Unit 2

Solutions

Objectives

2.1 Types of Solutions

 Solutions are homogeneous mixtures of two or more than two components. By homogenous mixture we mean that its composition and properties are uniform throughout the mixture. Generally, the component that is present in the largest quantity is known as solvent. Solvent determines the physical state in which solution exists. One or more components present in the solution other than solvent are called solutes. In this Unit we shall consider only binary solutions (i.e., consisting of two components). Here each component may be solid, liquid or in gaseous state and are summarised in Table 2.1.

2.2 Expressing Concentration of Solutions

 Composition of a solution can be described by expressing its concentration. The latter can be expressed either qualitatively or quantitatively. For example, qualitatively we can say that the solution is dilute (i.e., relatively very small quantity of solute) or it is concentrated (i.e., relatively very large quantity of solute). But in real life these kinds of description can add to lot of confusion and thus the need for a quantitative description of the solution.

There are several ways by which we can describe the concentration of the solution quantitatively.

(i) Mass percentage (w/w): The mass percentage of a component of a solution is defined as:

Mass % of a component

=                               (2.1)

For example, if a solution is described by 10% glucose in water by mass, it means that 10 g of glucose is dissolved in 90 g of water resulting in a 100 g solution. Concentration described by mass percentage is commonly used in industrial chemical applications. For example, commercial bleaching solution contains 3.62 mass percentage of sodium hypochlorite in water.

(ii) Volume percentage (v/v): The volume percentage is defined as:

Volume % of a component =                     (2.2)

For example, 10% ethanol solution in water means that 10 mL of ethanol is dissolved in water such that the total volume of the solution is 100 mL. Solutions containing liquids are commonly expressed in this unit. For example, a 35% (v/v) solution of ethylene glycol, an antifreeze, is used in cars for cooling the engine. At this concentration the antifreeze lowers the freezing point of water to 255.4K (–17.6°C).

(iii) Mass by volume percentage (w/v): Another unit which is commonly used in medicine and pharmacy is mass by volume percentage. It is the mass of solute dissolved in 100 mL of the solution.

 (iv) Parts per million: When a solute is present in trace quantities, it is convenient to express concentration in parts per million (ppm) and is defined as:

Parts per million =       (2.3)

As in the case of percentage, concentration in parts per million can also be expressed as mass to mass, volume to volume and mass to volume. A litre of sea water (which weighs 1030 g) contains about 6 × 10–3 g of dissolved oxygen (O2). Such a small concentration is also expressed as 5.8 g per 106 g (5.8 ppm) of sea water. The concentration of pollutants in water or atmosphere is often expressed in terms of µg mL–1 or ppm.

(v) Mole fraction: Commonly used symbol for mole fraction is x and subscript used on the right hand side of x denotes the component. It is defined as:

Mole fraction of a component =      (2.4)

For example, in a binary mixture, if the number of moles of A and B are nA and nB respectively, the mole fraction of A will be

xA =                                                                                                     (2.5)

For a solution containing i number of components, we have:

xi = =                                                                              (2.6)

It can be shown that in a given solution sum of all the mole fractions is unity, i.e.

x1 + x2 + .................. + xi = 1                                                                           (2.7)

Mole fraction unit is very useful in relating some physical properties of solutions, say vapour pressure with the concentration of the solution and quite useful in describing the calculations involving gas mixtures.

 (vi) Molarity: Molarity (M) is defined as number of moles of solute dissolved in one litre (or one cubic decimetre) of solution,

                                                       (2.8)

For example, 0.25 mol L–1 (or 0.25 M) solution of NaOH means that 0.25 mol of NaOH has been dissolved in one litre (or one cubic decimetre).

 (vii) Molality: Molality (m) is defined as the number of moles of the solute per kilogram (kg) of the solvent and is expressed as:

Molality (m) =                                                              (2.9)

For example, 1.00 mol kg–1 (or 1.00 m) solution of KCl means that 1 mol (74.5 g) of KCl is dissolved in 1 kg of water.

Each method of expressing concentration of the solutions has its own merits and demerits. Mass %, ppm, mole fraction and molality are independent of temperature, whereas molarity is a function of temperature. This is because volume depends on temperature and the mass does not.

2.3 Solubility

 Solubility of a substance is its maximum amount that can be dissolved in a specified amount of solvent at a specified temperature. It depends upon the nature of solute and solvent as well as temperature and pressure. Let us consider the effect of these factors in solution of a solid or a gas in a liquid.

2.3.1 Solubility of a Solid in a Liquid

 Every solid does not dissolve in a given liquid. While sodium chloride and sugar dissolve readily in water, naphthalene and anthracene do not. On the other hand, naphthalene and anthracene dissolve readily in benzene but sodium chloride and sugar do not. It is observed that polar solutes dissolve in polar solvents and non polar solutes in non-polar solvents. In general, a solute dissolves in a solvent if the intermolecular interactions are similar in the two or we may say like dissolves like.

Solute + Solvent  ⇋  Solution                                                (2.10)

 At this stage the concentration of solute in solution will remain constant under the given conditions, i.e., temperature and pressure. Similar process is followed when gases are dissolved in liquid solvents. Such a solution in which no more solute can be dissolved at the same temperature and pressure is called a saturated solution. An unsaturated solution is one in which more solute can be dissolved at the same temperature. The solution which is in dynamic equilibrium with undissolved solute is the saturated solution and contains the maximum amount of solute dissolved in a given amount of solvent. Thus, the concentration of solute in such a solution is its solubility.

Earlier we have observed that solubility of one substance into another depends on the nature of the substances. In addition to these variables, two other parameters, i.e., temperature and pressure also control this phenomenon.

Effect of temperature

The solubility of a solid in a liquid is significantly affected by temperature changes. Consider the equilibrium represented by equation 2.10. This, being dynamic equilibrium, must follow Le Chateliers Principle. In general, if in a nearly saturated solution, the dissolution process is endothermic (∆sol H > 0), the solubility should increase with rise in temperature and if it is exothermic (∆sol H < 0) the solubility should decrease. These trends are also observed experimentally.

Effect of pressure

Pressure does not have any significant effect on solubility of solids in liquids. It is so because solids and liquids are highly incompressible and practically remain unaffected by changes in pressure.

2.3.2 Solubility of a Gas in a Liquid

 Henry was the first to give a quantitative relation between pressure and solubility of a gas in a solvent which is known as Henry’s law. The law states that at a constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas present above the surface of liquid or solution. Dalton, a contemporary of Henry, also concluded independently that the solubility of a gas in a liquid solution is a function of partial pressure of the gas. If we use the mole fraction of a gas in the solution as a measure of its solubility, then it can be said that the mole fraction of gas in the solution is proportional to the partial pressure of the gas over the solution. The most commonly used form of Henry’s law states that “the partial pressure of the gas in vapour phase (p) is proportional to the mole fraction of the gas (x) in the solution” and is expressed as:

p = KH x                                                                                             (2.11)

 Here KH is the Henry’s law constant. If we draw a graph between partial pressure of the gas versus mole fraction of the gas in solution, then we should get a plot of the type as shown in Fig. 2.2.

Fig. 2.2: Experimental results for the solubility of HCl gas in cyclohexane at 293 K. The slope of the line is the Henry’s Law constant, KH.

Different gases have different KH values at the same temperature (Table 2.2). This suggests that KH is a function of the nature of the gas.

Table 2.2: Values of Henry’s Law Constant for Some Selected Gases in Water

It is obvious from equation (2.11) that higher the value of KH at a given pressure, the lower is the solubility of the gas in the liquid. It can be seen from Table 2.2 that KH values for both N2 and O2 increase with increase of temperature indicating that the solubility of gases increases with decrease of temperature. It is due to this reason that aquatic species are more comfortable in cold waters rather than in warm waters.

 Henry’s law finds several applications in industry and explains some biological phenomena. Notable among these are:

• To increase the solubility of CO2 in soft drinks and soda water, the bottle is sealed under high pressure.
• Scuba divers must cope with high concentrations of dissolved gases while breathing air at high pressure underwater. Increased pressure increases the solubility of atmospheric gases in blood. When the divers come towards surface, the pressure gradually decreases. This releases the dissolved gases and leads to the formation of bubbles of nitrogen in the blood. This blocks capillaries and creates a medical condition known as bends, which are painful and dangerous to life. To avoid bends, as well as, the toxic effects of high concentrations of nitrogen in the blood, the tanks used by scuba divers are filled with air diluted with helium (11.7% helium, 56.2% nitrogen and 32.1% oxygen).
• At high altitudes the partial pressure of oxygen is less than that at the ground level. This leads to low concentrations of oxygen in the blood and tissues of people living at high altitudes or climbers. Low blood oxygen causes climbers to become weak and unable to think clearly, symptoms of a condition known as anoxia.

Effect of Temperature

2.4 Vapour Pressure of Liquid Solutions

 Liquid solutions are formed when solvent is a liquid. The solute can be a gas, a liquid or a solid. Solutions of gases in liquids have already been discussed in Section 2.3.2. In this Section, we shall discuss the solutions of liquids and solids in a liquid. Such solutions may contain one or more volatile components. Generally, the liquid solvent is volatile. The solute may or may not be volatile. We shall discuss the properties of only binary solutions, that is, the solutions containing two components, namely, the solutions of (i) liquids in liquids and (ii) solids in liquids.

2.4.1 Vapour Pressure of Liquid-Liquid Solutions

Let us consider a binary solution of two volatile liquids and denote the two components as 1 and 2. When taken in a closed vessel, both the components would evaporate and eventually an equilibrium would be established between vapour phase and the liquid phase. Let the total vapour pressure at this stage be ptotal and p1 and p2 be the partial vapour pressures of the two components 1 and 2 respectively. These partial pressures are related to the mole fractions x1 and x2 of the two components 1 and 2 respectively.

 The French chemist, Francois Marte Raoult (1886) gave the quantitative relationship between them. The relationship is known as the Raoult’s law which states that for a solution of volatile liquids, the partial vapour pressure of each component of the solution is directly proportional to its mole fraction present in solution.

Thus, for component 1

p1 ∝ x1

and p1 = x1                                                                                                                  (2.12)

where is the vapour pressure of pure component 1 at the same temperature.

Similarly, for component 2

p2 = p20 x2                                                                                                   (2.13)

where p20 represents the vapour pressure of the pure component 2.

According to Dalton’s law of partial pressures, the total pressure () over the solution phase in the container will be the sum of the partial pressures of the components of the solution and is given as:

ptotal = p1 + p2                                                                                                                    (2.14)

Substituting the values of p1 and p2, we get

ptotal = x1 p10 + x2 p20

= (1 – x2) p10 + x2 p20                                                                                  (2.15)

= p10 + (p20 – p10) x2                                                                                   (2.16)

 Following conclusions can be drawn from equation (2.16).

(i) Total vapour pressure over the solution can be related to the mole fraction of any one component.

(ii) Total vapour pressure over the solution varies linearly with the mole fraction of component 2.

(iii) Depending on the vapour pressures of the pure components 1 and 2, total vapour pressure over the solution decreases or increases with the increase of the mole fraction of component 1.

A plot of p1 or p2 versus the mole fractions x1 and x2 for a solution gives a linear plot as shown in Fig. 2.3. These lines (I and II) pass through the points for which x1 and x2 are equal to unity. Similarly the plot (line III) of ptotal versus x2 is also linear (Fig. 2.3). The minimum value of ptotal is p10 and the maximum value is p20, assuming that component 1 is less volatile than component 2, i.e., p10 < p20.

Fig. 2.3: The plot of vapour pressure and mole fraction of an ideal solution at constant temperature. The dashed lines I and II represent the partial pressure of the components. (It can be seen from the plot that p1 and p2 are directly proportional to x1 and x2, respectively). The total vapour pressure is given by line marked III in the figure.

The composition of vapour phase in equilibrium with the solution is determined by the partial pressures of the components. If y1 and y2 are the mole fractions of the components 1 and 2 respectively in the vapour phase then, using Dalton’s law of partial pressures:

p1 = y1 ptotal                                                                                                (2.17)

p2 = y2 ptotal                                                                                                                      (2.18)

In general

pi = yi ptotal                                                                                                                        (2.19)

2.4.2 Raoult’s Law as a special case of Henry’s Law

p = KH x.

If we compare the equations for Raoult’s law and Henry’s law, it can be seen that the partial pressure of the volatile component or gas is directly proportional to its mole fraction in solution. Only the proportionality constant KH differs from p10. Thus, Raoult’s law becomes a special case of Henry’s law in which KH becomes equal to p10.

2.4.3 Vapour Pressure of Solutions of Solids in Liquids

 Another important class of solutions consists of solids dissolved in liquid, for example, sodium chloride, glucose, urea and cane sugar in water and iodine and sulphur dissolved in carbon disulphide. Some physical properties of these solutions are quite different from those of pure solvents. For example, vapour pressure. We have learnt in Unit 5, Class XI, that liquids at a given temperature vapourise and under equilibrium conditions the pressure exerted by the vapours of the liquid over the liquid phase is called vapour pressure [Fig. 2.4 (a)]. In a pure liquid the entire surface is occupied by the molecules of the liquid. If a non-volatile solute is added to a solvent to give a solution [Fig. 2.4.(b)], the vapour pressure of the solution is solely from the solvent alone. This vapour pressure of the solution at a given temperature is found to be lower than the vapour pressure of the pure solvent at the same temperature. In the solution, the surface has both solute and solvent molecules; thereby the fraction of the surface covered by the solvent molecules gets reduced. Consequently, the number of solvent molecules escaping from the surface is correspondingly reduced, thus, the vapour pressure is also reduced.

Raoult’s law in its general form can be stated as, for any solution the partial vapour pressure of each volatile component in the solution is directly proportional to its mole fraction.

In a binary solution, let us denote the solvent by 1 and solute by 2. When the solute is non-volatile, only the solvent molecules are present in vapour phase and contribute to vapour pressure. Let p1 be the vapour pressure of the solvent, x1 be its mole fraction, pi0 be its vapour pressure in the pure state. Then according to Raoult’s law

p1 ∝ x1

and p1 = x1                                                                                         (2.20)

The proportionality constant is equal to the vapour pressure of pure solvent, . A plot between the vapour pressure and the mole fraction of the solvent is linear (Fig. 2.5).

Fig. 2.5 If a solution obeys Raoult’s law for all concentrations, its vapour pressure would vary linearly from zero to the vapour pressure of the pure solvent.

2.5 Ideal and Non-ideal Solutions

Liquid-liquid solutions can be classified into ideal and non-ideal solutions on the basis of Raoult’s law.

2.5.1 Ideal Solutions

 The solutions which obey Raoult’s law over the entire range of concentration are known as ideal solutions. The ideal solutions have two other important properties. The enthalpy of mixing of the pure components to form the solution is zero and the volume of mixing is also zero, i.e.,

∆mixH = 0 ,              ∆mixV = 0                                                                       (2.21)

It means that no heat is absorbed or evolved when the components are mixed. Also, the volume of solution would be equal to the sum of volumes of the two components. At molecular level, ideal behaviour of the solutions can be explained by considering two components A and B. In pure components, the intermolecular attractive interactions will be of types A-A and B-B, whereas in the binary solutions in addition to these two interactions, A-B type of interactions will also be present. If the intermolecular attractive forces between the A-A and B-B are nearly equal to those between A-B, this leads to the formation of ideal solution. A perfectly ideal solution is rare but some solutions are nearly ideal in behaviour. Solution of n-hexane and n-heptane, bromoethane and chloroethane, benzene and toluene, etc. fall into this category.

2.5.2 Non-ideal Solutions

Fig.2.6 The vapour pressures of two component systems as a function of composition (a) a solution that shows positive deviation from Raoult’s law and (b) a solution that shows negative deviation from Raoult’s law.

The cause for these deviations lie in the nature of interactions at the molecular level. In case of positive deviation from Raoult’s law, A-B interactions are weaker than those between A-A or B-B, i.e., in this case the intermolecular attractive forces between the solute-solvent molecules are weaker than those between the solute-solute and solvent-solvent molecules. This means that in such solutions, molecules of A (or B) will find it easier to escape than in pure state. This will increase the vapour pressure and result in positive deviation. Mixtures of ethanol and acetone behave in this manner. In pure ethanol, molecules are hydrogen bonded. On adding acetone, its molecules get in between the host molecules and break some of the hydrogen bonds between them. Due to weakening of interactions, the solution shows positive deviation from Raoult’s law [Fig. 2.6 (a)]. In a solution formed by adding carbon disulphide to acetone, the dipolar interactions between solute-solvent molecules are weaker than the respective interactions among the solute-solute and solvent-solvent molecules. This solution also shows positive deviation.

This decreases the escaping tendency of molecules for each component and consequently the vapour pressure decreases resulting in negative deviation from Raoult’s law [Fig. 2.6. (b)].

Some liquids on mixing, form azeotropes which are binary mixtures having the same composition in liquid and vapour phase and boil at a constant temperature. In such cases, it is not possible to separate the components by fractional distillation. There are two types of azeotropes called minimum boiling azeotrope and maximum boiling azeotrope. The solutions which show a large positive deviation from Raoult’s law form minimum boiling azeotrope at a specific composition. For example, ethanol-water mixture (obtained by fermentation of sugars) on fractional distillation gives a solution containing approximately 95% by volume of ethanol. Once this composition, known as azeotrope composition, has been achieved, the liquid and vapour have the same composition, and no further separation occurs.

The solutions that show large negative deviation from Raoult’s law form maximum boiling azeotrope at a specific composition. Nitric acid and water is an example of this class of azeotrope. This azeotrope has the approximate composition, 68% nitric acid and 32% water by mass, with a boiling point of 393.5 K.

2.6 Colligative Properties and Determination of Molar Mass

2.6.1 Relative Lowering of Vapour Pressure

 We have learnt in Section 2.4.3 that the vapour pressure of a solvent in solution is less than that of the pure solvent. Raoult established that the lowering of vapour pressure depends only on the concentration of the solute particles and it is independent of their identity. The equation (2.20) given in Section 2.4.3 establishes a relation between vapour pressure of the solution, mole fraction and vapour pressure of the solvent, i.e.,

p1 = x1 p10                                                                                                                  (2.22)

The reduction in the vapour pressure of solvent (∆p1) is given as:

∆p1 = p10 – p1 = p10 - p10 x1

= p10 (1 – x1)                                                                                         (2.23)

Knowing that x2 = 1 – x1, equation (2.23) reduces to

∆p1 = x2 p10                                                                                                               (2.24)

 In a solution containing several non-volatile solutes, the lowering of the vapour pressure depends on the sum of the mole fraction of different solutes.

Equation (2.24) can be written as

= = x2                                                                                                (2.25)

=                                             (2.26)

=                                                                                     (2.27)

or =                                                                           (2.28)

Here w1 and w2 are the masses and M1 and M2 are the molar masses of the solvent and solute respectively.

From this equation (2.28), knowing all other quantities, the molar mass of solute (M2) can be calculated.

2.6.2 Elevation of Boiling Point

 We have learnt in Unit 5, Class XI, that the vapour pressure of a liquid increases with increase of temperature. It boils at the temperature at which its vapour pressure is equal to the atmospheric pressure. For example, water boils at 373.15 K (100° C) because at this temperature the vapour pressure of water is 1.013 bar (1 atmosphere). We have also learnt in the last section that vapour pressure of the solvent decreases in the presence of non-volatile solute. Fig. 2.7 depicts the variation of vapour pressure of the pure solvent and solution as a function of temperature. For example, the vapour pressure of an aqueous solution of sucrose is less than 1.013 bar at 373.15 K. In order to make this solution boil, its vapour pressure must be increased to 1.013 bar by raising the temperature above the boiling temperature of the pure solvent (water). Thus, the boiling point of a solution is always higher than that of the boiling point of the pure solvent in which the solution is prepared as shown in Fig. 2.7. Similar to lowering of vapour pressure, the elevation of boiling point also depends on the number of solute molecules rather than their nature. A solution of 1 mol of sucrose in 1000 g of water boils at 373.52 K at one atmospheric pressure.

Fig. 2.7: The vapour pressure curve for solution lies below the curve for pure water. The diagram shows that ∆Tb denotes the elevation of boiling point of a solvent in solution.

 Let be the boiling point of pure solvent and be the boiling point of solution. The increase in the boiling point is known as elevation of boiling point.

Experiments have shown that for dilute solutions the elevation of boiling point (∆Tb) is directly proportional to the molal concentration of the solute in a solution. Thus

∆Tb ∝ m                                                                                                (2.29)

or ∆Tb = Kb m                                                                                        (2.30)

Here m (molality) is the number of moles of solute dissolved in 1 kg of solvent and the constant of proportionality, Kb is called Boiling Point Elevation Constant or Molal Elevation Constant (Ebullioscopic Constant). The unit of Kb is K kg mol-1. Values of Kb for some common solvents are given in Table 2.3. If w2 gram of solute of molar mass M2 is dissolved in w1 gram of solvent, then molality, m of the solution is given by the expression:

m = =                                                                                (2.31)

Substituting the value of molality in equation (2.30) we get

∆Tb =                                                                                 (2.32)

M2 =                                                                                   (2.33)

Thus, in order to determine M2, molar mass of the solute, known mass of solute in a known mass of the solvent is taken and ∆Tb is determined experimentally for a known solvent whose Kb value is known.

2.6.3 Depression of Freezing Point

 The lowering of vapour pressure of a solution causes a lowering of the freezing point compared to that of the pure solvent (Fig. 2 8). We know that at the freezing point of a substance, the solid phase is in dynamic equilibrium with the liquid phase. Thus, the freezing point of a substance may be defined as the temperature at which the vapour pressure of the substance in its liquid phase is equal to its vapour pressure in the solid phase. A solution will freeze when its vapour pressure equals the vapour pressure of the pure solid solvent as is clear from Fig. 2.8. According to Raoult’s law, when a non-volatile solid is added to the solvent its vapour pressure decreases and now it would become equal to that of solid solvent at lower temperature. Thus, the freezing point of the solvent decreases.

Fig. 2.8: Diagram showing ∆Tf, depression of the freezing point of a solvent in a solution.

 Let be the freezing point of pure solvent and be its freezing point when non-volatile solute is dissolved in it. The decrease in freezing point.

is known as depression in freezing point.

Similar to elevation of boiling point, depression of freezing point (∆Tf) for dilute solution (ideal solution) is directly proportional to molality, m of the solution. Thus,

∆Tf ∝ m

or ∆Tf = Kf m                                                                                                (2.34)

 The proportionality constant, Kf, which depends on the nature of the solvent is known as Freezing Point Depression Constant or Molal Depression Constant or Cryoscopic Constant. The unit of Kf is K kg mol-1. Values of Kf for some common solvents are listed in Table 2.3.

 If w2 gram of the solute having molar mass as M2, present in w1 gram of solvent, produces the depression in freezing point ∆Tf of the solvent then molality of the solute is given by the equation (2.31).

m =                                                                                              (2.31)

Substituting this value of molality in equation (2.34) we get:

∆Tf =

∆Tf =                                                                                     (2.35)

M2 =                                                                                     (2.36)

Thus for determining the molar mass of the solute we should know the quantities w1, w2, ∆Tf, along with the molal freezing point depression constant.

The values of Kf and Kb, which depend upon the nature of the solvent, can be ascertained from the following relations.

Kf =                                                                                          (2.37)

Kb =                                                                                          (2.38)

Here the symbols R and M1 stand for the gas constant and molar mass of the solvent, respectively and Tf and Tb denote the freezing point and the boiling point of the pure solvent respectively in kelvin. Further, ∆fusH and ∆vapH represent the enthalpies for the fusion and vapourisation of the solvent, respectively.

Table 2.3: Molal Boiling Point Elevation and Freezing Point Depression Constants for Some Solvents

2.6.4 Osmosis and Osmotic Pressure

 There are many phenomena which we observe in nature or at home. For example, raw mangoes shrivel when pickled in brine (salt water); wilted flowers revive when placed in fresh water, blood cells collapse when suspended in saline water, etc. If we look into these processes we find one thing common in all, that is, all these substances are bound by membranes. These membranes can be of animal or vegetable origin and these occur naturally such as pig’s bladder or parchment or can be synthetic such as cellophane. These membranes appear to be continuous sheets or films, yet they contain a network of submicroscopic holes or pores. Small solvent molecules, like water, can pass through these holes but the passage of bigger molecules like solute is hindered. Membranes having this kind of properties are known as semipermeable membranes (SPM).

Assume that only solvent molecules can pass through these semi-permeable membranes. If this membrane is placed between the solvent and solution as shown in Fig. 2.9, the solvent molecules will flow through the membrane from pure solvent to the solution. This process of flow of the solvent is called osmosis.

 The flow will continue till the equilibrium is attained. The flow of the solvent from its side to solution side across a semipermeable membrane can be stopped if some extra pressure is applied on the solution. This pressure that just stops the flow of solvent is called osmotic pressure of the solution. The flow of solvent from dilute solution to the concentrated solution across a semipermeable membrane is due to osmosis. The important point to be kept in mind is that solvent molecules always flow from lower concentration to higher concentration of solution. The osmotic pressure has been found to depend on the concentration of the solution.

The osmotic pressure of a solution is the excess pressure that must be applied to a solution to prevent osmosis, i.e., to stop the passage of solvent molecules through a semipermeable membrane into the solution. This is illustrated in Fig. 2.10. Osmotic pressure is a colligative property as it depends on the number of solute molecules and not on their identity. For dilute solutions,  it has been found experimentally that osmotic pressure is proportional to the molarity, C of the solution at a given temperature T. Thus:

π = C R T                                                                                                         (2.39)

Here π is the osmotic pressure and R is the gas constant.

π = (n2 /V) R T                                                                                                 (2.40)

π V =                                                                                                  (2.41)

or M2 =                                                                                               (2.42)

Thus, knowing the quantities w2, T, π and V we can calculate the molar mass of the solute.

 Measurement of osmotic pressure provides another method of determining molar masses of solutes. This method is widely used to determine molar masses of proteins, polymers and other macromolecules. The osmotic pressure method has the advantage over other methods as pressure measurement is around the room temperature and the molarity of the solution is used instead of molality. As compared to other colligative properties, its magnitude is large even for very dilute solutions. The technique of osmotic pressure for determination of molar mass of solutes is particularly useful for biomolecules as they are generally not stable at higher temperatures and polymers have poor solubility.

Two solutions having same osmotic pressure at a given temperature are called isotonic solutions. When such solutions are separated by semipermeable membrane no osmosis occurs between them. For example, the osmotic pressure associated with the fluid inside the blood cell is equivalent to that of 0.9% (mass/volume) sodium chloride solution, called normal saline solution and it is safe to inject intravenously. On the other hand, if we place the cells in a solution containing more than 0.9% (mass/volume) sodium chloride, water will flow out of the cells and they would shrink. Such a solution is called hypertonic. If the salt concentration is less than 0.9% (mass/volume), the solution is said to be hypotonic. In this case, water will flow into the cells if placed in this solution and they would swell.

2.6.5 Reverse Osmosis and Water Purification

 The direction of osmosis can be reversed if a pressure larger than the osmotic pressure is applied to the solution side. That is, now the pure solvent flows out of the solution through the semi permeable membrane. This phenomenon is called reverse osmosis and is of great practical utility. Reverse osmosis is used in desalination of sea water. A schematic set up for the process is shown in Fig. 2.11. When pressure more than osmotic pressure is applied, pure water is squeezed out of the sea water through the membrane. A variety of polymer membranes are available for this purpose.

The pressure required for the reverse osmosis is quite high. A workable porous membrane is a film of cellulose acetate placed over a suitable support. Cellulose acetate is permeable to water but impermeable to impurities and ions present in sea water. These days many countries use desalination plants to meet their potable water requirements.

2.7 Abnormal Molar Masses

 We know that ionic compounds when dissolved in water dissociate into cations and anions. For example, if we dissolve one mole of KCl (74.5 g) in water, we expect one mole each of K+ and Cl– ions to be released in the solution. If this happens, there would be two moles of particles in the solution. If we ignore interionic attractions, one mole of KCl in one kg of water would be expected to increase the boiling point by 2 × 0.52 K = 1.04 K. Now if we did not know about the degree of dissociation, we could be led to conclude that the mass of 2 mol particles is 74.5 g and the mass of one mole of KCl would be 37.25 g. This brings into light the rule that, when there is dissociation of solute into ions, the experimentally determined molar mass is always lower than the true value.

Molecules of ethanoic acid (acetic acid) dimerise in benzene due to hydrogen bonding. This normally happens in solvents of low dielectric constant. In this case the number of particles is reduced due to dimerisation. Association of molecules is depicted as follows:

It can be undoubtedly stated here that if all the molecules of ethanoic acid associate in benzene, then ∆Tb or ∆Tf for ethanoic acid will be half of the normal value. The molar mass calculated on the basis of this ∆Tb or ∆Tf will, therefore, be twice the expected value. Such a molar mass that is either lower or higher than the expected or normal value is called as abnormal molar mass.

Here abnormal molar mass is the experimentally determined molar mass and calculated colligative properties are obtained by assuming that the non-volatile solute is neither associated nor dissociated. In case of association, value of i is less than unity while for dissociation it is greater than unity. For example, the value of i for aqueous KCl solution is close to 2, while the value for ethanoic acid in benzene is nearly 0.5.

Inclusion of van’t Hoff factor modifies the equations for colligative properties as follows:

Relative lowering of vapour pressure of solvent,

Elevation of Boiling point, ∆Tb = i Kb m

Depression of Freezing point, ∆Tf = i Kf m

Osmotic pressure of solution, Π = i n2 R T / V

Table 2.4 depicts values of the factor, i for several strong electrolytes. For KCl, NaCl and MgSO4, i values approach 2 as the solution becomes very dilute. As expected, the value of i gets close to 3 for K2SO4.

Summary

A solution is a homogeneous mixture of two or more substances. Solutions are classified as solid, liquid and gaseous solutions. The concentration of a solution is expressed in terms of mole fraction, molarity, molality and in percentages. The dissolution of a gas in a liquid is governed by Henry’s law, according to which, at a given temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas. The vapour pressure of the solvent is lowered by the presence of a non-volatile solute in the solution and this lowering of vapour pressure of the solvent is governed by Raoult’s law, according to which the relative lowering of vapour pressure of the solvent over a solution is equal to the mole fraction of a non-volatile solute present in the solution. However, in a binary liquid solution, if both the components of the solution are volatile then another form of Raoult’s law is used. Mathematically, this form of the Raoult’s law is stated as:. Solutions which obey Raoult’s law over the entire range of concentration are called ideal solutions. Two types of deviations from Raoult’s law, called positive and negative deviations are observed. Azeotropes arise due to very large deviations from Raoult’s law.

The properties of solutions which depend on the number of solute particles and are independent of their chemical identity are called colligative properties. These are lowering of vapour pressure, elevation of boiling point, depression of freezing point and osmotic pressure. The process of osmosis can be reversed if a pressure higher than the osmotic pressure is applied to the solution. Colligative properties have been used to determine the molar mass of solutes. Solutes which dissociate in solution exhibit molar mass lower than the actual molar mass and those which associate show higher molar mass than their actual values.

Quantitatively, the extent to which a solute is dissociated or associated can be expressed by van’t Hoff factor i. This factor has been defined as ratio of normal molar mass to experimentally determined molar mass or as the ratio of observed colligative property to the calculated colligative property.

Excercise

EXEMPLAR QUESTION

Multiple Choice Questions (MCQs)

1. Which of the following units is useful in relating concentration of solution with its vapour pressure?

(a) Mole fraction

(b) Parts per million

(c) Mass percentage

(d) Molality

2. On dissolving sugar in water at room temperature solution feels cool to touch. Under which of the following cases dissolution of sugar will be most rapid? 

(a) Sugar crystals in cold water

(b) Sugar crystals in hot water

(c) Powdered sugar in cold water

(d) Powdered sugar in hot water

3. At equilibrium the rate of dissolution of a solid solute in a volatile liquid solvent is  ...... .

(a) less than the rate of crystallisation

(b) greater than the rate of crystallisation

(c) equal to the rate of crystallisation

(d) zero

4. A beaker contains a solution of substance 'A' .Precipitation of substance ‘A’ takes place when small amount of 'A' is added to the solution. The solution is ........ . 

(a) saturated

(b) supersaturated

(c) unsaturated

(d) concentrated

5. Maximum amount of a solid solute that can be dissolved in a specified amountof a given liquid solvent does not depend upon ......... .

(a) temperature

(b) nature of solute

(c) pressure

(d) nature of solvent

6. Low concentration of oxygen in the blood and tissues of people living at high altitude is due to .........

(a) low temperature

(b) low atmospheric pressure

(c) high atmospheric pressure

(d) Both low temperature and high atmospheric pressure

7. Considering the formation, breaking and strength of hydrogen bond, predict which of the following mixtures will show a positive deviation from Raoult’s law?

(a) Methanol and acetone

(b) Chloroform and acetone

(c) Nitric acid and water

(d) Phenol and aniline

8. Colligative properties depend on ......... .

(a) the nature of the solute particles dissolved in solution

(b) the number of solute particles in solution

(c) the physical properties of the solute particles dissolved in solution

(d) the nature of solvent particles

EXEMPLAR QUESTION

9. Which of the following aqueous solutions should have the highest boiling point?

(a) 1.0 M NaOH

(b) 1.0 M Na₂SO₄ 

(c) 1.0 M NH₄NO₃

(d) 1.0 M KNO₃

NEETprep Answer

10. The unit of ebullioscopic constant is

(a) K kg mol^-1 or K (molality)^-1

(b) mol kg K^-1 or K^-1 (molality)

(c) kg mol^-1 K^-1 or K^-1 (molality)^-1

(d) K mol kg^-1 or K (molality)

NEETprep Answer

11. In comparison to a 0.01 M solution of glucose, the depression in freezing point of a 0.01 M MgCl₂ solution is ..........

(a) the same

(b) about twice

(c) about three times

(d) about six times

NEETprep Answer

12. An unripe mango placed in a concentrated salt solution to prepare pickle shrivels because ......... .

(a) it gains water due to osmosis

(b) it loses water due to reverse osmosis

(c) it gains water due to reverse osmosis

(d) it loses water due to osmosis

NEETprep Answer

13. At a given temperature, osmotic pressure of a concentrated solution of a substance......... .

(a) is higher than that of a dilute solution

(b) is lower than that of a dilute solution

(c) is same as that of a dilute solution

(d) cannot be compared with osmotic pressure of dilute solution

NEETprep Answer

14. Which of the following statements is false?

(a) Two different solutions of sucrose of same molality prepared in different solvents will have the same depression in freezing point.

(b) The osmotic pressure of a solution is given by the equation $\mathrm{\pi }$ = CRT (where, C is the molarity of the solution)

(c) Decreasing order of osmotic pressure for 0.01 M aqueous solutions of barium chloride, potassium chloride, acetic acid and sucrose is

BaCl₂ > KCl > CH₃COOH > sucrose

(d) According to Raoult’s law, the vapour pressure exerted by a volatile component of a solution is directly proportional to its mole fraction in the solution.

NEETprep Answer

15.  The values of van’t Hoff factors for KCl, NaCl and K₂SO₄ respectively are .......... .

(a) 2, 2 and 2

(b) 2, 2 and 3

(c) 1, 1 and 2

(d) 1, 1 and 1

NEETprep Answer

16. Which of the following statements is false?

(a) Units of atmospheric pressure and osmotic pressure are the same

(b) In reverse osmosis, solvent molecules move through a semipermeable membrane from a region of lower concentration of solute to a region of higher concentration

(c) The value of molal depression constant depends on nature of solvent

(d) Relative lowering of vapour pressure, is a dimensionless quantity

NEETprep Answer

EXEMPLAR QUESTION

17. Value of Henry's constant K_H ........ .

(a) increases with increase in temperature

(b) decreases with increase in temperature

(c) remains conslant

(d) first increases then decreases

18. The value of Henry's constant, K_H is ......... .

(a) greater for gases with higher solubility 

(b) greater for gases with lower solubility

(c) constant forall gases

(d) not related to the solubility of gases

19. Consider the figure and mark the correct option.

(a) Water will move from side (A) to side (B) if a pressure lower osmotic pressure is applied on piston (B)

(b) Water will move from side (B) to side (A) if a pressure greater than osmotic pressure is applied on piston (B)

(c) Water will move from side (B) to side (A) if a pressure equal to osmotic pressure is applied on piston (B)

(d) Water will movefrom side (A) to side (B) if pressure equal to osmotic pressure is applied on piston (A)

20. We have three aqueous solutions of NaCl labelled as ‘A', ‘B’ and ‘C with concentrations 0.1 M, 0.01 M and 0.001 M, respectively. The value of van’t Hoff factor for these solutions will be in the order ...... .

(a) i_A < i_B < i_C

(b) i_A > i_B > i_C

(c) i_A = i_B = i_C

(d) i_A < i_B > i_C

21. On the basis of information given below mark the correct option.

Information

(i) In bromoethane and chloroethane mixture intermolecular interactions of A—A and B—B type are nearly same as A—B type interactions.

(ii) In ethanol and acetone mixture A—A or B—B type intermolecular interactions are stronger than  A—B type interactions.

(iii) In chloroform and acetone mixture A—A or B—B type intermolecular interactions are weaker than A—B type interactions.

(a) Solution (ii) and (iii) will follow Raoult’s law

(b) Solution (i) will follow Raoult’s law

(c) Solution (ii) will show negative deviation from Raoult’s law

(d) Solution (iii) will show positive deviation from Raoult’s law

22. Two beakers of capacity 500 mL were taken. One of these beakers, labelled as “A”, was filled with 400 mL water whereas the beaker labelled “B“ was filled with 400 mL of 2M solution of NaCl. At the same temperature both the beakers were placed in closed containers of same material and same capacity as shown in figure.

At a given temperature, which of the following statement is correct about the vapour pressure of pure water and that of NaCl solution?

(a) Vapour pressure in container (A) is more than that in container (B)

(b) Vapour pressure in container (A)is jess than that in container (B)

(c) Vapour pressure is equal in both the containers

(d) Vapour pressure in container (B) is twice the vapour pressure in container(A)

23 If two liquids A and B form minimum boiling azeotrope at some specific composition then

(a) A—B interactions are stronger than those between A—A or B—B

(b) vapour pressure of solution increases because more number of molecules of liquids A and B can escape from the solution

(c) vapour pressure of solution decreases because less number of molecules of only one of the liquids escape from the solution

(d) A—B interactions are weaker than those between A—A or B—B

24. 4 L of 0.02 M aqueous solution of NaCl was diluted by adding 1 L of water. The molality of the resultant solution is ......... .

(a) 0.004

(b) 0.008

(c) 0.012

(d) 0.016

EXEMPLAR QUESTION

25. On the basis of information given below mark the correct option.

Information

On adding acetone to methanol some of the hydrogen bonds between methanol molecules break.

(a) At specific composition methanal-acetone mixture will form minimum boiling azeotrope and will show positive deviation from Raoult’s law

(b) At specific composition methanol-acetone mixture will form maximum boiling azeotrope and will show positive deviation from Raoult’s law

(c) At specific composition methanol-acetone mixture will form minimum boiling azeotrope and will show negative deviation from Raoult’s law

(d) At specific composition methanol-acetone mixture will form maximum boiling azeotrope and will show negative deviation from Raoult’s law

NEETprep Answer

26. K_H value for Ar(g), CO₂ (g), HCHO (g) and CH₄(g) are 40.39, 1.67, 1.83 x 107° and 0.413 respectively.

Arrange these gases in the order of their increasing solubility.

(a) HCHO < CH₄ < CO₂ < Ar

(b) HCHO < CO₂ < CH₄ < Ar

(c) Ar < CO₂ < CH₄ < HCHO

(d) Ar < CH₄ < CO₂ < HCHO

NEETprep Answer

Multiple Choice Questions (More Than One Options)

27. Which of the following factor(s)affect the solubility of a gaseous solute in the fixed volume of liquid solvent?

(i) Nature of solute

(ii) Temperature

(iii) Pressure

(a) (i) and (iii) at constant T

(b) (i) and (ii) at constant p

(c) (ii) and(iii)

(d) Only (iii)

NEETprep Answer

28. Intermolecular forces between two benzene molecules are nearly of same strength as those between two toluene molecules. For a mixture of benzene and toluene, which of the following are not true?

(a) ${∆}_{\mathrm{mix}}$ H= zero

(b) ${∆}_{\mathrm{mix}}$ V = Zero

(c) These will form minimum boiling azeotrope

(d) These will not form ideal solution

NEETprep Answer

29. Relative lowering of vapour pressure is a cothgative property because ......... .

(a) it depends on the concentration of a non-electrolyte solute in solution and does not depend on the nature of the solute molecules

(b) it depends on number of particles of electrolyte solute in solution and does not depend on the nature of the solute particles

(c) it depends on the concentration of a non-electrolyte solute in solution as well as on the nature of the solute molecules

(d) it depends on the concentration of an electrolyte or non-electrolyte solute in solution as well as on the nature of solute molecules

NEETprep Answer

30. van't Hoff factor (i) is given by the expression

(a) $i=\frac{\text{ normal molar mass }}{\text{ abnormal molar mass }}$

(b) $i=\frac{\text{ abnormal molar mass }}{\text{ normal molar mass }}$

(c) $i=\frac{\text{ observed colligative property }}{\text{ calculated colligative property }}$

(d) $i=\frac{\text{ calculated colligative property }}{\text{ observed colligative property }}$

NEETprep Answer

31. Isotonic solutions must have the same......... .

(a) solute

(b) density

(c) elevation in boiling point

(d) depression in freezing point

NEETprep Answer

32. Which of the following binary mixtures will have same composition in liquid and vapour phase?

(a) Benzene-toluene

(b) Water-nitric acid

(c) Water-ethanol

(d) n-hexane-n-heptane

NEETprep Answer

EXEMPLAR QUESTION

33. In isotonic solutions ......... .

(a) solute and solvent both are same

(b) osmotic pressure is same

(c) solute and solvent may or may not be same

(d) solute is always same solvent may be different

NEETprep Answer

34. For a binary ideal liquid solution, the variation in total vapour pressure versus composition of solution is given by which of the curves?

(a) 

(b) 

(c) 

(d) 

NEETprep Answer

35. Colligative properties are observed when ......... .

(a) a non-volatile solid is dissolved in a volatile liquid

(b) a non-volatile liquid is dissolved in another volatile liquid

(c) a gas is dissolved in non-volatile liquid

(d) a volatile liquid is dissolved in another volatile liquid

NEETprep Answer

Short Answer Type Questions

36. Components of a binary mixture of two liquids A and B were being separated by distillation. After some time separation of components stopped and composition of vapour phase became same as that of liquid phase. Both the components started coming in the distillate. Explain why this happened?

NEETprep Answer

37. Explain why on addition of 1 mole of NaCl to 1 L of water, the boiling point of water increases, while addition of 1 mole of methyl alcohol to 1 L of water decreases its boiting point.

NEETprep Answer

38. Explain the solubility rule “like dissolves like” in terms of intermolecular forces that exist in solutions.

NEETprep Answer

39. Concentration terms such as mass percentage, ppm, mole fraction and molality are independent of temperature, however molarity is a function of temperature. Explain.

NEETprep Answer

40. What is the significance of Henry’s law constant K_H ?

NEETprep Answer

EXEMPLAR QUESTION

41. Why are aquatic species more comfortable in cold water in comparision to warm water?

NEETprep Answer

42. (a) Explain the following phenomena with the help of Henry’s law.

(i) Painful condition known as bends.
(ii) Feeling of weakness and discomfort in breathing at high altitude.

(b) Why soda water bottle kept at room temperature fizzes on opening?

NEETprep Answer

43. Why is the vapour pressure of an aqueous solutiun of glucose lower than that of water?

NEETprep Answer

44. How does sprinkling of salt help in clearing the snow covered roads in hilly areas? Explain the phenomenon involved in the process.

NEETprep Answer

45. What is “semipermeable membrane”?

NEETprep Answer

46. Give an example of a material used for making semipermeable membrane for carrying out reverse asmosis.

NEETprep Answer

Matching The Columns

47. Match the items given in Column I and Column II.

NEETprep Answer

48. Match the items given in Column I with the type of solutions given in Column II.

NEETprep Answer

EXEMPLAR QUESTION

49. Match the laws given in Column I with expressions given in Column II.

50. Match the terms given in Column I with expressions given in Column II.

Assertion and Reason

In the following questions a statement of assertion (A) followed by a statement of reason (R) is given. Choose the correct answer out of the following choices.

(a) Assertion and reason both are correct statements and reason is correct explanation for assertion.

(b) Assertion and reason both are correct statements but reason is not correct explanation for assertion.

(c) Assertion is correct statement but reason is wrong statement.

(d) Assertion and reason both are incorrect statements.

(e) Assertion is wrong statement but reason is correct statement.

51. Assertion (A) Molarity of a solution in liquid state changes with temperature.

Reason (R) The volume of a solution changes with change in temperature.

52. Assertion (A) When methyl alcohol is added to water, boiling point of water increases.

Reason (R) When a volatile solute is added to a volatile solvent elevation in boiling point is observed.

53. Assertion (A) When NaCl is added to water a depression in freezing point is observed.

Reason (R) The lowering of vapour pressure of a solution causes depression in the freezing point.

54. Assertion (A) When a solution is separated from the pure solvent by a semipermeable membrane, the solvent molecules pass through it from pure solvent side to the solution side.

Reason (R) Diffusion of solvent occurs from a region of high concentration solution to a region of low concentration solution.

Long Answer Type Questions

55. Define the following modes of expressing the concentration of a solution? Which of these modes are independent of temperature and why?

(a) w/w (mass percentage)

(b) V/V (volume percentage)

(c) w/V (mass by volume percentage)

(d) ppm (parts per million)

(e) $\chi$ (mole fraction)

(f) M (molarity)

(g) m (molality)

EXEMPLAR QUESTION

56. Using Raoult’s law explain how the total vapour pressure over the solution is related to mole fraction of components in the following solutions.

(a) CHCl₃ (l) and CH₂Cl₂ (l)

(b) NaCl (s) and H₂O (l)

NEETprep Answer

57. Explain the terms ideal and non-ideal solutions in the light of forces of interactions operating between molecules in liquid solutions.

NEETprep Answer

58. Why is it not possible to obtain pure ethanol by fractional distillation? What general name is given to binary mixtures which show deviation from Raoult’s law and whose components cannot be separated by fractional distillation. How many types of such mixtures are there?

NEETprep Answer

59. When kept in water, raisin swells in size. Name and explain the phenomenon involved with the help of a diagram. Give three applications of the phenomenon.

NEETprep Answer

60. Discuss biological and industrial applications of osmosis.

NEETprep Answer

61. How can you remove the hard calcium carbonate layer of the egg without damaging its semipermeable membrane? Can this egg be inserted into a bottle with a narrow neck without distorting its shape? Explain the process involved.

NEETprep Answer

62. Why is the mass determined by measuring a colligative property in case of some solutes abnormal? Discuss it with the help of van’t Hoff factor.

NEETprep Answer