Chapter 1. Introduction to Conductivity

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1 Chapter 1 Introduction to Conductivity

2 CHAPTER 1 INTRODUCTION TO CONDUCTIVITY 1. INTRODUCTION The present modem measuring instruments are the fruits of Science and Technology. The tremendous changes in research and development provided New Science instruments for the study of nature and these studies in through Produced new inventions. The precise and accurate measurement of physical and chemical properties plays a vital role change the mysteries of nature. Conductivity is one of the important chemical parameter that gives valuable information to Chemists in determining solubility products, dissociation constants and others properties of electrolytic solutions and also for quality control purposes. It depends on the total number of ions present in the solution and various physical and chemical phenomena lead to variations in conductance. Conductivity measurements are extensively used in research & laboratory analysis and in industrial environments. A typical example is the identification, sorting and control of circulation of fluids. Solution conductance measurements are non-specific, which restricts their quantitative analytical use to situations wherein only a single electrolyte is present or where the total quantity of ionic species is to be determined. In these l

3 situations conductance measurements are extremely sensitive. Traditionally, the measurement of electrolytic conductance has been one of the most accurate and precise of all electrochemical techniques. For example, conductivity measurements are employed in monitoring the deflection of ion exchanging lesions in water softening facilities, to monitor ground water, to detect oil in petroleum bore wells. Conductivity measurements also plays a vital role in (i) stopped-flow mixing which require rapid response, (ii) determination of end points in conduct metric titration s A recent technique used to determine the conductivity and dielectric constant of solution without the introduction of electrodes in direct contact with solution called High Frequency Conductrometric titration. Ion exchange chromatography is another area employing the conductance measurement. The requirement of all electrical phenomena is a cell, consisting of minimum of two electrodes that are both in contact with a solution called an electrolyte. Under the influence of the electric field, ions of the electrolyte migrate from one electrode to the other. Therefore electrolytic conductivity can be defined as a measure of the ability of a solution to carry electric current. They obey ohms few similar to metallic conductors Deviations from the ohms law occur only in abnormal conditions such as very high voltages or high frequency currents. Thus, it can be inferred that for an applied electro-motive force V, which in maintained at a constant value greater than the 9

4 decomposition value of the electrolyte, the current I flowing through the electrolyte between the electrodes varies inversely with the resistance of the electrolytic solution. In many electrochemical processes, the main focus is on the diffusion or charge transfer process occurring at on near the electrode surface for particular ions. In such instances, the ions of interest are generally in relatively low concentration and are assumed not be significantly involved in the charge conduction process between the electrodes. This condition is realized in practice by adding a relatively large concentration of non-interfering ions to provide the interelectrode conductance and minimize the electric field gradient between the electrodes. Important assumption in the addition of non-interfering ions (inert electrolyte) is that the interelectrode conductance part of the total electrochemical cell is negligible On the other hand, there are some practical important electrochemical techniques wherein the ions of interest provide a significant portion of the interelectrode conductance and for which the cell solution conductivity is the important electrochemical parameter that is measured. How well a solution conducts is dependent upon mobility of the ions present. Therefore, measurement of conductivity of a simple one-solute solution gives an indication of the concentration of ions or the mobility of ions. 3

5 But in the case of multiple solute solutions, the contribution of a single ionic solute to the total solution conductivity cannot be determined by conductance measurements alone. This lack of selectivity in conjunction with the level of medium associated with the measurement of electronic conductivity discouraged the widespread development of this technique in earlier days. But today, owing to phenomenal advancement in the field of instrumentation, measurement and evaluation, there has been the significant growth in automated precision conductrometric instrumentation. Application are being developed in which conductometry is employed to trace the course of highly specific chemical reactions. The basic consideration and techniques of conductance measurements (dc contact) are dealt in the following section. This theory also helps to understand the applications of common resistive indicator devices such as thermistor in temperature sensing, light sensitive resistance in intensity measurement, strain gauges for mechanical deformation studies. 1.1 THEORY OF CONDUCTIVITY AND BASIC RELATIONSHIPS Theory of conductivity Conductivity is the ability of a solution, a metal or a gas - to pass an electric current. In solutions the current is carried by cations and anions whereas in metals it is carried by electrons and the conductivity of a solution conducts electricity depends on a number of factors: 4

6 * Concentration * Mobility of ions * Valence of ions All substances possess some degree of conductivity. In aqueous solutions the level of ionic strength varies from the low conductivity of ultra pure water to the high conductivity of concentrated chemical samples. Conductivity may be measured by applying an alternating electrical current (I) to two electrodes immersed in a solution and measuring the resulting voltage (V). During this process, the cations migrate to the negative electrode, the anions to the positive electrode and the solution acts as an electrical conductor. Electrical current, I Fig. 1. Migration of ions in solution Conductivity is typically measured in aqueous solutions of electrolytes. Electrolytes are substances containing ions, i.e. solutions of ionic salts or of compounds that ionize in solution. The ions formed in solution are responsible for carrying the electric current. Electrolytes include acids, bases and salts and can be either strong or weak. Most conductive solutions measured are aqueous solutions, as water has the capability of stabilizing the ions formed by a process called solvation. 5

7 1.1.2 Strong electrolytes Strong electrolytes are substances that are fully ionized in solution. As a result, the concentration of ions in solution is proportional to the concentration of the electrolyte added. They include ionic solids and strong acids, for example HC1. Solutions of strong electrolytes conduct electricity because the positive and negative ions can migrate largely independently under the influence of an electric field Weak electrolytes Weak electrolytes are substances that are not fully ionized in solution. For example, acetic acid partially dissociates into acetate ions and hydrogen ions, so that an acetic acid solution contains both molecules and ions. A solution of a weak electrolyte can conduct electricity, but usually not as well as a strpng electrolyte because there are fewer ions to carry the charge from one electrode to the other Definition of terms (i) Resistance The resistance of the solution (R) can be calculated using Ohm s law V = I * R R= V/I Where: V = voltage (volts) 1 = current (amperes) R = resistance of the solution (ohms) 6

8 (ii) Conductance Conductance (G) is defined as the reciprocal of the electrical resistance (R) Of a solution between two electrodes. G=l/R (S) The conductivity meter in fact measures the conductance, and displays the reading converted into conductivity. (iii) Cell constant This is the ratio of the distance (d) between the electrodes to the area (a) Of the electrodes. K=d/a K = cell constant (cm-1) a = effective area of the electrodes (cm2) d = distance between the electrodes (cm) (iv) Conductivity Electricity is the flow of electrons. This indicates that ions in solution will conduct electricity. Conductivity is the ability of a solution to pass current. The conductivity reading of a sample will change with temperature. K=G*K 0= conductivity (S/cm) G = conductance (S), where G = 1/R K = cell constant (cm-1) Resistively This is the reciprocal of the conductivity value and is measured in ohm*cm. It is generally limited to the measurement of ultra pure water, the conductivity of which is very low. (v) Calibration Determination of the cell constant required to convert conductance readings into conductivity results. Standard solution 7

9 A solution of known conductivity that is used to calibrate the conductivity measuring chain. (vi) Reference temperature Conductivity readings are often referenced to a specific temperature, typically 20 C or 25 C, for comparative purposes. Automatic temperature correction Algorithms for automatic conversion of sample conductivity to a reference temperature. Cable correction The cable correction takes into account the cable resistance and the cable capacitance. Gm = Gs/l+(Re.Gs) Gm = measured conductance (siemens) Gs = solution conductance (siemens) Rc = cable resistance (Q) Cable resistance A cable has a given length, therefore a given resistance. It induces error on the result when the resistance of the solution is low, i.e. at high conductivity. The cable resistance only influences measurements with 2 or 3-pole cells. For the 4-pole cells the cable resistance has no influence, so if during programming of the conductivity meter a value is demanded, enter zero. (vii) Cable capacitance A cable of a given length has a given capacity. The cable capacitance influences low Conductance measurements (below 4jiS). Entering a value of cable capacitance in the conductivity meter allows this influence to be corrected. 8

10 1.2 BASIC RELATIONSHIPS Materials containing charged particles that are free to move through the material exhibit the property of Electrical conductivity. When such materials are brought under the effect of a dc voltage, the charge particles experience a force, which is along the electric field opposite in direction to their change. The resulting motion the charged particles constitute an electric current. For a given applied electric field, the conductivity is directly proportional to the current produced. Therefore, the extent of conductivity of an electrolytic solution depends upon concentration, charge & mobility of the constituent charged particles A changed particle in a liquid or a solid nude the influence of electric field, quickly attains a limiting average velocity of motion in the direction of the field opposite to the sign of its charge. The velocity V, (i may be an electron or ion) is given by. V, (cm/s) = p, E (1.1) Where (J, is the particles mobility and E is the electric field strength *V/cm). Ji= V,Nj Q, (1.2) Where N, q, are the number of i particles per cubic cm & the columbic charge on each particle respectively. A change in sign of q, results a change in the sign of V resulting in J, being always positive irrespective of the particles sign. J,= EN, q, p, (1.3) 9

11 1.2.1 (a). Ionic Conductivity When we talk about conductivity, we have to know about the available media through which electricity passes. The typical media are Solids, Liquids, and Gasses. When current flows through solid the charge carriers are electrons. So, this type of conductivity is called electron conductivity. But in case of liquids current is carried by only ions (+ve, -ve). So, this type of conductivity is called Ionic Conductivity. The net current density T of the individual current density of charge carriers in the material under consideration in given by J = zn Ji = E I" N, q, M, (1.4) <=i i=i The current density per unit electric field gives electrical conductivity K K = J/E (1.5) The combination of equations (1.4 &A 1.5) gives the following relation. K-I" N, q, p, (1.6) 1=1 The iron of above equation it can be observed that any change in the substance, that affects the concentration or mobility of any one of the charge carries will affect the conductivity of the substance. Temperature is an important parameter that affects the conductivity of majority of substances. For example, electrons are the charge carriers in metallic conductors. The increase in temperature results in the decrease in conductivity. In the case 10

12 of semiconductors, an increase in temperature leads to an increase in the concentration of holes and electrons. This shows that the temperature effect on conductivity for semiconductors is opposite to that of metals. The effect of temperature on the conductivity of ionic solutions is a complex analysis. This analysis is described as follows. The concentration of solutions in normally expressed in the units of ions/cc. But it is a useful practice to express in mol/ml. The relation between number of particles per cubic cm (Ni), molar concentration Ci and Avogadro s number N by the relation. Ni = CM 1000 (1.7) The equation for total current density Ji can be expressed as Ji = E CM 1000 /qi/p (1.8) The charge on an ion qi is given by qi = Zi qe Where Zi is the charge number of the ion and qe is the unit electron charge in coulombs. The quantity N qe is defined as faraday (F). Therefore, qi 1 Zi! F N (1.9) Hence the individual ion current density can be expressed as Ji = E CiF 1000 Zi (1.10) 11

13 Considering, contributions from all species, the net conductivity is given by K= 1000 XCi zi pi (1.11) Consider a simple salt dissolved in a solution, then due to solvation and dissociation of the salt, cations & anions are produced, which act as charge carriers. Hence, the expression for conductance may be elaborated as K=i^o[c+lZi+I ^++C+-IZLI ^ (L12) Assuming that the salt is completely dissociated and electrical neutrality is maintained, normality of solution C* is given by C+ Zi+ =C. Zi (1.13) The equivalent conductance of the salt solution whether the salt is completely dissociated or not is defined as A = 1000 K C* (1.14) It follows from above equation that A depends on the degree of dissociation of the salt and has a lower value for lower can be studied by measuring A as a functions of C*. [1,2]. Further, the above equation does not require complete dissociation. is given by But it the salt is completely dissociated the conductance of the solution K = C* F 1000 (p++p. (1.15) 12

14 A = F(n++n.) (1.16) The ionic equivalent conductance for each ion is defined as X+ = F p+ i "l X.= Fp.i (1.17) X, = F p. i Substituting values for X+ and X. m equations 1.15 & 1.16 we get the conductance for complete dissociation as K= e*/1000 (X+& X ) and A = X+.&X. C 1000 (1.18) The factors on which the ionic equivalent conductance depends on the mobility of the ions, ion type and solution parameters (Solvent, solute concentration, temperature etc). At very low, solute concentrations & reaches a steady state value (limiting value) X. This value X often tabulated for the common ions in water solvent at specific temperatures. By applying the X values for different ions in the equation, it is possible to estimate the conductivity of a completely dissociated salt solution. Table 1.1 gives the limiting equivalent conductance of ions in water at 25 C. 13

15 Table Limiting equivalent conductance of ions in water at 298 K [6] Cations L + Scm2 mof1 Anions if OFT Scm2 mof (199.2) Lf 38.7 F 55.4 Na cr 76.4 K (73.5)* Br* 78.1 Rb T 76.8 Ag N03' 71.4 NH/ 73.4 C Mg2* 53.1 C ai3+ 3 ica2* 2 Fe2+ 2 -Fe3+ 3 Ni2+ 2 -Cu2+ 2 Zn2+ 2 -Ba2+ 2 -La Hg J_ Pb ICV hso Mn CN HC hcoct CH3C C2H5C C (69.3)* 63.6 iso po

16 -Ce j Fe (CN)g Tf Fe (CN) (CH3)2 nh2 + (CH3)3 NH* (CH3)4 N+ (n-bu)4 N+ I Co (CN) HC c6h5co For finite salt concentration, calculated values are indicative, but not exact. Accurate values can be calculated from A,0 values under circumstances that can be obtained by using equations developed by Onsager et al. [3]. At infinite dilution the ions are theoretically independent of other and therefore each ion contributed its part to the total conductance Therefore, Aoo^ n(a+)+ a-) (1-19) i=l Where A+ and A. represent the ionic conductance of cations and anions respectively at infinite dilution. At finite concentration, the ionic motilities are decreased due to interionic forces. In case of complete dissociation or actual ion concentrations, the sample contains many species of ions with each contributing to the total conductivity. Then, the net conductivity is expressed as K = 1 Za 0, ^ = ZQ Ci I Zi+I A, - --(1.20) iooo.-i 1000,

17 Where C, * and C, denote the normality and molarity (of the ionic species present in the solution) respectively. It is imperative that all ionic species present must be considered for the estimation of conductivity using above equation. Also, another point to be observed from above equation is that the variation in concentration or mobility of ionic species will result in change a K. Variations in temperature can affect ion dissociation, complication and solvation equilibrium and- solvent viscosity. This is turn affects the ion concentration and mobility. The combined effects are offer complex and rarely negligible [4], (b) Conductance When a voltage source of V volts is connected across the contacts of a current carrying conductor of length T cms, the changes are set into motion in response to the field. The electric field applied to the conductor is E=V/L. The current density J from equation K=J/E is given by J = EK = ( j) K (1.21) (cm2) The net current I is given by the product of current density and area a I = Ja = V(yT (1.22) Thus, the current flowing through a conductor is proportional to the Kq voltage across it. The proportionality constant is defined as the conductance G. Therefore 16

18 G = -j- = K. (j) (1.23) The V - I relationships is simple I = VG, which given by the reciprocal of resistance R of the conductor. In case of electrolytic solutions, the conductance of a cell filled with the sample solution is measured. The relationship between the conductance of an actual cell and the conductivity of the solution, and the geometry of the cell can be expressed as G = G.(y) From above it is defined that conductance of solution is directly proportional to the area a of electrodes and inversely proportional to the separation between the electrodes T. The conductivity can be expressed as K = G (-) Kr Where ( ) is called cell constant (H). The direct measurement of area a a and length.7 can be possible only in some specially designed conductivity cell. Usually, the effective area is not equal to the geometric area because same current is carried by ions, which are outside the volume of solution directly between electrodes. Generally, it is not possible to calculate theoretically the effective current path between electrodes except in restricted cases. The cell constant can be determined by filling the cell with a solution of own G\ This is because; the geometric measurement doesn t give the exact cell constant. [5]. The most commonly used solutions are KCl, and the conductivities for which are given in table

19 Table 1.2: conductivities of certain KCl Solutions Concentration Mass of KCl v jq3 Conductivity/cm 1 Mol dm'3 Mass of H20 29IK 298K / X D O I DIP TYPE Fig: Type of Conductivity Cells Specific resisitance Q Cm Specific conductnce ps.cmf1 100M 10M 100QK. I00K 10K A A A 1000 A 10k A 100k 1000k ULTRAPURE WATER GOOD QUALLITY DISTILLED WATER EXCELLENT QUALITY RAW WATER SEA WATER 0.05% Nad 30% H2S04 Fig 1.1 (b) Specific resistance and conductance ranges for some.typical materials 18

20 The following equation is used to calculate the net conductivity Conductivity = f Measured ' f Cell ' Conduc v tan ce y [consanl / K= 10'3 [ZD 1=l Ci Zi+ Z, ](H) (1.25) Fig. 1.1 depicts certain commercially available conductivity cells along with specific resistance a conductance ranges for typical materials. The terms specific conductance and conductivity are interchangeably used. The experimental set up required to measure the solution conductance and the instrumentation developed in the present study, form the core of the succeeding chapters. 1.3 APPLICATIONS OF CONDUCTIVITY MEASUREMENTS The measurements of conductivity will have a wide range of applications like 1. Conductivity measurements. 2. Resistivity measurements 3. TDS measurements. 4. Concentration measurements Conductivity measurements Measuring conductivity simply detects the presence of electrolytes and is therefore a non-specific measurement. Conductivity applications encompass for instance monitoring of water purity, drinking water and process water quality. It is also a rapid and inexpensive way of determining the ionic strength 19

21 of a solution. The conductivity Qis calculated using the conductance G and the cell constant K: = G K (S/cm) Resistivity measurements Resistivity measurements are used as a reliable indicator of ionic water quality, especially for ultrapure water (UPW) and more generally when a resistivity value is preferred to a conductivity value, for example when Checking for water contamination in organic solvents. The resistivity of a solution is calculated on the basis of the conductance G compensated for the cable resistance, cell capacitance and cell constant of the conductivity cell used. The resistivity is calculated as follows: p = l/kocm TDS measurements TDS measurements in the pulp and paper industry measure accurately and easily the total organic and inorganic dissolved solids in water. The TDS (Total Dissolved Solids) corresponds to the total weight of cations, anions and the undissociated dissolved species in one liter of water. The standard method 1 to determine TDS is to evaporate a measured sample of water to dryness at 180 C, under strict laboratory conditions, and carefully weigh the amount of dry solids remaining. The precision of the standard method depends on the nature of the dissolved species. The TDS method in a typical conductivity 20

22 meter offers a quicker and easier way of determining TDS by measuring the conductivity, then using a conversion factor to give TDS readings Concentration measurements Since the charge of the ions in solution facilitates the conductance of electrical current, the conductivity of a solution is highly (but not totally) proportional to its ion concentration. As conductivity is a non-specific technique, concentration calculation using conductivity measurements is valid for samples containing only the species of interest. The first step to measuring concentration is to know the conductivity of the solution as a function of the concentration of the specie of interest. This data can come from published conductivity vs. concentration curves for electrolytes, or from laboratory measurements. Over large conductivity ranges, conductivity will increase with concentration, but may reach a maximum and then decrease with increasing concentration. When using conductivity measurement to determine the concentration, it is important to work at constant temperature for calibration and measurements as the shape of the conductivity vs. concentration curve will change with temperature. 21

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Downloaded from I.I.T.Foundation - XI Chemistry MCQ #10 Time: 45 min Student's Name: Roll No.: Full Marks: 90 Solutions I. MCQ - Choose Appropriate Alternative 1. Molarity is the number of moles of a solute dissolved