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1 In this chapter we will study about: a. Types of solutions b. Units of concentrations of solutions c. Solid solutions d. Vapour pressure of liquids e. Raoult s law f. Relative lowering of vapour pressure g. Ideal and non-ideal solutions h. Azeotropic mixtures i. Colligative properties j. Elevation in boiling points k. Depression in freezing points l. Osmosis and osmotic pressure For more Study Material and Question Bank visit www. 1

2 Solution is a single phase homogeneous system, containing two or more substances. The component of a solution forming the larger proportion is referred to as solvent; while the other component which is present in minor proportion in solution is called solute. The composition of the solution may vary within wide limits. Examples of solutions are common salt in water, alcohol in water, sugar in water etc. TYPES OF SOLUTIONS Solutions may exist in any one of the three physical states solid, liquid or gaseous. Any state of matter viz., gas, liquid or solid may act as a solute or a solvent. Depending upon the physical state of solute and the solvent, there are nine types of solutions possible. These are given in the table. Solvent Solute Example Gas Gas mixture of gases, air Gas Liquid water vapours in air (humidity) Gas Solid sublimation of solid (e.g., camphor) into a gas, dust or smoke particles in air Liquid Gas CO 2 dissolved in water Liquid Liquid Mixture of miscible liquids, i.e., alcohol in water. Liquid solid salt in water, sugar in water Solid Gas phenomenon of adsorption of gases over metals ; hydrogen over palladium Solid Liquid mercury in copper, mercury in gold Solid solid homogeneous mixture of two or more metals (alloys, e.g., copper in gold, zinc in copper), coloured stones, gems etc. The most important types of solutions are those which are in the liquid phase and may be categorised as: 1. Solid in liquid solutions 2. Gas in liquid solutions and 3. Liquid in liquid solutions SOLID IN LIQUID SOLUTIONS The solubility of a solid in a liquid at any temperature is defined as the maximum amount of solid (solute) in grams which can dissolve in 100 g of the liquid (solvent) to form the saturated solution at that temperature. Factors that affect the solubility of a solid I. Nature of the solute and the solvent Solid dissolves in a liquid which is chemically similar to it. This is expressed by saying 'like dissolves like''. This statement implies that ionic compounds dissolve in polar solvents like water and are very little soluble or almost insoluble in nonpolar solvents like benzene, ether etc. Similarly non-polar compounds are soluble in non-polar solvents like benzene, ether, carbon tetrachloride etc. and are very little soluble in water. Common salt (an ionic compound) is more soluble in water than sugar (a covalent compound). Their solubilities in water are 5.3 moles per litre and 3.8 moles per litre respectively. For more Study Material and Question Bank visit www. 2

3 II. Iodine (a covalent substance) is more soluble in alcohol or carbon tetrachloride (covalent liquids) than in water. The reason for the behaviour observed above may be explained as follows: For ionic compounds being soluble in polar solvents, the solubility is on account of the fact that there are strong electrostatic forces of attraction between the ions of the crystal and the polar solvent molecules ; the negative ions being attracted by the positive poles of the polar solvent molecules and positive ions by the negative poles of the solvent molecules. Thus, the water molecules pull the ions of the crystal apart and the electrostatic forces of attraction existing between the ions of the crystal are cut off. Further, the ions are surrounded by water molecules which act as an envelope around the ions and prevent the recombination of the ions. The ions thus moving freely in the solution are said to be hydrated. Energy is required for splitting of the ionic compound into ions (called lattice energy) and energy is given out when ions get hydrated (hydration energy). A substance dissolves if there is net evolution of energy. Lowering of energy occurs if hydration energy is greater than the lattice energy. For non-polar compounds being soluble in non-polar solvents, the solubility is due to similar solute-solute, solute-solvent and solvent-solvent interactions. Temperature various ionic substances are divided into following categories a. Those whose solubility increases continuously with increase of temperature. Most of the substances like NaNO 3, NaCl, and KCl etc. fall into this category. The reason for this behaviour is that in case of all such substances, the process of dissolution is endothermic, i.e., Solute + Solvent Solution Applying Le Chatelier's principle, as the temperature is increased, equilibrium will shift in a direction in which the heat is absorbed i.e., in the forward dir; consequently more of the solute passes into the solution. b. Those whose solubility decreases continuously with increase in temperature. There are a few substances like ceric sulphate, lithium carbonate, sodium carbonate monohydrate (Na 2 CO 3. H 2 O) etc. whose solubility decreases with increase of temperature. Obviously it is due to the fact that the process of dissolution of these substances is exothermic i.e., accompanied by evolution of heat. GAS IN LIQUID SOLUTIONS Henry's Law Gases dissolve in liquids to form true solutions. Such solutions are examples of two component systems. The solubility of a gas depends on: (a) the temperature of the solution (b) the pressure of the gas over the solution, (c) the nature of the gas, and (d) the nature of the solvent. Substances which have similar chemical characteristics are readily soluble in each other than the substances which have different chemical characteristics. For more Study Material and Question Bank visit www. 3

4 The solubility of different gases in the same solvent (say water) varies considerably. It has been observed that gases like nitrogen, oxygen etc. dissolve to a small extent than the gases like ammonia, sulphur dioxide, hydrogen chloride etc. The solubility of latter gases with water to form ammonium hydroxide, sulphurous acid respectively. NH 3 + H 2 O NH OH SO 3 + H 2 O H 2 SO 3 HCl + H 2 O H 3 O + + Cl The solubility of a gas is usually determined by measuring the volume rather than the mass that dissolves. It is frequently expressed in terms of Busen absorption coefficient (α) which is defined as the volume of the gas at STP (273 K and 1 atm pressure) dissolved by unit volume of the solvent at the given temperature under a partial pressure of 1 atmosphere of the gas. If V o is the volume of the gas that dissolves reduced to STP, V is the volume of the solvent and p the partial pressure of the gas in atmosphere, then the absorption coefficient α, is given by : α = V o / V p Effect of temperature on solubility Gases generally dissolve in a liquid with evolution of heat. Hence Le-Chatelier's principle predicts that an increase in temperature result in a decrease in solubility of gas. It is for this reason that gases are readily expelled from solutions on boiling. However, there are certain gases such as hydrogen and inert gases in non-aqueous solvents where the solubility increases with increase in temperature. At constant pressure variation of solubility with temperature is given by: = where S is the solubility in mol dm 3 of the gas in the solvent and ΔH is the enthalpy of the solution. If ΔH is regarded as temperature independent then integration of the above equation within limits gives: In S S = H RT T (T T where S 2 and S 1 are the solubilities at T 2 and T 1 respectively. Effect of pressure on solubility Henry's Law Le Chatelier's principle predicts that the increase of pressure on solubility of a gas should increase. Consider a system at equilibrium, containing a gas in contact with its solution in a given solvent. On increasing the pressure, the volume of the gas will be reduced and hence an increase in solubility will result from an increase of pressure. William Henry in 1803 made a systematic investigation of the solubility of a gas in a liquid and observed the following law known as Henry's law. The law states that the mass of a gas dissolved by unit volume of a solvent at constant temperature is directly proportional to the pressure of the gas with which it is in equilibrium. If X 2 is the mole fraction of the gas dissolved by unit volume of the solvent at equilibrium pressure P, then : X 2 α P or X 2 = K' H P P = K H X 2 (i) Where, K H is a proportionality constant known as Henry's law constant. The magnitude of K H depends on the nature of the gas, solvent and units of pressure. For more Study Material and Question Bank visit www. 4

5 Equation (i) is an equation of a straight line passing through the origin. Thus a plot of solubility of the gas against equilibrium pressure at a given temperature gives a straight line passing through the origin. This shows the validity of Henry's law. Different gases have different K H values at the same temperature. This suggests that K H is a function of the nature of gas. The following TABLE gives K H values of some common gases at specified temperatures. Values of Henry's Law constant (K H ) for some selected gases in water Gases Temperature (K) K H (bar) He H N N O O It is obvious from equation (1) that higher the value of K H at a given pressure, lower is the solubility of the gas in the liquid. It can be seen from the TABLE that K H value for both N 2 and O 2 increases with increase of temperature indicating that solubility of gases decreases with increase of temperature. It is due to this reason aquatic species are more comfortable in cold waters than warm waters. Applications of Henry's law Henry's law finds several applications in industry and explains some biological phenomena. Notable among these are: 1. To increase the solubility of CO 2 in soft drinks and soda water, the bottle is sealed under high pressure. 2. To minimise the painful effects accompanying the decompression of deep sea divers, oxygen diluted with less soluble helium gas is used as breathing gas. 3. In lungs where oxygen is present in air with high partial pressure, haemoglobin combines with oxygen to form oxyhaemoglobin. In tissues where partial pressure of oxygen is low, oxyhaemoglobin releases oxygen for utilization in cellular activities. Limitations of Henry's law Henry's law is applicable only if the following conditions are satisfied. 1. The pressure should be low and the temperature should be high i.e., the gas should behave like an ideal gas. 2. The gas should not undergo compound formation with the solvent or association or dissociation in the solvent. For example, the law is not applicable in the case of dissolution of ammonia in water, because it undergoes compound formation followed by dissociation. NH 3 (g) + H 2 O (l) NH 4 OH (aq) NH 4 OH (aq) NH + 4 (aq) + OH (aq) similarly, the law is not applicable to the dissolution of HCl gas in water because it For more Study Material and Question Bank visit www. 5

6 undergoes dissociation after dissolution. HCl(g) + aq H + (aq) + Cl (aq) SOLUBILITY OF SOLIDS IN LIQUIDS The solubility of solids in liquids varies greatly with the nature of the solid and liquid, temperature and to a much lesser degree the pressure of the system. When a solid (solute) is dissolved in a liquid solvent at a given temperature, the dissolution continues until the solution attains a certain maximum concentration. The solution at this stage is said to be saturated solution at that temperature. The maximum amount of solute that can be dissolved by the solvent at a particular temperature is called its solubility. Thus, solubility of a substance at a given temperature is defined as the amount of solid that dissolves in 100 g of the solvent at a given temperature to form a saturated solution. The solubility is also expressed as molar solubility which gives the molar concentration of a substance in a saturated solution. For example, if the concentration of glucose in its saturated solution at 20 C is 6 mol L 1. Thus, the concentration of the solute has the highest value in a saturated solution. In other words, a saturated solution represents the limit of solute's solubility in a given quantity of solvent. The temperature has a marked effect on the solubility of a solid in a solvent. The solubility may increase or decrease with increase in temperature. Thus, in General: a. If solute dissolves with absorption of heat (endothermic process), the solubility increases with rise in temperature. b. If the solute dissolves with evolution of heat (exothermic process), the solubility decreases with rise in temperature. However, for some substances the solubility behaviour is not regular. For example, the solubility of sodium sulphate (Na 2 SO 4 ) increases up to a certain temperature and then decreases as temperature is further raised. The temperature corresponding to the break in solubility curve is known as the transition temperature. For example, the solubility curve of sodium sulphate shows a sharp break at 32.8 C. This is due to change in one solid form into another solid form. For example in the case of Na 2 SO 4 10 H 2 O, at 32.8 C, there is an equilibrium between solid decahydrate Na 2 SO 4 10 H 2 O and anhydrous Na 2 SO 4. Below this temperature, only sodium sulphate decahydrate (Na 2 SO 4 10 H 2 O) exists while above this temperature, anhydrous sodium sulphate (Na 2 SO 4 ) exists. The effect of pressure on the solubility of solids in liquids is generally very small. For example, a change of 500 atm in pressure increases the solubility of sodium chloride in water only by 2.3%. LIQUID IN LIQUID SOLUTIONS When two liquids are mixed, the mixture may be of the following types: 1. The two components may be almost immiscible In this case; one of the liquid is polar, while the other is non-polar nature. For example benzene and water. For more Study Material and Question Bank visit www. 6

7 2. The miscibility of the component may be partial if the intermolecular attraction of one liquid is different from intermolecular attraction of the other, there may be partial miscibility of the two liquids. For example ether and water. 3. The two components may be completely miscible In this case, the liquids are of the same nature, i.e., they are either polar (like alcohol and water) or non-polar (like benzene and hexane). Cause of Miscibility of Liquids Chemically alike substances dissolve in one another more freely as compared to others. For example, alkanes are miscible in all proportions with one another. Alkanes however are, not miscible with water because they cannot form H-bonds with water molecules. 1. Dipole-Dipole interactions also play an important role in forming liquid solutions. 2. Molecular sizes of liquids which are mutually soluble are also approximately the same. UNITS OF CONCENTRATIONS OF SOLUTIONS The concentration of a solution may be defined as the amount of solute present in the given quantity of the solution. It is usually expressed in any one of the following ways. Mass Percentage The mass percentage of a component in a given solution is the mass of the component in 100 g of the solution. If m A and m B are the masses of the two components A and B respectively, in a binary solution, then: Mass percentage of A = m 100 m m Volume Percentage Volume percentage is defined as the volume of the component per 100 parts by volume of solution. If V A ml is the volume of one component A and V B ml is the volume of the second component B, then: Volume percentage of A = V 100 V V Parts per million (ppm) When a solute is present in very minute amounts, the concentration is expressed in parts per million abbreviated as ppm. It is the parts of a component per million parts of a solution. It is expressed as: Parts per million = mass of solute 10 Mass of solution This mode is generally used to express very low concentration such as hardness of water or concentration of chlorine in public supply of potable water. The concentration of atmospheric pollutants in cities is often expressed in terms of mg ml 1. For more Study Material and Question Bank visit www. 7

8 Molarity (M) It is the number of moles of the solute dissolved per litre of the solution. If n B moles of solute are present in V litres of solution, then: Molarity = n number of moles of solute = V volume in litres of solution = ( ) ( ) A solution having molarity one is called molar solution. Such a solution contains one mole of solute per litre of solution. Molarity is expressed in mole dm 3. Molarity of a solution changes with change in temperature. Molality (m) It is the number of moles of the solute dissolved per 1000 g (= 1 kg) of the solvent. Molality (m) = number of moles of solute weight of solvent in kg number of moles of solute x 1000 = weight of solvent in gm If n B is the number of moles of solute and W A is the weight of the solvent in grams, then molality of the solution is: ( ) = 1000 A solution containing one mole of solute per 1000 g of solvent has molality equal to one is called a molal solution. Molality is expressed in units of moles per kilogram ( mol kg 1 ). Molality is considered better for expressing the concentration as compared to molarity because the molarity changes with temperature because of expansion or contraction of the liquid with temperature. However, molality does not change with temperature because mass of the solvent does not change with change in temperature. Normality (N) It is the number of gram equivalents of the solute dissolved per litre of solution. ( ) = A solution having normality equal to one is called a normal solution. Such a solution contains one gram equivalent of solute per litre of solution. A decinormal solution contains 0.1 g equivalents of solute per litre of solution. A seminormal solution contains ½ g equivalents per litre. A centinormal solution contains 0.01 g equivalents per litre. Relationship between Normality and Molarity of solution The molarity and normality of the solution are related as: = For more Study Material and Question Bank visit www. 8

9 For acids, Normality = Molarity x Basicity of acid Basicity is the number of H + ions furnished by each molecule of acid in aqueous solutions. For bases, Normality = Molarity Acidity of a base. Acidity is the number of OH ions furnished by each molecule of base in solutions. Mole fraction (X) Mole fraction of any component in a solution is the ratio of the number of moles of that component to total number of moles of solute plus solvent in solution. Let us suppose that a solution contains n A moles of solvent and n B moles of solute: The sum of the mole fractions must be equal to 1 i.e., + = + Thus, if the mole fraction of one component is known, that of the other can be calculated. For example, X A = 1 X B or X B = 1 X A Formality (F) Formality of a solution may be defined as the number of gram formula masses of ionic solute dissolved per litre of the solution. ( ) = Formality is used to express the concentration of the ionic solids which do not exist as molecules but exist as network of ions. A solution containing one gram formula mass of the solute per litre of solution has formality equal to one and is called formal solution. Formality of a solution changes with change in temperature. SOLID SOLUTIONS Solid solutions are formed by mixing two solid components. Solid solutions are of two types: substitutional solid solutions and interstitial solid solutions. In substitutional solid solutions, atoms, molecules or ions one substance takes the place of similar species of other substance in its crystal lattice. (a) Substitutional solid solution in which particles of the solute replace particles in the host lattice (solvent). Brass, bronze, Monel metal and steel are familiar examples of this type of solid solution. Interstitial solid solutions constitute the other type and are formed by placing atoms of one kind into voids or interstices that exist between atoms in the host lattice. (b) Interstitial solid solution in which the solute particles fit in spaces between particles of the host lattice (the solvent) Tungsten carbide WC, an extremely hard substance, is an example of interstitial solid solution. Here tungsten atoms are arranged in a face-centred cubic pattern with carbon + = = = 1 For more Study Material and Question Bank visit www. 9

10 atoms surrounded by six tungsten atoms at the vertices of an octahedron. Tungsten carbide has many industrial uses in making of cutting and grinding tools. VAPOUR PRESSURE OF LIQUIDS When a liquid is kept in an open vessel, its fastest moving molecules escape into the free space as gas or vapour. This process in which liquids automatically evaporate is known as evaporation. If the liquid is in the open vessel, evaporation continues, till the entire liquid changes into vapour form. If the liquid is kept in a closed vessel, evaporation starts. However, some of the vaporised molecules possessing low energies, are likely to be attracted on striking the surface of the liquid. This process of conversion of vapour molecules into liquid phase is known as 'condensation of vapour''. Thus in a closed vessel, two opposing processes of evaporation and condensation take place simultaneously, till a state of dynamic equilibrium is attained. At this point, the relative amounts of the liquid and the vapour become constant, the molecules in the vapour phase exerts pressure, called equilibrium vapour pressure or simply vapour pressure. Thus, vapour pressure of a liquid at a given temperature is defined as the pressure of the vapour in equilibrium with the liquid at that temperature. The vapour pressure of a liquid may be determined by using static method (Fig) in which the liquid is caused to evaporate in vacuum and the depression of mercury column, at equilibrium state, is noted as vapour pressure. Every pure liquid exerts a vapour pressure in the space above it The vapour pressure of a liquid depends on: Nature of liquid: Liquids, which have weak intermolecular forces are volatile and have greater vapour pressure. For example, dimethyl ether has greater vapour pressure than ethyl alcohol. Temperature: Vapour pressure increases with increase in temperature. This is due to the reason that with increase in temperature more molecules of the liquid can go into vapour phase. Lowering of Vapour pressure Consider the addition of a small amount of a non-volatile solute to the liquid (solvent) to form a solution. In such a case the vapour pressure of the solution is because of solvent, as solute is non-volatile. It is found that the vapour pressure of the solution is less than that of pure solvent. Explanation: The lowering of vapour pressure can be explained on the basis of the surface area of the liquid from which evaporation occurs. In the case of solution, a part of the liquid surface is occupied by solute particles; therefore evaporation of liquid will take place from a lesser surface area. In other words, the particles (or molecules) of the liquid will now have a less tendency to change into vapours. This will, therefore, result in lowering of vapour pressure. RAOULT'S LAW Raoult carried out a series of experiments to study the vapour pressure of a number of binary solutions. On the basis of the results of experiments, he proposed a generalisation called Raoult's law, which states that: the vapour pressure of a solution For more Study Material and Question Bank visit www. 10

11 containing non-volatile solute is directly proportional to the mole fraction of the solvent. In case of solution containing two components A (volatile solvent) and B (non-volatile solute), the vapour pressure of the solution is given by : Vapour pressure of solution α Vapour pressure of solvent in solution P A α Mole fraction of solvent X A P A α X A P A = k X A where k is a proportionality constant. For pure liquids, X A = 1; then k becomes equal to the vapour pressure of the pure solvent which is denoted by P o A. Thus, P A = P o A X A P solution = P pure solvent mole fraction of solvent In a solution of two miscible volatile liquids A and B, the partial vapour pressure P A of a liquid is proportional to its mole fraction X A and the partial vapour pressure P B of liquid B is proportional to its mole fraction X B. Thus, P A α X A P A = P o A X A Also, P B = P o B X B Where, P o A and P o B are the vapour pressures of pure components A and B respectively. The relationship is called Raoult's Law. It states that for a solution of two or more miscible volatile liquids, the partial vapour pressure of each component of the solution at a particular temperature is directly proportional to its mole fraction. According to Raoult's law a plot of P A against X A should give a straight line passing through P o A when X A = 1 (shown by broken lines I in Fig ) Similarly, a plot of P B against X B is a straight line passing through P o B when X B = 1 ( broken line II in Fig ). The total vapour pressure, P exerted by the solution is the sum of P A and P B as required by Dalton s Law of partial pressures. P = P A + P A or P = P o A X A + P o BX B = P o A(1 X B ) + P o BX B ( Since X A + X B = 1 ) = P o A P o A X B + P o B X B = (P o B P o A)X B + P o A.. (1) Similarly, by putting X B = 1 X A, we can arrive at the following relation : P = (P o A - P o B)X A + P o B. (2) Since P o A and P o B are constants at a particular temperature, therefore equations (1) and (2) reveal that the total pressure P is linear function of X B ( or X A ). This means that a plot of P vs X B or P vs X B should be a straight line. The variation of P with mole fraction is given by the solid line III in the graph. The solutions which obey Raoult's law are called ideal solutions. For such solutions, the For more Study Material and Question Bank visit www. 11

12 vapour pressure of the solution always lies between the vapour pressures of the pure components. RELATIVE LOWERING OF VAPOUR PRESSURE When a non-volatile solute is added to a solvent, the vapour pressure of the solution decreases. Let X A be the mole fraction of the solvent, X B the mole fraction of the solute and P o A be the vapour pressure of the pure solvent and P be the vapour pressure of solution. Since the solute is non-volatile, there will be no contribution of solute to the vapour pressure and the vapour pressure of the solution will be only due to the solvent. Therefore, in such cases, the vapour pressure of the solution (P) will be equal to the vapour pressure of the solvent (P A ), over the solution, i.e., P = P A But according to Raoult's law, the vapour pressure of the solvent is given as: P A = P o A X A or P = P A = P o A X A. (1) Since X A is always less than one, the vapour pressure of the solution is always less than P o A, i.e., vapour pressure of the pure solvent. But for a binary solution, X A + X B = 1 or X A = 1 X B Substituting in equation (1) we get: P A = P o A (1 X B ) = P o A P o A X B P o A - P A = P o A X B Here P o A P A (difference in vapour pressure of pure solvent and solution) represents the lowering in vapour pressure on the formation of a solution. Now, by dividing the lowering in vapour pressure with the vapour pressure of pure solvent, i.e., (P o A P A ) / P o A, we get the relative lowering in vapour pressure. This is also an alternate statement of Raoult's law. Thus, the Raoult's law in its modified form may be sated as: The relative lowering of vapour pressure of a solution containing a non-volatile solute is equal to the mole fraction of the solute in solution. According to equation (3), the relative lowering in vapour pressure depends only on the molar concentration of the solute (mole fraction ) and is independent of its nature. Therefore, relative lowering of vapour pressure is a colligative property. IDEAL AND NON-IDEAL SOLUTIONS The binary solutions may be of two types: 1. Ideal solutions 2. Non-ideal solutions Ideal Solutions An ideal solution may be defined as the solution which obeys Raoult's law over the entire range of concentration and temperature and during the formation of which no change in enthalpy and no change in volume takes place. For more Study Material and Question Bank visit www. 12

13 The condition for the formation of ideal solution are: It should obey Raoult's law, i.e., P A = P o A X A and P B = P o B X B ΔH mixing = 0 ΔV mixing = 0 There is no solution which behaves strictly as an ideal solution. However, the solutions in which solvent-solvent and solute-solute interactions are almost the same type as solvent-solute interactions behave nearly as ideal solutions. This type of solutions are possible if molecules of solute and solvent are almost of the same size and have identical polarity. For example, solutions of following pairs almost behave as ideal solutions. 1. n-heptane and n-hexane 2. Chlorobenzene and bromobenzene 3. Ethyl bromide and ethyl iodide 4. Carbon tetrachloride and silicon tetrachloride. In such solutions, the interactions between molecules remain almost of the same type before and after mixing, therefore such solutions are not accompanied by any change in enthalpy or volume, i.e., ΔH mixing = 0 and ΔV mixing = 0. For such solutions, the vapour pressure of the solution is always intermediate between the vapour pressures of pure components A and B, i.e., P o A and P o B.It may be noted that although most of the solutions show deviation from ideal behaviour, yet they behave as ideal solutions when the concentration of the solution is very low. In other words, most of the dilute solutions behave as ideal solutions. Non-Ideal Solutions The solutions which do not obey Raoult's law are called non-ideal solutions. Therefore for such solutions: P A P o A X A and P B P o B X B In non-ideal solutions, there is a noticeable change in the volume and heat energy when the two components are mixed. Most of the real solutions are non-ideal because they deviate from ideal behaviour to more or less extent. Thus for non-ideal solutions: i) P A P o A X A and P B P o B X B i.e., none of the components obey Raoult's law. ii) ΔH mixing 0 iii) ΔV mixing 0 The non-ideal solutions are classified into two types: 1. Solutions showing positive deviations. 2. Solutions showing negative deviations. Non-ideal Solutions showing Positive deviations Consider binary solutions of two components A and B. If A B interactions in the solution are weaker than A A and B B interactions in the two liquids forming the solution, then the escaping tendency of A and B types of molecules from the solution becomes more than from the pure liquids. As a result, each component of the solution has a partial vapour pressure greater than For more Study Material and Question Bank visit www. 13

14 expected on the basis of Raoult's law. The total vapour pressure will be greater than the corresponding vapour pressure expected in the case of ideal solution of the same composition. The boiling points of such solutions are lowered. This type of behaviour of solution is described as positive deviation from Raoul's law. Mathematically, it may be represented as: P A > P o A X A and P B > P o B X B The positive deviations have been shown in Fig in which dotted lines show the ideal behaviour upon mixing, while, the thick lines exhibit the actual behaviour. A few examples of solution showing positive deviations are: 1. cyclohexane and ethyl alcohol 2. carbon disulphide and acetone 3. acetone and benzene 4. chloroform and carbon tetrachloride For solutions with positive deviations, there is an intermediate composition for which the vapour pressure of the solution is maximum and the boiling point is minimum. At this composition, the solution distils at constant temperature without change in composition. A solution which distils without change in composition at a particular temperature is called azeotrope or azeotropic mixture. The azeotrope in solutions with positive deviations is called minimum boiling azeotropes. Explanation for positive deviations Consider a solution of ethyl alcohol and cyclohexane. In alcohol, the molecules are held together due to hydrogen bonding as shown below: When cyclohexane is added to ethyl alcohol, the molecules of cyclohexane tend to occupy the spaces between ethyl alcohol molecules. Consequently some hydrogen bonds in alcohol molecules break and the attractive forces in alcohol molecules are weakened. For such solutions, there is an increase in volume i.e., ΔV mixing is positive and there is also absorption of certain amount of energy to overcome the hydrogen bonding i.e., ΔH mixing is positive. There is also a slight increase in vapour pressure on mixing. NON-IDEAL SOLUTIONS SHOWING NEGATIVE DEVIATIONS In such deviations, the A B interactions are stronger than A A and B B interactions in the two liquids forming the solution Due to stronger A B interactions, the escaping tendency of A and B types of molecules from the solution becomes less than from pure liquids. Consequently, each component of the solution has a partial vapour pressure less than expected on the basis of Raoult's law. As a result, the total vapour pressure becomes less than the corresponding vapour pressure expected in the case of ideal solution. The solutions are said to have negative deviations from Raoult's law as: P A < P o A X A and P B < P o B X B The negative deviations have been shown in Fig 9 in which dotted lines show the ideal behaviour upon mixing, while the thick lines show the actual behaviour. A few solutions showing negative deviations are: 1. Acetone and chloroform For more Study Material and Question Bank visit www. 14

15 2. Chloroform and nitric acid 3. Chloroform and benzene For solutions with negative deviations, there is an intermediate composition for which vapour pressure of the solution is minimum and hence boiling point is maximum. At this composition, the solution distils at constant temperature without change in composition. So it is an azeotrope. The azeotrope in solutions with negative deviation is called maximum boiling azeotrope. Explanation for negative deviations Consider a solution of acetone and chloroform. When acetone and chloroform are mixed, there are new attractive forces due to intermolecular hydrogen bonding. Thus the attractive forces become stronger and the escaping tendency of each liquid from the solution decreases. For such solutions, there is a decrease in volume upon mixing, i.e., ΔV mixing is also negative and due to the energy released on account of hydrogen bonding ΔH mixing is also negative. The vapour pressure of the solution is also less than what is expected for an ideal solution. Examples for non-ideal solutions showing positive and negative deviations are given in the following TABLE. Solutions showing positive deviations Solutions showing negative deviations CH 3 COCH 3 + CS 2 CH 3 COOH + C 5 H 5 N (CH 3 ) 2 CO + C 2 H 5 OH CHCl 3 + (CH 3 ) 2 CO C 6 H 6 + (CH 3 ) 2 CO CHCl 3 + C 6 H 6 CCl 4 + CHCl 3 CHCl 3 + (C 2 H 5 ) 2 O CCl 4 + C 6 H 5 CH 3 H 2 O + HCl H 2 O + C 2 H 5 OH H 2 O + HNO 3 CH 3 CHO + CS 2 (CH 3 ) 2 CO + C 6 H 5 NH 2 AZEOTROPIC MIXTURES When a binary solution of volatile liquids is boiled, its vapours, in general do not have the same composition of the components as that in solution. The mole fraction of the more volatile component is higher in vapours. This forms the basis of fractional distillation. But many binary solutions at definite compositions behave like pure liquids For more Study Material and Question Bank visit www. 15

16 because their vapours have same composition of the two components as in solution. Such solutions are called azeotropic mixtures or azeotropes. Thus azeotropes are defined as the mixture of liquids which boil at constant temperature like pure liquid and possess same composition of components in liquid as well as in vapour phase. Azeotropes are called constant boiling mixtures because whole of the azeotrope changes into vapour state at constant temperature and their components cannot be separated by fractional distillation. Azeotropes are of two types: 1. Minimum boiling azeotropes 2. Maximum boiling azeotropes Minimum boiling azeotropes These azeotropes are formed by those liquid pairs which show positive deviation from ideal behaviour. Such azeotropes have boiling points lower than either of the components. Some examples are given below : Components mass % Boiling point (K) of B A B B A B Azeotrope H 2 O C 2 H 5 OH H 2 O C 3 H 7 OH CHCl 3 C 2 H 5 OH (CH 3 ) 2 CO CS Maximum boiling azeotropes Azeotropes are formed by those liquids which show negative deviation from ideal behaviour. Such azeotropes have boiling points higher than either of the components. Some examples are given below : Components mass % of B Boiling point (K) A B B A B Azeotrope H 2 O HCl H 2 O HNO H 2 O HClO Note Mole fraction of a component in vapour phase may be calculated as: h = Mole fraction of compound B in vapour phase = COLLIGATIVE PROPERTIES The dilute solutions of non-volatile solutes exhibit certain characteristic properties which do not depend upon the nature of the solute but depend only on the number of particles (molecules or ions) furnished by the solute, i.e., on the molar concentration of the solute. These are called colligative properties. The properties of a solution which For more Study Material and Question Bank visit www. 16

17 depend only on the number of solute particles but not on the nature of the solute are called colligative properties. Some of the colligative properties are : 1. Relative lowering of vapour pressure 2. Elevation of boiling point 3. Depression of freezing point 4. Osmotic pressure Relative Lowering of Vapour Pressure When a non-volatile solute is added to a solvent, the vapour pressure of the solution decreases. Let X A be the mole fraction of the solvent A, X B the mole fraction of the solute B and P o A be the vapour pressure of the pure solvent and P be the vapour pressure of solution. Since the solute is non-volatile, there will be no contribution of solute to the vapour pressure and the vapour pressure of the solution will only be due to the solvent. Therefore, in such cases, the vapour pressure of the solution (P) will be equal to the vapour pressure of the solvent (P A ), over the solution, i.e., P = P A But according to Raoult's law, the vapour pressure of the solvent is given as : P A = P o A X A or P = P A = P o A X A (1) Since X A is always less than one, the vapour pressure of the solution is always less than P o A i.e., vapour pressure of the pure solvent. But for a binary solution : X A + X B = 1 or X A = 1 X B Substituting in equation (1) we get : P A = P o A (1 X B ) P A = P o A P o A X B P o A P A = P o A X B or, Hence P o A P A (difference in vapour pressure of pure solvent and solution) represents the lowering of vapour pressure on the formation of a solution. Now by dividing the lowering in vapour pressure with vapour pressure of pure solvent, i.e., (P o A P A ) / P o A, we get the relative lowering in vapour pressure. This is also an alternate statement of Raoult s law. Thus, the Raoult's law in its modified form may be stated as: Relative lowering in vapour pressure of an ideal solution (dilute solution) is equal to the mole fraction of the solute at a given temperature. According to Equation (3), the relative lowering in vapour pressure depends only on the molar concentration of the solute (mole fraction) and is independent of its nature. Therefore, relative lowering of vapour pressure is a colligative property. Calculation of Molecular mass from Relative Lowering of Vapour pressure Molecular mass of non-volatile substance can be determined from relative lowering of vapour pressure. A known mass For more Study Material and Question Bank visit www. 17

18 (W B ) of the solute is dissolved in a known mass of the solvent (W A ), to prepare a dilute solution and relative lowering of vapour pressure is determined experimentally. Knowing the molecular mass of the solvent (M A ), the molecular mass of solute (M B ) can be determined as shown under : Relative lowering of vapour pressure is given by : For dilute solutions, W B / M B << W A / M A and hence in the above expression, W B /M B may be neglected in the denominator as compared with W A /M A. in this equation, all the parameters except M B are known and hence M B can be calculated. ELEVATION IN BOILING POINT The boiling point of a liquid is the temperature at which its vapour pressure becomes equal to atmospheric pressure (i.e., 760 mm of Hg). Since the vapour pressure of a solution, containing non-volatile solute is less than that of solvent, it means that the solution has to be heated to a higher temperature so that its vapour pressure becomes equal to atmospheric pressure. Thus the boiling point of the solution is always higher than that of the pure solvent. The difference in the boiling point of the solution (T 1 ) and pure solvent (T o ) is called Elevation in Boiling Point ( ΔT b ).The elevation in boiling point on the addition of a non-volatile solute to a solvent can be easily illustrated graphically (Fig ). The curves AB and CD are the vapour pressure curves for the pure liquid solvent and solution of a For more Study Material and Question Bank visit www. 18

19 non-volatile solute with solvent respectively. It is evident from the plot that at each temperature the vapour pressure of the solution is lower than that of the pure solvent and thus the vapour pressure curve for the solution runs below that of the pure solvent. At temperature T o, the vapour pressure of the pure solvent becomes equal to the atmospheric pressure and thus, T o is the boiling point of the pure solvent. The vapour pressure of the solution at T o is much less than the atmospheric pressure and therefore, it is necessary to heat the solution to a higher temperature, T 1, in order that its vapour pressure becomes equal to the atmospheric pressure. Thus T 1 is the boiling point of the solution. Thus it is clear that the solution boils at a higher temperature than the pure solvent. Evidently, (T 1 T o ) or (ΔT b ) is the elevation in boiling point. Since its magnitude is determined by the vapour pressure lowering, the elevation in boiling point is also proportional to the solute concentration. Thus, ΔT b α ΔP α X B For dilute solutions, W B / M B << W A /M A and hence in the above expression, W B /M B may be neglected in the denominator as compared with W A /M A. Therefore, Since (W B / M B ) = n B If W A is the weight of solvent in kg, then (n B /W A ) is equal to molality (m) of the solution. ΔT b = k M A m Here k and M A are constants and hence their product, i.e., k M A is replaced by another constant K b. ΔT b = K b m. (4) where K b is molal elevation constant or molal ebullioscopic constant of the solvent. From equation (4) it is clear that, the elevation of boiling point depends upon the relative number of moles of solute and solvent, but does not depend upon the nature of solute, so it is a colligative property. When molality (m) of the solution is one, Equaion (4) becomes : ΔT b = K b Hence, molal elevation constant of the solvent may be defined as the elevation in its boiling point when one mole of non-volatile solute is dissolved per kilogram ( = 1000 g) of solvent. The unit of K b are K kg mol 1. The value of K b depends only upon the solvent and is independent of the nature of solute and concentration of the solution. Some times the value of K b is given for 100 g of the solvent. In such an event this constant is ten times the value of the molal elevation constant. K b is related to molar enthalpy of vaporisation of solvent according to the For more Study Material and Question Bank visit www. 19

20 relation: Where M A = Molecular mass of the solvent, R = Universal gas constant T b = Boiling point of pure solvent ΔH vap = Enthalpy of vaporisation of solvent. The Molal Elevation constant K b for different solvents are given in the following TABLE. Solvent Boilig point (K) K b (K kg mol 1 ) Water Carbontetrachloride Carbon disulphide Chloroform Ethyl alcohol Ether Acetic acid Camphor Nitrobenzene Calculation of Molecular mass of an unknown solute from Elevation in Boiling point To calculate the molecular mass of an unknown non-volatile compound, a known mass (say W B g) of it is dissolved in a known mass (say W A g) of some suitable solvent and elevation in boiling point (ΔT b ) is determined. Let M B be the molecular mass of the compound. Then: Knowing K b, W B, W A and ΔT b the molecular mass of the compound can be calculated from the above relation. The method of determining molecular mass by the study of elevation in boiling point is known as Ebullioscopic method. DEPRESSION IN FREEZING POINT Freezing point is the temperature at which the solid and the liquid states of the substance have the same vapour pressure. It has been found that when a nonvolatile solute is added to a solvent, the freezingpoint of the solution is always lower than that of the pure solvent. This is illustrated in Fig. In the above Fig, the curve BC gives the vapour pressure For more Study Material and Question Bank visit www. 20

21 of the pure solvent. We know that the addition of a non-volatile solute lowers the vapour pressure and the curve AB gives the vapour pressure curve of the solution at different temperatures. The curve AB corresponds to the vapour pressure of solid solvent at different temperatures. The temperature corresponding to the point B, where the solid and liquid solvent meet (i.e., solid and liquid states have the same vapour pressure) represents the freezing point temperature of pure solvent (T o ). The temperature corresponding to the point A' where the solid solvent and liquid solution meet (i.e., solid and liquid states have the same vapour pressure) represents the freezing point temperature of the solution (T 1 ). Since T 1 is less than T o, this shows that the freezing point of the solution is less than that of pure solvent and the depression in freezing point (ΔT f ) is given as: ΔT f = T o T 1 It has been determined experimentally that the depression in freezing point of a solution is proportional to the molal concentration of the solution, i.e., ΔT f α m or ΔT f = K f m.. (5) where K f is the molal depression constant. It is also called molal cryoscopic constant. If m = 1 ; ΔT f = K f. Thus Molal depression constant is defined as the depression in freezing point for 1 molal solution, i.e., a solution containing 1 g mole of the solute dissolved in 1000 g of solvent. As K f is constant; ΔT f α m Thus, the depression in freezing point temperature is directly proportional to the molal concentration of the solute (i.e., number of molecules) and therefore, it is a colligative property. K f is related to the molar enthalpy of fusion as : where M A = Molecular mass of solvent R = Universal gas constant T f = freezing point of the pure solvent ΔH fusion = Enthalpy of fusion of the pure solvent. The molal depression constants of some solvents are given in the following TABLE Solvent Freezing point (K) K f (K kg mol 1 ) Acetic acid Benzene Camphor Carbondisulphide Carbon tetrachloride Chloroform Ether Ethyl alcohol Naphthalene water Nitrobenzene For more Study Material and Question Bank visit www. 21

22 DETERMINATION OF MOLECULAR MASS FROM DEPRESSION IN FREEZING POINT To calculate the molecular mass of an unknown non-volatile compound, a known mass (WB g) of it is dissolved in a known mass (say W A g) of some suitable solvent and depression in freezing point ( ΔT f ) is determined. Let M B be the molecular mass of the compound. Then molality of the solution: Knowing K f, W B, W A and ΔT f the molecular mass of the compound can be calculated from the above relation. Antifreeze Solutions Water is used in radiators as cooling liquid. If the vehicle is to be used at high altitudes where the temperature is sub-zero, water would freeze in the radiators. To avoid the difficulty, a solution of ethylene glycol in water is used in radiators. This solution has freezing point lower than zero. Freezing point can be lowered to the desired extent by changing the concentration. Experimental Determination of Depression in Freezing Point Depression in freezing point is measured by Beckmann method. A known weight of the solvent is taken in a freezing point tube (Fig ). It is cooled, with constant stirring to about below its freezing point (super cooling). Then on vigorous stirring, the temperature of the solution rises to the freezing point, which becomes constant. The freezing point temperature is also indicated by the appearance of crystals of the solvent. After remelting of the solvent, a known weight of the solute is added and freezing point of the solution is determined. The difference between the freezing point of the pure solvent and of the solution gives the depression in freezing point. Knowing the value of the mass of the solute, the mass of solvent, depression in freezing point and molal depression constant for the solvent, we can calculate the molecular mass of the solute. OSOMOSIS AND OSMOTIC PRESSURE This was studied for the first time by Abbe Nollet in Let us consider an aqueous solution of sugar placed in an inverted thistle funnel having a semipermeable membrane such as animal bladder or parchment paper, attached to its bottom. The thistle funnel is lowered into a beaker containing water. The membrane is such that it allows only For more Study Material and Question Bank visit www. 22

23 the molecules of the solvent and not the solute to pass through it. Thus there will be movement of water molecules through pure solvent(less concentrated) into solution (more concentrated). As a result, water passes into the thistle funnel and level of solution in the thistle funnel rises gradually (Fig). This process is known as osmosis. Thus, the phenomenon of the flow of solvent through a semipermeable membrane from pure solvent to the solution is called osmosis. Osmosis can take place between the solutions of different concentrations. In such cases, the solvent molecules move from the solution of low solute concentration to that of higher solute concentration. The flow of the solvent through the semipermeable membrane will continue till the equilibrium is reached when the hydrostatic pressure of the liquid column exactly balances the tendency of water to pass inward through the semipermeable membrane. The hydrostatic pressure set up as a result of osmosis is a measure of the osmotic pressure of the solution. Thus the osmotic pressure of a solution at a particular temperature may be defined as the excess pressure that builds up when the solution is separated from the solvent by a semipermeable membrane. It is denoted by π. The osmotic pressure can be defined in another way. In order to understand this, let us consider the phenomenon of osmosis in a special type of apparatus as shown in Fig. The apparatus consists of a chamber divided into water-tight compartments ( S and W) by semipermeable membrane and fitted with water-tight pistons. On putting the solution in compartment S and water in compartment W, the piston P' will be displaced upwards due to the movement of water from W to S. To stop this movement of water, we have to apply mechanical pressure on the solution side. The pressure just sufficient to stop osmosis will be the osmotic pressure. Thus osmotic pressure may be defined as the excess pressure on the solution side to prevent the passage of solvent into it through a semipermeable membrane. If the pressure applied on the solution is greater than the osmotic pressure, then the solvent starts passing from the solution into solvent. This is called reverse osmosis. The phenomenon of reverse osmosis is generally used for purification of sea water or hard water. Sea water which is a dilute solution of many undesirable salts is placed in contact with pure water through a semipermeable membrane. Pressure greater than osmotic pressure is applied on sea water. This causes movement of pure water from sea water to pure water side. Semipermeable Membrane Semipermeable membrane is one which allows only the solvent to pass through it. Various substances which serve as semipermeable membranes are parchment paper, animal membranes and cellophane. In nature, plant cells and cells in animal body are surrounded by semipermeable walls. These are however very weak and or not perfectly semipermeable. In the laboratory, an artificial membrane of copper ferrocyanide is generally employed. In order to make it strong enough to withstand very high pressures, copper ferrocyanide is deposited in the walls of a porous pot as follows. A porous pot thoroughly cleaned by washing it successively with acid solution, water, alkali and finally distilled water. After washing, it is soaked in distilled water for a few For more Study Material and Question Bank visit www. 23

24 hours or distilled water is forced through its pores under pressure. This removes any air present in its pores. The porous pot is filled with 2.5% solution of copper sulphate and then placed in a trough containing 2.5% solution of potassium ferrocyanide. An electric field is applied by dipping platinum electrodes inside and outside the porous pot. The Cu 2+ and [Fe(CN) 6 ] 4 ions move towards the oppositely charged electrodes and form a gelatinous deposit of copper ferrocyanide in the pores of the porous pot. 2 Cu 2+ + [Fe(CN) 6 ] 4 Cu 2 [Fe(CN) 6 ] Importance of Osmosis Osmosis is a process of prime importance in living organisms. The salt concentration in blood plasma due to different species is equivalent to 0.9% of aqueous sodium chloride has by mass. If blood cells are placed in pure water, water molecules rapidly move into the cell. The movement of water molecules into the cell dilutes the salt content. The blood cells as a result of this transfer of water molecules, swell and burst. Hence care is always taken to ensure that solutions that flow into the blood stream are of the same osmotic pressure as that of blood. Sodium ion Na + and potassium ion K + are responsible for maintaining proper osmotic pressure balance inside and outside of the cells of organism. Osmosis is also critically involved in the functioning of kidneys. Isotonic Solutions Two solutions having equal osmotic pressure are called isotonic solutions. A solution having osmotic pressure greater than some other solution is said to be hypertonic with respect to the other solution. A solution having lower osmotic pressure relative to some other solution is called hypotonic. A 0.91% solution of sodium chloride solution often called saline water is isotonic with human blood corpuscles. In this solution, the corpuscles neither shrink nor swell. Consequently, medicines are mixed with saline water before being injected into the veins. LAWS OF OSMOTIC PRESSURE van't Hoff showed the existence of a close analogy between gases and solutions. He observed that the osmotic pressure of a dilute solution was equal to the pressure which the solute would have exerted as a gas at the same temperature of the solution and occupied a volume equal to that of the solution. He established that a dilute solution behaves like an ideal gas and the different gas laws are applicable to dilute solutions or ideal solutions. Using the data on the study of osmotic pressure, van't Hoff put forward the laws of osmotic pressure. They are : 1. van't Hoff -Boyle Law It states that at constant temperature(t), the osmotic pressure( p.) of a dilute solution is directly proportional to the molar concentration of the solute ( C), i.e. π α C 2. van't Hoff - Charle's Law It states that at constant concentration, the osmotic pressure (π) of a dilute solution is proportional to the temperature in kelvin (T). i.e., π α T Combining the two laws : π α C T π = R C T. (6) For more Study Material and Question Bank visit www. 24

25 where R is a constant of proportionality known as van't Hoff constant for solutions or simply solution constant. But the molar concentration, C = (n / V), where n = number of moles of solute. π = (n R T) / V or π. V = n R T. (7) Equation (7) is the van't Hoff equation for osmotic pressure of solutions. This equation is similar to the general gas equation, PV = n R T Osmotic Pressure - A Colligative Property For a given solvent, the osmotic pressure depends only upon the molar concentration of the solute but does not depend on its nature. Osmotic pressure is related to the number of moles of the solute by the following relation : Here, C = concentration of solution in moles per litre. R = gas constant, T = temperature n = number of moles of solute V = volume of solution Equation (8) is called van't Hoff equation. DETERMINATION OF OSMOTIC PRESSURE - Berkley and Hartley's Method The apparatus used (Fig ) consists of a porous pot containing a deposit of copper ferrocyanide in its walls to act as semipermeable membrane. It is fitted into a gun metal container (outer vessel), which is provided with a piston and a pressure gauge. The porous pot is then fitted with a capillary indicator tube on one side and a solvent reservoir on the other side. The solution, whose osmotic pressure is to be measured, is taken in the metal container ; while the solvent is filled in the porous pot. Solvent from the porous pot tends to move into the solution, through the semipermeable membrane as a result of phenomenon of osmosis. This is indicated by the fall in the level of solvent in the capillary tube. Then, suitable external pressure (which is measured by pressure gauge) is applied on the piston so that the level of the solvent in the capillary indicator tube remains stationary, i.e., does not rise or fall with time. The applied pressure at the time of stationary level in the capillary indicator tube directly gives the osmotic pressure of the solution. Determination of molecular mass from Osmotic Pressure According to van't Hoff equation : For more Study Material and Question Bank visit www. 25

26 where n B is the number of moles of solute dissolved in V litres of solution. By applying the above formula, the molecular mass of the solute can be calculated. This method is especially suitable for the determination of molecular masses of macromolecules such as proteins and polymers. This is due to the reason that for these substances the values of other colligative properties such as elevation in boiling point or depression in freezing point are too small to be measured. On the other hand, osmotic pressure of such substances are measurable. For getting accurate value of molecular masses The solute must be non-volatile The solution must be dilute The solute should not undergo dissociation or association. Biological Significance of osmosis Osmosis plays a significant role in the absorption of water by the plants which is taken in by the roots. The absorption of water by plants from the soil through the roots and its movement to different parts of plants due to the process of osmosis. Plants and animal bodies are composed of very large number of cells. The cells contain a fluid (called cell sap) and the walls of the cells are made up of living cytoplasmic membrane which acts as a semi-permeable membrane. These membranes allow water to pass through but block the passages of the enzymes and proteins that have been synthesised in the cell. The cell saps have generally higher osmotic pressure and, therefore, when the cells come in contact with water, there is tendency of water to enter into the cell due to osmosis. Therefore, the osmosis process helps the plants to absorb soil water and push it up to the stem and other parts of the plants and trees. Plants which grow in marshy lands have more concentrated saps which develop an osmotic pressure of the order of twenty five atmospheres. Thus, the plant may absorb excess of water from the soil which might cause bursting of root hair. Ultimately the plant decays. The addition of fertiliser may raise the osmotic pressure of the soil water. Consequently, the cell sap is not in a position to absorb excessive water and the decay of the plant is thus, checked. The use of salt and sugar as preservatives in pickles and jams has its basis in preventing growth of fungi and bacteria by osmosis. ABNORMAL MOLECULAR MASSES In derivation of colligative properties, it has assumed that the molecular form of the solute remains unchanged in solution. Furthermore if the solutions are dilute, they behave ideally. In such cases experimental value of colligative property is in agreement with theoretically calculated values. However, there are certain substances like solutions of salts, acids or bases in water or acetic acid in benzene where experimental value differs considerably from the calculated value. Such solutions are said to be abnormal solutions. The abnormalities observed in such solutions are of two types : 1. Association of solute molecules 2. Dissociation of solute molecules. For more Study Material and Question Bank visit www. 26

27 Association of solute molecules Certain solutes in solution are found to associate. This virtually leads to a decrease in the number of molecular particles in solutions. Thus it results in a decrease in the values of colligative properties. The colligative properties are inversely proportional to the molecular masses. Therefore higher values are obtained for molecular masses than normal values of un-associated molecules. For example, acetic acid dissolved in benzene shows a molecular mass of 120 (normal molecular mass = 60). Similarly, benzoic acid dissolved in benzene shows a molecular mass of double of its normal molecular mass. This is explained by the fact that both acetic acid and benzoic acid form dimers in solution due to hydrogen bonding. Dissociation of Solute molecules A number of electrolytes dissociate in solution to give two or more particles (ions). Therefore, the number of solute particles, in solutions of such substances, is more than the expected value. Accordingly such solutions exhibit higher values of colligative properties. Such colligative properties are inversely proportional to molecular masses, therefore molecular masses of such substances are calculated from colligative properties will be less than their normal values. For example, KCl dissociates into K + and Cl ions when dissolved in water. So the number of solute particles in its solution would be double the number of particles if no dissociation had taken place. Hence it is expected to have molecular mass (on the basis of colligative properties) equal to half of its normal molecular mass, i.e., 74.5/2 = However, the molecular mass of KCl is found to be 40.3 by studies of depression in freezing point. The difference in two values is due to the fact that there are strong attractive forces present in the oppositely changed ions of the strong electrolyte in solution. These electrical forces hold together a number of the ion pairs. Thus such electrolytes are completely dissociated and number of ions formed in solution is not exactly the double but is somewhat less. Consequently, there is difference in the values of the molecular masses. Van't Hoff factor i ' In order to account for the abnormal behaviour of solutions in which solute undergoes association or dissociation, van't Hoff introduced a correction factor i ' which is called van't Hoff factor and is defined as the ratio of the experimental value of colligative property to the calculated value of property, i.e., Since the colligative property is proportional to the number of solute particles in solution, hence : or we may write : For more Study Material and Question Bank visit www. 27

28 where M is the molecular mass of the solute, ΔT b, ΔT f, ΔP / P o and π are the boiling point elevation, freezing point depression, relative lowering of vapour pressure and osmotic pressure of the solution respectively. The subscripts obs' and cal' refer to experimental and calculated values of the colligative properties. Introduction of van't Hoff factor modifies the equation for the colligative properties as follows: Relative lowering of vapour pressure = (P o P A ) / P o = i X B Elevation in boiling point = ΔT b = i K b m Depression in freezing point = ΔT f = i K f m Osmotic pressure = π = i C R T From the values of i ' it is possible to calculate the degree of dissociation or degree of association of the substance in solution. DEGREE OF DISSOCIATION Consider an electrolyte A x B y which partially dissociate in solution yielding x ions of A y+ and y' ions of B x and α is the degree of dissociation i.e., the fraction of the total number of molecules which dissociates and C be initial concentration of the solute, then the dissociation equilibrium in solution can be represented as : The above equation is applicable to any colligative property and provides an important method for calculating the degree of dissociation. If α = 1, i.e., the dissociation is complete, i = x + y, the observed colligative property will be (x + y ) times the calculated value. On the other hand, when no dissociation occurs α = 0 and i = 1 ; the calculated and observed values will be equal. Association of Solute Consider the association of a solute A into its associated form (A) n according to the relation : n A (A) n where n ' is the number of solute which combine to form an associated species. If C is the initial concentration and α the degree of association of the solute, then at equilibrium the number of moles of the undissociated solute is C (1 α ) and that of associated solute is C ( α / n). The total number of moles in the solution is given by : For more Study Material and Question Bank visit www. 28

29 C (1 α ) + C ( α / n) or C [(1 α ) + α / n ] Hence van't Hoff factor : If association is complete α = 1 : i = 1/ n, the observed value of a colligative property will be (1/n) times the calculated value and if α = 0 ; no association occurs in solution, i.e., i = 1 and observed and calculated values will be equal. For more Study Material and Question Bank visit www. 29