Viscosity describes a fluid's internal resistance to flow and may be thought of as a measure of fluid friction. All real fluids (except super fluids) have some resistance to stress and therefore are viscous, but a fluid which has no resistance to shear stress is known as an ideal fluid or inviscid fluid. Consider the flow of liquid through a narrow pipe. All parts of the liquid do not flow with the same velocity. A thin layer, immediately in contact with the wall of tube, is almost stationary. Each succeeding thin layer of the liquid moves with gradually increasing velocity which become maximum as the centre of the tube is approached. The resistance that one part of a liquid flowing with a certain velocity offers to another part of the liquid flowing with a different velocity is 188

196 known as viscosity. It may be defined as the force of friction between two layers of liquid moving past one another with different velocities. Consider a cylindrical liquid layer of area A cm 2 which moves over another similar layer at a distance of s cm with velocity difference of cm/sec. The tangential force of friction (F) required maintaining a constant velocity difference is given as Or. 1 Where, is a constant at a given temperature and is known as coefficient of viscosity, which depends upon the nature of the liquid. If A = 1 cm 2 and = 1 cm/sec and s = 1 cm, then Hence, coefficient of viscosity of a liquid may be defined as the force in dynes. sec/cm 2 required to maintaining a difference of velocity of 1 cm/sec between two parallel layers of liquid held at a distance of 1 cm from one another. The reciprocal of coefficient of viscosity of a liquid is called as fluidity ( ) which is depending on the convention used, measured in reciprocal poise (cm s g 1 ), sometimes called the rhe.. 2 Units of viscosity: The equation of coefficient of viscosity is When, F represent in dynes, s in cm, A in cm 2 and is in cm/sec, then the units of are dynes. sec/cm 2. For the simplicity, this unit of viscosity is called as poise. Still the more convenient units of viscosity are centipoises, and millipoise. The SI unit of viscosity is kg/m.sec. We let be the viscosity of the pure solvent and be the viscosity of a solution using that solvent. Several methods exist for characterizing the solution viscosity, or more specifically, the capacity of the solute to increase the viscosity of the solution. That capacity is quantified by using one of several different measures of solution viscosity. The most common solution viscosity terms are: 1. Relative viscosity: 2. Specific viscosity: = 189

197 3. Inherent viscosity: 4. Intrinsic viscosity: [ ] = In these equations, is solution viscosity, is viscosity of the pure solvent, and c is concentration. Relative viscosity is self-explanatory. Specific viscosity expresses the incremental viscosity due to the presence of the polymer in the solution. The remaining form for the viscosity is the inherent viscosity. Like, ln is zero for pure solvent and increases with increasing concentration, thus ln also expresses the incremental viscosity due to the presence of the polymer in the solution. Determination of viscosity: There are number of methods for measuring the viscosity of liquids. Poiseuille s equation (following equation) is the basis of most of the methods employed for the determination of coefficient of viscosity, i.e.,. 1 Where, V is the volume in cm 3 of the liquid flowing in t second through a narrow tube of radius r cm and length cm under hydrostatic pressure of P dyne.sec/cm 2 and is the coefficient of viscosity in poise. The hydrostatic pressure (P) of a liquid column is given by 2 Where, h is the height of the column and d is the density of the liquid. Put the equation (2) in equation (1), we have.. 3 Ostwald viscometer method: It is not necessary to find the all factors on right hand side of equation (3), but the usual procedure is to determine the viscosity of a liquid with reference to that of water, whose viscosity has been measured quite accurately. This value of viscosity of water is termed as relative viscosity. The relative viscosity of ordinary liquids is commonly determined with the help of Ostwald viscometer. It consist of a special U-shaped tube with bulbs in each limb. There are marking in one of the limb. All we do to measure the relative viscosity is to measure the times of flow for equal volumes of water and the liquid under examination through the same capillary. 190

198 If and are the times of flow of same volume of water and liquid, respectively and and are their respective coefficients of viscosity, then The value of h is the same in both the cases, as equal to volumes of both liquids are taken and they stand at same height, then - Or 4 The density of water can be separately determined by means of a pyknometer. Adequate precaution must be taken to maintain constant temperature and the tube must be thoroughly cleaned before use. 191

199 Liquid crystal: Introduction: Liquid crystals (LCs) are matter in a state that has properties between those of conventional liquid crystal and solid crystal. The liquid crystal may be flow like liquid, but its molecules may be oriented in a crystal like way. There are many different types of liquid-crystal phases, which can be distinguish by their different optical properties. Liquid crystal materials may not always be liquid crystal phase (just as water may turn into ice or steam). The liquid crystals can be divided into thermotropic, lyotropic and metallotropic phases. Thermotropic and lyotropic liquid crystals consist of organic molecules. Thermotropic liquid crystals exhibit a phase transition into the liquid crystal phase as temperature changed while lyotropic exhibit phase transitions as a function of both temperature and concentration of the liquid crystal molecules in a solvent (typically water). Metallotropic liquid crystals are composed of both organic and inorganic molecules; their liquid crystal transition depends not only on temperature and concentration, but also on the inorganic-organic composition ratio. Liquid crystals can be found both in the natural world and in technological applications. E.g. Lyotropic liquid crystalline phases are abundant in living systems. Many proteins and cell membranes are liquid crystals. Other examples are solution of soap and detergent, etc. History: In 1888, Austrian botanical physiologist Friedrich Reinitzer working at the Karl- Ferdinands University, examined the physic-chemical properties of various derivatives of cholesterol which now belong to the class of materials known as cholesterol liquid crystals. He 192

200 perceived that color changes in a derivative of cholesteryl benzoate were not the most peculiar feature. He found that cholesteryl benzoate does not melt in a same manner as other compounds, but has two melting points. At C, it melts into a cloudy liquid, and at C, it melt again and cloudy liquid become clear. This phenomenon is reversible. These two forms of cholesteryl benzoate (turbid and liquid form) shows different ability for the rotation of plane polarized light. This work was further extended by Lehmann and Vorlander. They have synthesized most of the liquid crystals which are not popular into the scientist at that time. George Gray and his group (England) synthesized many new materials that exhibited the liquid crystalline state and developed a better understanding for the design of such molecules. Liquid crystal materials become a topic of research into the development of flat panel electrical displays beginning in 1962 in RCA laboratories. When physical chemist Richard William applied an electric field to a thin layer of a nematic liquid crystal at C, he observed the formation of a regular pattern that he called domains. This research carried forward by his colleague George Heilmeier on liquid crystal based flat panel display to replace the cathode ray vacuum tube used in televisions. They discovered para-azoxyanisole which works above C which is impractical. In 166, Joel E Goldmacher and Joseph A Castellona, research chemist in Heilmeier group discovered that mixtures made exclusively of nematic compounds that differed only in number of carbons in the terminal side chain could yield room temperature nematic liquid crystals. A ternary mixture of Schiff base compounds resulted in material that had a nematic range C. This is used to made first liquid crystal display. This team then prepared numerous mixtures of nematic compounds many of which had lower melting points. Classification and structure of thermotropic liquid crystal: The various liquid crystal phases (called mesophases) can be the type of ordering. Most thermotropic liquid crystals will have an isotropic phase at high temperature i.e. heating will eventually drive them into a conventional liquid phase characterized by random and isotropic molecular ordering, and fluid-like flow behavior. A. Thermotropic liquid crystals: Thermotropic phases are those that occur in a certain temperature range. If the temperature rising is too high, thermal motion will destroy the delicate 193

201 cooperative ordering of the liquid crystal phase, pushing the material into a conventional isotropic liquid phase. In contrast to the high temperature, at too low T, most liquid crystal materials will form a typical crystal. a) Nematic phase: One of the most common liquid crystal phase is the nematic, where the molecules have no positional order (free to move in space), but they have long range orientational order. Therefore, the molecules flow just like in a liquid, but they all point in the same direction. Most nematics are uniaxial. Some liquid crystals are biaxial nematics, meaning that in addition to orienting their long axis, they also orient along a secondary axis. b) Smectic phases: The smectic phases, which are found at lower temperature, form welldefined layers that can slide over one another in a manner similar to that of soap. The smectics are thus positionally ordered along one direct ion in the smectic A phase, the molecules are oriented along the layer normal, while in the smectic C phase they are tilted away from the layer normal. These phases are liquid-like within the layers. c) Chiral phases: The chiral nematic phase exhibits chirality. This phase is often called the cholesteric phase because it was first observed for cholesterol derivatives. This phase exhibits a twisting of the molecules perpendicular to the director, with the molecular axis parallel to the director. In the smectic C phase, the molecules have positional ordering in a layered structure, with the molecules tilted by a finite angle with respect to the layer normal. The chiral pitch, p, refers to the distance over which the liquid crystal molecules undergo a full 360 twist but, the structure of the chiral phase repeats itself every half-pitch, since in this phase directors at 0 and 180 are equivalent. 194

202 B. Lyotropic liquid crystals: A lyotropic liquid crystal consists of two or more components that exhibit liquid-crystalline properties in certain concentration ranges. In the lyotropic phases, solvents molecules fill the space around the compounds to provide fluidity to the system. In contrast to thermotropic liquid crystals, these lyotropics have another degree of freedom of concentration that enables them to induce a variety of different phases. The lyotropic liquid crystals are composed of cubic, hexagonal, lamellar, reverse hexagonal phase, etc a) Hexagonal phase: A hexagonal phase of lyotropic liquid crystal is formed by some amphiphilic molecules when they are mixed with water or another polar solvent. In this phase the amphiphile molecules are aggregated into cylindrical structures of indefinite length and these cylindrical aggregates are disposed on a hexagonal lattice, giving the phase long-range orientational order. b) Micellar cubic phase: A micellar cubic phase is a lyotropic liquid crystal phase formed when the concentration of micelles dispersed in a solvent is sufficiently high that they are forced to pack into a structure having long-ranged positional order. 195

203 c) Liquid crystalline phases and composition/temperature: The simplest crystalline phase that is formed by spherical micelles is the micellar cubic, denoted by the symbol I 1. This is a highly viscous, optically isotropic phase in which the micelles are arranges on a cubic lattice. At higher amphiphile concentrations, the micellar cubic phase is converted to hexagonal phase, denoted by symbol H I. At more higher concentrations, the lamellar phase is formed (L α ). This phase consists of amphiphilic molecules arranged in bilayer sheers separated by layers of water. For most amphiphiles that consist of a single hydrocarbon chain, one or more phases are formed at intermediate phase between the hexagonal phase and lamellar phase. This intermediate phase often is called a biscontinuous cubic phase (V I ). Applications of liquid crystals: (a) Display applications: By virtue of their fluid nature, LCs can be easily processed into thin films, yet they retain the optical properties of crystalline materials such as the ability to rotate plane polarized light. In addition, the orientation of the molecules in liquid crystal films can be modulated on a relatively short time scale using a low electric field. Because the birefringence in a liquid crystal phase is a function of the angle formed by plane-polarized light and the director n, it can effectively function as an ON/OFF light shutter between crossed polarizers under the influence of an electric field. Most LC applications are indeed based on this simple concept of an ON/OFF light shutter. Majority of the liquid crystals displays (LCDs) fabricated today use either the twisted nematic (TN) or super twisted nematic (STN) displays. The nematic phase formed by discotic mesogens has recently been reported to be useful for wide viewing angle LCDs because of their negative birefringence. (b) Temperature sensors: Chiral nematic (cholesteric) liquid crystals reflect light with a wavelength proportional to the magnitude of pitch. Because the pitch is dependent upon temperature, the color reflected also is dependent upon temperature. Thus, cholesteric LCs make it possible to accurately gauge temperature just by looking at the color. By mixing different 196

204 cholesteric LCs, a device for practically any temperature range can be built. This property has been exploited for practical applications in diverse areas including medicine, packing industry and electronics. Cholesteric liquid crystals as fever strips are in use as disposable thermometers. LC thermal sensors can be attached to skin to show a thermal map. This is useful because often physical problems such as tumors have a different temperature than the surrounding tissue. LC temperature sensors can also be used to find bad connections on a circuit board by detecting the characteristic higher temperature. (c) Columnar fluid phases as a promising media for modern applications: As discussed earlier, the preferential self-organizing ability of discotic mesogens to form columnar (Col) mesophases is driven by favorable π-π interactions between the aromatic cores. Columnar mesophase offers a one-dimensional pathway for the electronic charge migration, where the central aromatic core is the conducting unit, with external peripheral chains as the insulating mantle. This LC state is of great importance because it allows the possibility to combine different physical properties (optical, conductive) with orientational control of the molecular order, self healing of structural defects and ease of processability. Most importantly all these properties can be tailored by careful molecular engineering. Thus, Col LC phases can be used as promising media for various device applications such as (a) field effect transistor; (b) Photovoltaic or solar cells; (c) gas sensors and (d) organic light emitting diodes. Currently the solar cells used for the direct conversion of light into electricity by the photovoltaic effect are fabricated from inorganic semiconductors; in particular they are based on the single or polycrystalline silicon cells. On the other hand, organic thin-film solar cells having single crystalline material are also promising flatplate photovoltaic technology. However, the flat-plate technology based on either of these two materials is rather difficult and expensive. Most importantly, the large quantity of inorganic semiconductors used in such a technology is hazardous to the environment. Thus, for the solar cell applications, new organic materials with low cost and good processability, large absorption coefficient, efficient photo generation of charge and good charge carrier mobility are needed. In this context, the Col phases formed by the electron rich/poor discotic mesogens appear to be promising given the fact that their structure resembles the aromatic stacking in single crystalline conductors. In particular, segregated stacks of columnar mesophases made up of donor and acceptor type discotics in their face on orientation imitate the same morphology of solar cells. The edge on orientation of the Col phases can be translated into field effect transistors (FET) 197

205 which are the vital components in molecular electronic devices. The high mobility for photo induced charge carriers in the Col phases also make them suitable for their use as the active charge transport layer in fast and high resolution xerographic and laser printing applications. The Col phase has a unique conductive surface layer due to the fluctuations along the lengths of the column. The carrier mobility along the surface is fluctuation assisted and the tunneling rates are exponentially dependent on the molecular core spacings. The core separation fluctuates with the surface and changes as soon as the surface is disturbed. The electrical conductivity of this surface layer is, therefore, very sensitive to the absorption of molecules. Thus columnar liquid crystals can be used as sensitive gas sensors for both polar and nonpolar molecules. Recently Col phases gaining importance in the construction of organic light emitting diodes (OLEDs) as they can act as good emitting and conductive layers with proper structural design. Columnar phases with a combination of hol/electron transporting and luminescence properties are an ideal media for the fabrication of OLEDs. (d) Other applications: Liquid crystals have other applications also. Polymers form an important subclass of liquid crystal materials and occur in nature as solutions of some biopolymers and are important in the processing of advanced high-modulus engineering materials like Kevlar. Liquid crystals are employed as anisotropic solvents for the study of various physiochemical properties. The nematic phase, in which the molecules can be homogeneously oriented by a magnetic field such that the optic axis lies parallel to the field, is employed as anisotropic solvent in NMR spectroscopy. This technique provides information regarding the anisotropy of the chemical shifts and molecular geometry. Liquid crystals are used as solvents to alter the rates of uni- or bi-molecular thermal and photochemical reactions. This technique is based on the ability of the mesophase to control the orientation of solutes, impart constraints on their mobility and remove the randomness of molecular motions and orientations. A combination of the analytical strengths of gas chromatography and the unique structure and shape selective properties of the LC phase has led to the wide spread use of LCs as stationary phases in chromatography. Effective and selective separation of positional and geometric isomers can be brought about by the interaction of the solute with the orientational order provided by the anisotropy of the LC stationary phase. Cholesteric LCs is also used for chiral recognition. Lyotropic LCs is exploited for applications in commercial detergents and cosmetics 198

206 and for the simulation of bio membranes. Recently, another important application of LCs as a medium for controlled drug release has been envisaged Phase Equilibria: The various terms involved in the phase equilibria are - System: A system is part of physical universe isolated from all others for the specific study. Homogeneous system: System with only one phase. Heterogeneous system: System with more than one phases. Phase: A phase (Greek word appearance) is a homogeneous, physically distinct and mechanically separable portion or part of system. Homogeneous means system has identical composition and physical properties throughout the whole system. Physically distinct means a phase should have definite boundary surface (two immiscible liquids, two different crystals of same or different solid materials, precipitate formed in solution, etc). Mechanically separable means the phases can be separated by simple mechanical operation such as filtration, decantation, hand picking, separation by using separating funnel, etc. Number of Phases (P): It is number of physically distinct states such as solids, liquids and gaseous present in the system at equilibrium. To explain the number of phase (P) consider the following examplesa) For gaseous system: 199

207 Only one phase is possible for any composition of different gaseous or vapours because the gaseous or vapours are completely miscible with each others in all proportions (P= 1). b) For liquid system: i. A mixture of two or more completely soluble liquids in all proportions is considered as single phase. E.g. Water + Ethyl alcohol (P = 1), Chloroform + Carbon tetrachloride (P = 1), etc. ii. A mixture of two or more completely immiscible liquids will forms number of phases equal to number of immiscible liquids present in the system. e.g. Water + Carbon tetrachloride (P = 2), Water + Chloroform + Mercury (P = 3). iii. Any vapour of gases in contact with liquid has two phases (P = 2). c) For solid systems: i. For mixture of solids, there will be number of phases equal to number of solids which are in equilibrium. Every solid is considered as a separate phase. E.g. Mixture of crystalline NaCl and KCl (P = 2), Heating of CaCO 3 in closed vessel, there are solid CaCO 3, solid CaO and gaseous CO 2 are in equilibrium with each other; therefore P = 3. CaCO 3 (s) CaO (s) + CO 2 (g). ii. When solid dissolve completely forms homogeneous solution is considered as single phase system but if solid forms saturated solution and some solid remains undissolve then P = 2. iii. Each polymeric form of polymeric material and allotropic modification are considered as separate phase. A phase may consist of any amount, large or small. It may be in one unit or subdivided into smaller units. For example:- Ice represent one phase whether it is a single block or subdivided into many pieces. Constituents of system: A chemical species (ions or molecules) which are present in system. Components: Chemically independent constituents of a system. Number of Components (C): The term component does not mean constituents of the system. It is used to explain chemical composition of each phase of the system. It is the smallest number of independent variable, chemical constituents by means of which the compositions of each phase can be explained either directly or by means of chemical equation. This term can be explain with the help of following examples- 200

208 1. One component system (C = 1): Water system is a typical example of one component system exist equilibrium between the different phases of water. Solid water (ice) Liquid water (P = 2) Solid water (ice) Water vapour (P = 2) Liquid water Water vapour (P = 2) Solid water (ice) Liquid water Water vapour. (P = 3). Each phase contains only one chemical composition (water molecules) therefore it is one component system. 2. Two component System (C = 2): A typical example of two component system is decomposition of solid CaCO 3 in close vessel giving rise to following equilibrium. CaCO 3 (s) CaO (s) + CO 2 (g). During decomposition three phases are co-exist along with three chemical constituents. But whole system can be expressed completely by two chemical constituents in the form of equation of each phase hence it is example of two components system. There are three ways in which two chemical constituents can be selected to express every phase. i. Chemical constituents: CaO and CO 2 are choosen. Phase Composition x CaCO 3 x CaO + x CO 2 y CaO y CaO + 0 CO 2 z CO 2 0 CaO + z CO 2 ii. Chemical constituents: CaCO 3 and CaO are choosen. Phase Composition x CaCO 3 x CaCO CaO y CaO 0 CaCO 3 + y CaO z CO 2 z CaCO 3 - z CaO ii. Chemical constituents: CaCO 3 and CO 2 are choosen. Phase Composition x CaCO 3 x CaCO CO 2 y CaO y CaCO 3 - y CO 2 z CO 2 0 CaCO 3 + z CO 2 201

209 Any phase of the system can be completely expressed by two chemical constituents, hence it is example of two component system. Another example which is used to completely distinguish between one and two component system is the decomposition of ammonium chloride. NH 4 Cl NH 3 + HCl This system has two phase as solid (NH 4 Cl) and gaseous phase (NH 3 and HCl). If dissociation is carried out in vacuum, then the number of components of the system is one because in gaseous phase both NH 3 and HCl are present in equal amount, thus composition can be represented as [x NH 4 Cl = x NH 3 + x HCl]. But if dissociation is carried out in presence of trace amount of NH 3 or HCl, then number of components of the system becomes two. Solid phase [x NH 4 Cl = x NH 3 + x HCl]. Gaseous phase [x NH 4 Cl = x NH 3 + y HCl] or [x NH 4 Cl = y NH 3 + x HCl]. Two component system: Consider a system containing minimum two independent variable components. The number of phases exist in equilibrium are depends on the conditions such as temperature and pressure. These conditions are determined experimentally and plot a diagram is called as phase diagram. The phase diagram is plot of pressure against temperature Liquid Liquid mixtures When two immiscible liquids (which are not reacting chemically with each other) are brought in contact with each others resulting three types of binary liquid systems. i. Both liquids are completely miscible with each other in all proportions. E.g. Water + Ethyl alcohol, Benzene + Toluene, etc. ii. The liquid pairs are partially miscible with each others. e.g. Water + Phenol. iii. Liquid pairs are practically immiscible with each other such as Water + Benzene, Carbon disulphide + Water. a. Completely miscible liquid pairs The solution of two components are completely miscible with each other is ideal or non-ideal. Solutions which fill full the following conditions is said to be ideal. i. It should obey the Raoult s law of vapour pressure at all compositions. 202

210 ii. The chemical and physical nature of the components should not be change and the activity of each component should be equal to its mole fraction under all conditions of temperature, pressure and concentration. iii. There should be no change in volume ( V mixing = 0) on mixing. iv. There should be no change in enthalpy ( H mixing = 0) on mixing. The solution which does not obey these conditions is called as non-ideal solutions. The phase diagram for liquid-liquid mixtures is the plot of vapour pressure against composition and temperature against composition. Raoult s law: Consider binary solution containing two components A and B. Both the components are volatile forming ideal solution. Suppose p A and p B are the partial vapour pressures of A and B at equilibrium and p is the total vapour of the solution. According to the Dalton s law, the total vapour pressure of the solution isp = p A + p B. The partial vapour pressure of any component at equilibrium is depends on total vapour pressure of solution and composition of vapour. If x A and x B are the mole fraction of component A and B in the vapour mixture. p A = x A x p and p B = x B x p. The partial pressure can be varying with the nature of the components, their compositions in the mixture and temperature. Statement: Partial vapour pressure of any component of the mixture is equal to the multiplication of mole fraction (x A ) in solution and vapour pressure (p 0 A ) of it in pure state. 0 p A = x A x p A and p B = x B x p 0 B. Where, x A and x B are the mole fractions of A and B in liquid mixtures respectively and p 0 0 A and p B be the vapour pressure of the pure component at same temperature. p is the total vapour pressure is sum of partial vapour pressures of components of mixture. The variation of partial and total vapour pressure with composition of liquid mixture at constant temperature is shown below- 203

211 constant temperature P A 0 total pressure Vapour pressure P 0 B partial vapour pressure of liquid B partial vapour pressure of liquid A A x A x B = 1 = 0 mole fraction x A B = 0 x B = 1 Deviations from the Raoult s law (non-ideal solutions): Some mixtures (solutions) of two volatile liquid components A and B having different physical and chemical properties than the pure liquids. Such solutions are called as non-ideal solutions. These solutions do not obey Raoult s law. They show two types of deviations as- i. Positive deviations and, ii. Negative deviation from Raoult s law. i. Solution showing positive deviation: If the forces of attraction between unlike molecules i.e. between A and B are weaker than the forces of attraction between like molecules i.e. between A & A and B & B. Such solutions show positive deviations from Raoult s law. In such cases, the vapour pressure curves of the constituents and the mixture lie above those of ideal dotted lines. constant temperature P A 0 total pressure Vapour pressure P 0 B partial vapour pressure of liquid B partial vapour pressure of liquid A A x A x B = 1 = 0 mole fraction x A B = 0 x B = 1 The positive deviation indicates that the tendency of each molecule to escape from the solution to vapour is greater in non-ideal solutions than that in ideal solution. 204

212 The extend of positive deviation is depends on many factors, some of them are listed asi. Difference in polarity of the molecules. ii. Difference in length of hydrocarbon chain or groups in the molecules. iii. Difference in intermolecular forces of attraction. iv. Association of the constituents in the liquid state. e.g. Carbon tetrachloride + Heptane, Diethy ether + Acetone, Heptane + Ethyl alcohol. ii. Solutions showing negative deviation: P A 0 constant temperature Vapour pressure total pressure P 0 B partial vapour pressure of liquid B partial vapour pressure of liquid A A x A x B = 1 = 0 mole fraction x A B = 0 x B = 1 If the forces of attraction between unlike molecules i.e. between A and B are stronger than the forces of attraction between like molecules i.e. between A & A and B & B. Such solutions show negative deviations from Raoult s law. In such cases, the vapour pressure curves of the constituents and the mixture lie below those of ideal dotted lines. The negative deviation indicates that the tendency of each molecule to escape from the solution to vapour is relatively lower in non-ideal solutions than that in ideal solution. e.g. Pyridine + Formic acid, Chloroform + Acetone (due to partial association between the molecules through hydrogen bonding), Haloacid + Nitric acid. Partially miscible liquids: Two liquids are soluble to each others in limited range of concentration are called as partial miscible liquids. e.g. The small quantity of organic compounds such as phenol, ether or aniline are soluble in water at room temperature. If the addition of organic compound is continued, at particular stage where the 205

213 compound is not soluble and forming two layers. One is saturated solution of organic compound in water (aqueous layer) and other is saturated solution of water in organic compound (organic layer). On rising the temperature of the mixture, the mutual solubility of components of mixture is increased until both the phases reaches to the same composition where the boundary between the two phases is disappear. The temperature at which the two layers having same composition and become physically indistinguishable is called the critical solution temperature (CST) or consolute temperature of the system. Case-I: In some system, CST is lower than room temperature is called as lower CST. E.g. triethyl amine + water system, 1-methyl piperidine + water system, etc. Case-II: In some cases, CST is higher than room temperature is called upper CST. E.g. phenol + water system ( C), aniline + water system (167 0 C), aniline + hexane ( C), benzene + sulphur (163 0 C), methanol + cyclohexane ( C), methanol + carbon tetrachloride ( C), etc. Case-III: Some liquid systems having both upper and lower CST. E.g. nicotine + water system, m- toluidine + Glycerol system, etc. 1. Phenol + water system: When equal amounts of phenol and water are mixed to each others forming two layers, the upper layer is of water saturated with phenol and lower layer is of phenol saturated with water. Bothe these layer having different composition which is function of temperature. The critical solution temperature of phenol-water system is C and the composition of phenol is 36.1%. The mutual solubility of water and phenol with temperature can be explain with help of following temperature-composition diagram. one phase region C 68.9 Temperature 0 C A X B t two phase region Water 100% weight percent Phenol 100% 206

214 The curve has the shape of a parabola. At any given temperature, the compositions of conjugate solutions are given by the points on opposite branches of the parabola. E.g At temperature t, the line AB gives compositions of the conjugate solutions. Point A represent the composition of phenol in water and B the composition of water in phenol. Between A and B, all mixtures gives two layers of composition A and B. The X represents a system of two layers whose relative compositions are in between the compositions of A and B respectively. The relative weight of two layers are given by the Lever rule as- Weight of phenol layer Distance XA = Weight of water layer Distance XB Outside the parabola, two liquids are completely miscible (homogeneous) with each others. As temperature rises, the compositions of two layers are approaches to each others i.e. mutual solubility of two liquids are increases with increase the temperature. At point C (critical solution temperature), two layers have same compositions and miscible to each others forming single layer. 2. Triethylamine water system: In some cases, the mutual solubility of the components of system decreases with increase the temperature and get miscible at lower temperature. The temperature composition diagram is U shaped. E.g. triethylamine water system. Temperature 0 C two phase region 18.5 one phase region weight percent triethylamine The curve indicates that, mutual solubility of water and triethylamine increases with decrease in temperature. At C, both layers having same composition and miscible to each others and having composition 30% by weight of triethylamine in water. Above this temperature and inside the curve, both layers having different compositions and immiscible to each others & below this temperature and outside the curve, two liquids are miscible in all proportions. 207

215 3. Water Nicotine system: This is example of the system having two critical solution temperatures as upper CST and lower CST. If we start from any temperature between these two, the mutual solubility increases with increase the temperature and also decreases with temperature. The compositions of nicotine water system at upper CST (208 0 C) and lower CST ( C) is almost same as 34% of nicotine water. At point K (95 0 C), nicotine is least soluble in water, while at point L (130 0 C), water is least soluble in nicotine. The mutual solubility diagram is shown below - upper CST (208) Temperature 0 C two phase region L one phase region K lower CST (60.8) 0 80 weight percent Nicotine Water Nicotine At any temperature, the composition corresponding to any point within the curve represents two liquid layers (heterogeneous phase) at equilibrium while outside the curve, it exist in homogeneous phase. At particular external pressure, both upper and lower CST are merge to each others and exist in one phase at any composition and temperature. 208

216 5.2.Spectroscopy II Properties of light Electromagnetic radiation is a form of energy that is transmitted through space at enormous velocity. These radiations can have different properties due to particle and wave nature. The wave can be characterized by some properties as- wavelength (λ), frequency (υ), velocity, amplitude, wave number, etc. The light has two types of nature- wave nature and particle nature. Consider wave nature of light- crest wavelength crest dis. O time trough trough Electromagnetic radiation consists of energy associated with electric and magnetic fields resulting from the acceleration of the electronic charge. The electric and magnetic fielding does not have any supporting media and propagating trough the space or vacuum are at right angle to each other to the direction of propagation. The electronic radiation is considered as a simple harmonic propagated from source and traveling in a straight line. A simple harmonic wave has properties of sine wave given by the equation y = A sin θ Where y is vertical displacement, A is the maximum value of vertical displacement called amplitude; θ is the angle changing from 0 o to 360 o. 209

217 electric field dis. O magnetic field direction of wave A p o wt y 90/w 180/w t Consider the point traveled with uniform velocity ω radian per second in a circular path from point 0. After some time t, the angle θ which is equal to ωt radians. Then vertical displacement is given by equationy = A sin ωt As amplitude increases vertically, the angle θ is also increases and the amplitude is maximum when the angle θ is π\2. When θ is π, then amplitude become zero, also when θ is 3π\2, again amplitude become maximum and when the cycle become completed, the amplitude become zero, as shown in fig. the one cycle is completed at the time 2π\ω seconds. The above discussion shows that, in one second the point completes the cycles ω\2π times is called as frequency of wave. υ = ω\2π or ω = 2π υ Frequency is defined as the number of oscillation that occurs per second. The units of frequency are the hertz (Hz) or cycle per second and it has dimensions of reciprocal of time. The period T is the time interval required for the passage of successive maxima past at a fixed point in space. T = 1\ υ Therefore, the basic equation of wave motion isy = A sin 2πυt 1 Suppose, x is the distance traveled by the wave at time t, then velocity of light is c = x\t, or t = x\c 2 210

218 From equation 1 and 2, we have, y = A sin 2πυx/c 3 But, c/υ is the equation of wavelength (λ), y = A sin 2πx/λ 4 Where, λ is the wavelength and is defined as the distance between the two successive maxima or minima. In spectroscopy, most of data can be expressed in terms of wave number. It is reciprocal of wavelength of light and is expressed as = 1/λ. The frequency, wavelength and velocity are interrelated to each other asυ = c / λ (c is velocity of light in a vaccum). The wave nature of electromagnetic radiation was failed to explain phenomenon such as Compton Effect, photoelectric effect, etc. This can be explaining by particle nature of radiations. When a sample absorbs electromagnetic radiation it undergoes a change in energy. The interaction between the sample and the electromagnetic radiation is easiest to understand if we assume that electromagnetic radiation consists of a beam of energetic particles called photons. Photon is a particle of light carrying an amount of energy equal to hν. The energy of particle nature (quanta- Bundle or radiation) is proportional to frequency of the radiation and is given as- E = h. υ = λ = h.c x wave number. The study of interaction of electromagnetic radiations with mater is called as spectroscopy. Spectrochemical methods that use not only visible but also ultraviolet and infrared radiation are often called optical methods in spite of the fact that the human eye is not sensitive to UV or IR radiation. This terminology arises from the many common features of instruments for the three spectral regions and the similarities in the way we view the interactions of the three types of radiation with matter. 211

219 Terms Involved: 1. Radiant Power: It is denoted by the latter I or P. It is also called as intensity of electromagnetic radiation. It is defines as the number of photons of electromagnetic radiations incident per unit area per unit time. It is independent on wavelength or frequency of the radiations. The energy associated with radiations is given as hυ. 2. Transmittance (T): It is ratio of intensity of the transmitted radiations to that of the incident radiations. T = I t /I Percentage Transmittance (T%): Transmission is always express in percentage is called as percentage transmittance. T% = 100 x T. 4. Absorbance (A): It is negative logarithm to the base 10 of transmittance or logarithm to the base 10 of reciprocal of transmittance. A = -log T = log (1/T) = log(i 0 /I t ). When beam of light is incident on homogeneous medium, a portion of the incident light (I 0 ) is absorbed (I a ), some can be reflected (I r ) and remaining can be transmitted (I t ) with net effect of intensities. I 0 = I a + I r + I t. But it can be observed that, the amount of reflected radiations (I r ) is so small nearly 4% for all practically purposes, it can be eliminated for the air glass interface with glass cuvette. I 0 = I a + I t. 212

220 Every molecular species are capable of absorbing its characteristic wavelength of electromagnetic light. This process transfer energy to molecules which result decrease in intensity of transmitted radiation. Two additional wave properties are power, P, and intensity, I, which give the flux of energy from a source of electromagnetic radiation. Power is the flux of energy per unit time (P). Intensity is the flux of energy per unit time per area (I). Both quantities are proportional to the square of the amplitude of the electric field. Both spectrophotometry and colorimetry are based on same mathematical relations such as Beer s law, Lambert law, and Beer s-lambert law. The absorbance of radiation is depends concentration and path length can be explain by two independent laws are Beer s law and Lambert law. The combination of these two laws is called as Beer s law or Lambert-Beer s law. Every molecular species is capable of absorbing its own characteristic frequencies of electromagnetic radiation. The source used for measurement of absorbance emit light called polychromatic light but out of which particular wavelength or narrow wavelength band is absorbed by matter and remaining is transmitted through it. The Polychromatic radiations are the electromagnetic radiations of more than one wavelength. The term monochromatic radiation refers to radiation of a single color; that is, a single wavelength or frequency. In practice, it is virtually impossible to produce a single color of light. Monochromatic radiation is the electromagnetic radiation of a single wavelength which are obtained by using monochromator such as prism, filter or grating. Lambert law: This law can be stated by German mathematician Johann Heinrich Lambert in Absorbance of monochromatic radiation by the sample or solution is directly proportional to path length of solution. A α l (path length) (at constant concentration and fixed wavelength) A is absorbance and l is path length of solution. Proof: Suppose, di be the small change in intensity of radiation when it passes through infinitesimally small thickness (path length) dl. 213

221 I 0 I dl I-dI I t l = k 1 x dl. di is small change in intensity of incident radiation, negative sign indicates decrease in intensity with increases thickness of solution dl. k 1 is proportionality constant. Integrate above equation as - - ln I = k 1 x l + C 1. Put l = 0, therefore I = I 0. Therefore, - ln I 0 = 0 + C 1. - ln I = k 1 x l - ln I 0. ln I 0 - ln I = k 1 x l.. [A = -log T = Above equation indicates that, absorbance A is directly proportional to path length l of solution. Beers law: Absorbance of monochromatic radiation by the sample or solution is directly proportional to concentration of solution. A α c (concentration) (at fixed path length) A is absorbance and c is concentration of solution. Proof: = k 2 x dc. di is small change in intensity of incident radiation, negative sign indicates decrease in intensity with increases concentration of solution dc. k 2 is proportionality constant. Integrate above equation as- 214

222 - ln I = k 1 x c + C 2. Put l = 0, therefore I = I 0. Therefore, - ln I 0 = 0 + C 2. - ln I = x c - ln I 0. ln I 0 - ln I = x c. ln (I 0 /I) = x c. ln (1/T) = x c. [T = I/I 0 ] log (1/T) = / 2.303x c. [A = -log T = log (1/T) A = K 2 x c. [K 2 = /2.303]. Above equation indicates that, absorbance A is directly proportional to concentration c of solution. Lambert-Beer s law (Beer s law): Absorbance of solution is directly proportional to - 1. Path length of solution and 2. Concentration of the solution. When monochromatic light is passed through transparent medium, the rate of decrease of intensity of light with respect to thickness and concentration of absorbing species is proportional to a intensity of light. A α (l x c) A = K x l x c. K = a, A = a x l x c. K = ε, A = ε x l x c. a (absorptivity or extinction coefficient) and ε (molar absorptivity or molar extinction coefficient) is proportionality constant which is depends on unit of concentration. If c is expressed in terms of mol/dm 3 or mol/m 3, then K = ε (molar absorptivity or molar extinction coefficient), expressed in dm 3 /mol,cm or m 3 /mol,cm. If c is expressed in terms of gm/dm 3 or ppm (part per million), then K = a (absorptivity or extinction coefficient), expressed in dm 3 /gm,cm. Beer s law, as expressed can be used in several different ways. We can calculate molar absorptivities of species if the concentration is known. We can use the measured value of absorbance to obtain concentration if absorptivity and path length are known. Absorptivities, 215

223 however, are functions of such variables as solvent, solution composition, and temperature. Because of variations in absorptivity with conditions, it is never a good idea to depend on literature values for quantitative work. Hence, a standard solution of the analyte in the same solvent and at a similar temperature is used to obtain the absorptivity at the time of the analysis. Most often, we use a series of standard solutions of the analyte to construct a calibration curve, or working curve, of A versus c or to obtain a linear regression equation. It may also be necessary to duplicate closely the overall composition of the analyte solution in order to compensate for matrix effects. Alternatively, the method of standard additions is used for the same purpose. Beer s law also applies to solutions containing more than one kind of absorbing substance. Provided that there is no interaction among the various species, the total absorbance for a multicomponent system at a single wavelength is the sum of the individual absorbances. In other words, where the subscripts refer to absorbing components 1, 2,..., n. Molar extinction coefficient (ε): It is defined as the absorbance of a solution which has concentration of absorbing species as one mol per dm 3 and path length of a solution is equal to 1 cm. Molar extinction coefficient isi. It is characteristic of the absorbing species. ii. It is independent on the concentration of the absorbing species. iii. It measures the extent of absorption. Stronger the absorption higher will be the molar extinction coefficient. iv. The units of molar extinction coefficient (ε) depend on unit of concentration of the absorbing species. v. It is slope of the absorbance against concentration curve which is expected to be a straight line. Deviation from the Beer s Lambert Law: 216

224 Beer s law can be strictly applied for the dilute solution whose concentration is less than 0.01M because at this concentration, intermolecular interactions between the molecules are negligible. For homogeneous absorbing medium, a graph of absorbance against concentration is straight line passing through origin. This linear relationship is affected by some factors. There are two deviations observed in linearity of Beers law. When the observed absorbance is greater than calculated value, it is called as positive deviation and the reverse is called as negative deviation. Positive Expected Absorbance Negative Concentration The Lambert law can be valid for all path lengths of solution hence deviations are generally observed in Beers law. All the deviations are divided into following groups. 1. Real deviations: Beers law can be valid for dilute solution up to concentration 0.01M. At this concentration range, the absorbing species do not interact with each other which is possible in dilute solution (the distance between absorbing species is large). But at higher concentration, the intermolecular distance is increased and shows deviation from linearity of the law. 2. Instrumental deviation: The instrumental deviations are observed due to following reasons. i. Beers law gives good result when measurements are made with monochromatic light. Deviation is occurs by using heterochromatic light. ii. Stray radiations (with wavelength other than that of incident) arising due to reflection and scattering from the internal surface of instrument leads deviation from Beers law. This can be overcome by black coating inside the instrument. iii. The radiations to be detected after being absorbed by the sample emerge through a slit. If the width of slit is not narrow enough, then undesirable radiations are fall on the detector and causes apparent change in absorption of sample. iv. The monochromator of the instrument should be providing the wavelength which covers the λ max value as shown in A band. The variation of the absorbance from one edge of the band to the 217

225 other edge will be small. As detector measures the average absorbance, it will not be much different from actual value. Gives deviations from law Good for study B Absorbance A wavelength However, the wavelength provided by the instrument is in the range B, then the variation of the absorbance from one end of the band width to another will be will be considerable and the average value measured will differ from the actual considerably. It leads the deviation from the law. 3. Chemical deviations: The chemical deviations will be observed when absorbing sample undergoes association, dissociation, fragmentation, rearrangement, etc reactions in the solution. e.g.1. Benzyl alcohol undergoes tetramerization in chloroform and exist in tetramer form in equilibrium monomer. 4 C 6 H 5 CH 2 OH (C 6 H 5 CH 2 OH) 4 (monomer) (tetramer) Dissociation of polymer increases with dilution, the monomer and polymer absorb at different wavelengths and hence deviation is observed. In acidic medium Cr(VI) exist totally as Cr 2 O 2-7 and in alkaline medium as CrO 2-4. As the color of two ions are different and hence has different λ max value. At intermediate ph value, the Cr(VI) added will partly exist as chromate (yellow in color) and partly as dichromate (orange in color). The measured concentration will be correspond to either chromate or dichromate depending on the wavelength used and not on the Cr(VI) added initially. The total absorbance of the solution at any given point thus depends on the ratio of the species present in the solution. This will lead deviation from the law. 2-2 (Cr 2 O 7 ) + OH 2 2 HCrO 4 2 H (CrO 4 ) (Orange) (Yellow) 2-218

226 Deviation also occurs due to presence of impurities that absorbs or fluorescence at the absorption wavelength. Limitations of Beers Law: The are number of limitations of Beers law, some of them are - 1. Beer s can not be valid at higher concentration (greater than 0.01M solution). 2. The molar extinction coefficient depends on refractive index of the solution and change with change in it. The refractive index will be change with change the concentration of the solution. At higher concentration, this change will be appreciable but at concentration equal to or less than 0.01M, these change is negligible. 3. The change in solvent also affects the ε value. 4. The temperature fluctuation and stray light may affect the measurement of the absorbance. Quantitative analysis by calibration curve method: Ultraviolet and visible molecular absorption spectroscopy is one of the most useful tools available for quantitative analysis. The important characteristics of spectrophotometric and photometric methods are a. Wide applicability: A majority of inorganic, organic, and biochemical species absorb ultraviolet or visible radiation and are thus amenable to direct quantitative determination. Many non-absorbing species can also be determined after chemical conversion to absorbing derivatives. Of the determinations performed in clinical laboratories, a large majority is based on ultraviolet and visible absorption spectroscopy. b. High sensitivity: Typical detection limits for absorption spectroscopy range from 10-4 to 10-5 M. This range can often be extended to 10-6 or even 10-7 M with procedural modifications. c. Moderate to high selectivity: Often a wavelength can be found at which the analyte alone absorbs. Furthermore, where overlapping absorption bands do occur, corrections based on additional measurements at other wavelengths sometimes eliminate the need for a separation step. When separations are required, spectrophotometry often provides the means for detecting the separated species. d. Good accuracy: The relative errors in concentration encountered with a typical spectrophotometric or photometric procedure lie in the range from 1% to 5%. Such errors can often be decreased to a few tenths of a percent with special precautions. 219

227 e. Ease and convenience: Spectrophotometric and photometric measurements are easily and rapidly performed with modern instruments. In addition, the methods lend themselves to automation quite nicely. A first step in any photometric or spectrophotometric analysis is the development of conditions that yield a reproducible relationship (preferably linear) between absorbance and analyte concentration. Wavelength Selection: In order to realize maximum sensitivity, spectrophotometric absorbance measurements are usually made at the wavelength of maximum absorption because the change in absorbance per unit of concentration is greatest at this point. Common variables that influence the absorption spectrum of a substance include the nature of the solvent, the ph of the solution, the temperature, high electrolyte concentrations, and the presence of interfering substances. The effects of these variables must be known and conditions for the determination chosen such that the absorbance will not be materially affected by small, uncontrolled variations. These errors are minimized by calibration curve method. Following steps are involved in calibration curve methods - i. Several solutions of accurately known concentration (within the dynamic range) of given component are prepared. ii. Record the response or analytical signal (absorbance) for all concentrations of the component. iii. If required, the absorbance is corrected for the blank. iv. Plot a graph of absorbance against concentration is expected to be straight line passing through origin. Usually five signals are sufficient for the construction of calibration curve. But if required more concentration will have to be used. v. The absorbance is also recorded for unknown sample solution (provided that the expected concentration of unknown is in the range of concentrations used for plotting the calibration curve). vi. From the calibration curve and absorbance of unknown sample, concentration of unknown sample is determined. From the graph, the unknown concentration of the sample is determined. The success of method is depends on how accurately the concentrations of the standards are known and how closely the matrix of sample resembles that of the standard. 220

228 Responce Concentration Instrumentation: A spectrometer is a spectroscopic instrument that uses a monochromator or polychromator in conjunction with a transducer to convert the radiant intensities into electrical signals. Spectrophotometers are spectrometers that allow measurement of the ratio of the radiant powers of two beams, a requirement to measure absorbance. Spectrophotometers offer the considerable advantage that the wavelength used can be varied continuously, making it possible to record absorption spectra. If a filter is used as the wavelength selector, monochromatic light at only discrete wavelengths (using filter) is available, and the instrument is called a photometer. If a monochromator is used (that is a prism or grating) as the wave length selector, the instrument can provide monochromatic light over a continuous range of wave lengths and is called a spectrometer or spectrophotometer. Spectrophotometers can be double-beam instruments with two cuvette holders, one for the sample and the other for the blank, or reference sample. Advantages of the double beam instrument include the capability of making simultaneous corrections for changes in light intensity, grating efficiency, slit-width variation, and so on. It is particularly useful for obtaining spectral curves. 221

229 Principle: Working of the spectrophotometer based on Lambert-Beer s law. Absorbance spectroscopy is frequently used to measure concentration. According to the Beer-Lambert law measurements of absorbance for molecules of known ε allow calculation of concentration. Alternatively, if the concentration of the absorbing species is known, the ε can be determined. Single beam spectrophotometer: The single-beam spectrophotometer can be divided into seven basic components: 1. A stable source of radiant energy, 2. An entrance slit to focus the light, 3. A wavelength selector, 4. An exit slit to focus the light, 5. A device to hold the transparent container (cuvette), which contains the solution to be measured, 6. A radiant-energy detector, and 7. A device to read out the electrical signal generated by the detector. 1. Source: A tungsten-filament lamp is useful as the source of a continuous spectrum of radiant energy from 360 to 950 nm. Tungsten iodide lamps are often used as sources of visible and near-uv radiant energy. The tungsten halide filaments are longer lasting, produce more light at shorter wavelengths, and emit a higher intensity radiant energy than tungsten filaments do. Hydrogen and deuterium discharge lamps emit a continuous spectrum and are used for the UV region of the spectrum (220 to 360 nm). The deuterium lamp has more intensity than the hydrogen lamp does. Mercury-vapor lamps emit a discontinuous or line spectrum (313, 365, 405, 436, and 546 nm). This is useful for wave-length-calibration purposes but is not used in 222

230 many spectrophotometers. The mercury lamp is used in photometers or spectrophotometers employed for high-performance liquid chromatography (HPLC). Recently, light-emitting diodes have been employed as light sources. It is important to understand that the amount of light emitted from a light source is not constant over a continuous range of wavelengths. Thus a typical lamp has a complex transmittance spectrum maxima and minima. Lamps of different types and even from different manufacturers can vary. Therefore care must be taken in choosing a lamp for a particular analysis, because the amount of light emitted at the desired wave length may be too little or to much. For example, hydrogen or deuterium lamps, used for analysis have a maximum output of UV radiation in the 250 to 300 nm range. The output of radiant energy at longer wavelengths (greater than 340 nm) is considerably less and weak for many analyses. 2. An entrance slit to focus the light: It is metal or plastic fixed plate having narrow hole or slit. It provide the narrow optical beam image of light from source. 3. A wavelength selector: Isolation of the required wave-lengths or range of wave-lengths can be accomplished by use of a filter or monocromator. Filters are the simplest devices, consisting of only a material that selectively transmits the desired wavelengths and absorbs all other wavelengths. In a monochromator, a grating or prism disperses radiant energy from the source lamp into a spectrum from which the desired wavelength is isolated by mechanical slits. There are two types of filters (1) those with selective transmission characteristics, including glass and Wratten filters, and (2) those based on the principle of interference (interference filters). The Wratten filter consists of colored gelatin between clear glass plates; glass filters are composed of one or more layers of colored glass. Both types of filters transmit more radiant energy in some parts of the spectrum than in others. Interference filters work on a different principle. The principle is the same as that underlying the play of colors from a soap film, namely, interference. When radiant energy strikes the thin film some is reflected from the front surface, but some of the radiant energy that penetrates the film is reflected by the surface on the other side. If the two reflected rays are in phase, their resultant intensity is doubled, whereas, if they are out of phase, they destroy each other. Therefore, when white light strikes the film some reflected wavelengths will be augmented and some destroyed, resulting in colors. Monochromators can give a much narrower range of wavelengths than filters can and are easily adjustable over a wide spectral range. The dispersing element may be a prism or a grating. 223

231 Except for laser optical devices, the light obtained by a wavelength selector is not truly monochromatic (that is. of a single wavelength) but consists of a range of wavelengths. The degree of monochromicity is defined by the following terms. Band pass is that range of wavelengths that passes through the exit slit of the wavelength-selecting device. The nominal wavelength of this light beam is the wavelength at which the peak intensity of light occurs. The range of wavelengths obtained by a filter producing a symmetrical spectrum is usually noted by its half-band width (or half-hand pass). This describes the wavelengths obtained between the two sides of the transmittance spectrum at a transmittance equal to one half the peak transmittance. 4. An exit slit to focus the light: It is metal or plastic movable and rotable plate having narrow hole or slit. It is isolate the desired spectral band by blocking all of the dispersed radiation excepts that within a given resolution element. 5. Sample holder (cuvette): Most samples studied using visible and ultraviolet spectroscopy is liquids. The sample must therefore be placed in a transparent container to allow measurement. These containers are called cuvettes. Cuvettes are generally made from transparent plastic, glass, or quartz. Different cuvettes have different optical properties. Plastic cuvettes are increasingly popular because they do not shatter when dropped, and because their low price makes them disposable. However, plastic cuvettes tend to have considerable absorbance in the ultraviolet. Performing measurements in the far ultraviolet (below ~250 nm) requires relatively expensive (and relatively fragile) quartz cuvettes. Glass cuvettes are also opaque in the ultraviolet; unlike plastic cuvettes, glass cuvettes are effectively identical in physical appearance to quartz cuvettes. 6. A radiant-energy detector: The most commonly used detector is a photomultiplier tube (PMT). An incoming photon hits a thin metal film inside a vacuum tube. The metal film is maintained at a large negative potential, and emits electrons. These collide with a series of dynodes maintained at progressively lower potentials; each dynode emits several electrons in response to each incoming electron, resulting in a large amplification of the signal. Because the initial photon is required to initiate the process, most PMTs have very little dark current ( dark current is signal without light). Proper functioning of a PMT requires a constant voltage across the PMT. PMTs are wavelength dependent, with the degree of dependence being related to the metal used in the thin film; most PMTs exhibit the greatest sensitivity at ~400 nm. 224

232 An alternative type of detector uses photodiodes. Photodiodes are inexpensive but not very sensitive. Their low cost has allowed arrays of photodiodes to be set up to allow simultaneous detection of many wavelengths. In this type of spectrophotometer, the additional monochromator is located after the sample, so that it splits the multi-wavelength light leaving the sample. A charge coupled device (CCD) is a sensitive array detector. CCDs store charges released in response to photon impacts. Because the stored charges are stable for prolonged periods, a CCD can collect data for considerable time prior to readout of the signal. They are therefore potentially extremely sensitive. They will probably displace PMTs from some uses as their price decreases. CCDs are used in digital cameras and other consumer products and are rapidly becoming less expensive as a result of both economies of scale and the development of improved production techniques. 7. Read out device: The read out device convert that electrical signal generated by the detector to intensity of light incident on electrode of detector. Spectrophotometer readings are usually reported as absorbance, the instruments actually measure optical density. In the simplest terms, optical density (OD) has the same definition as absorbance: A signal processor is an electronic device that may amplify the electrical signal from the detector. In addition, the signal processor may convert the signal from dc to ac (or the reverse), change the phase of the signal, and filter it to remove unwanted components. The signal processor may also perform such mathematical operations on the signal as differentiation, integration, or conversion to logarithms. Several types of readout devices are found in modern instruments. Digital meters and computer monitors are two examples. Computers are often used to control various instrumental parameters, to process and store data, to print results and spectra, to compare results with various databases, and to communicate with other computers and network devices. Working: Having prepared the solution, we first select the appropriate wavelength. Usually the operator and mode of measurement (Transmittance/Absorption or Concentration) will know this in case of digital read out system. To obtain a percent transmittance reading, the digital readout is first zeroed with the sample compartment empty so that the occluder blocks the beam and no radiation reaches the detector. 225

233 This process is called the 0% T calibration, or adjustment. A cell containing the blank (often the solvent) is then inserted into the cell holder, and the pointer is brought to the 100% T mark by adjusting the position of the light control aperture and thus the amount of light reaching the detector. This adjustment is called the 100% T calibration, or adjustment. Finally, the sample is placed in the cell compartment, and the percent transmittance or the absorbance is read directly from the LCD display. Double beam spectrophotometer: With one detector and chopper: With separate detector and mirror splitter: Many modern photometers and spectrophotometers are based on a double-beam design. Two double-beam designs (b and c) compared with a single-beam system. A double-beam-in-space instrument in which two beams are formed by a V-shaped mirror called a beam-splitter. One beam passes through the reference solution to a photodetector, and the second simultaneously passes through the sample to a second, matched photodetector. The two outputs are amplified, and their ratio, or the logarithm of their ratio, is obtained electronically or computed and displayed on the output device. The remaining instrumentation part is same as like single beam spectrophotometer. In single detector system, alternatively the signals coming from sample and reference are detected and then compared. Double-beam instruments offer the advantage that they compensate for all but the most rapid fluctuations in the radiant output of the source. They also compensate for wide variations of source intensity with wavelength. Furthermore, the double-beam design is well suited for continuous recording of absorption spectra. 226

234 Photometric Titrations: A photometric titration involves the measurement of absorbance values during the titration. The absorbance of the solution is given by the Beer s-lambert s law as- Absorbance = A = logi 0 /I t = ε x C x l Where, I 0 is the intensity on incident light; I t is the intensity of transmitted light; C is the concentration of absorbing species in mol/lit; l is path length in cm and ε is the molar absorptivity. The absorbance of the solution is the function of concentration of absorbing species and is change with changing the concentration. Principle of Photometric titration: The titration can be represented as - Reactant + Titrant product. The end point can be obtained by plotting the graph of absorbance against volume of reagent added by using burette. The solvent used does not absorb any light during the course of titration. The absorbance of solution is measured by using spectrophotometer or photometer, if solution is colored; absorbance is measured by using colorimeter (working in visible region). 227

235 Instrumentation: The visible spectrophotometer is single beam ratio-indicating instrument with a wavelength range of nm (Nanometer). The basic wavelength range may be converted to nm by using accessory phototube and filters. Visible spectrophotometer essentially consists of following basic components: A. Radiation Source (Light) B. Optical System (Monochromatic) C. Sample Section D. Detector E. Filters F. Read Out Single beam spectrophotometer: Double beam spectrophotometer: A. RADIATION SOURCE: Most of the spectrometers use a tungsten lamp as the radiation source. These lamps provide a bright low-cost, broad band source of visible radiation. The advantage of tungsten lamp is continues output throughout the visible spectrum. For these lamps output decreases towards the ultra-violet, but there is more than sufficient output throughout the visible spectrum to energize the photo detector. Now a day's many manufacturers 228