After studying this Unit, you will be

able to

• describe the formation of different

types of solutions;

• express concentration of solution

in different units;

• state and explain Henry’s law and

Raoult’s law;

• distinguish between ideal and

non-ideal solutions;

• explain deviations of real solutions

from Raoult’s law;

• describe colligative properties of

solutions and correlate these with

molar masses of the solutes;

• explain abnormal colligative

properties exhibited by some

solutes in solutions.

In normal life we rarely come across pure substances.

Most of these are mixtures containing two or more pure

substances. Their utility or importance in life depends

on their composition. For example, the properties of

brass (mixture of copper and zinc) are quite different

from those of German silver (mixture of copper, zinc

and nickel) or bronze (mixture of copper and tin);

1 part per million (ppm) of fluoride ions in water

prevents tooth decay, while 1.5 ppm causes the tooth

to become mottled and high concentrations of fluoride

ions can be poisonous (for example, sodium fluoride is

used in rat poison); intravenous injections are always

dissolved in water containing salts at particular ionic

concentrations that match with blood plasma

concentrations and so on.

In this Unit, we will consider mostly liquid

solutions and their formation. This will be followed by

studying the properties of the solutions, like vapour

pressure and colligative properties. We will begin with

types of solutions and then various alternatives in

which concentrations of a solute can be expressed in

liquid solution.

SolutionsSolutions

Almost all processes in body occur in some kind of liquid solutions.

Objectives

2.1

Types of

Solutions

SolutionsSolutions

Solutions

Unit

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.,

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36Chemistry

Type of Solution Solute Solvent Common Examples

Gaseous Solutions Gas Gas Mixture of oxygen and nitrogen gases

Liquid Gas Chloroform mixed with nitrogen gas

Solid Gas Camphor in nitrogen gas

Liquid Solutions Gas Liquid Oxygen dissolved in water

Liquid

Liquid Ethanol dissolved in water

Solid Liquid Glucose dissolved in water

Solid Solutions Gas Solid Solution of hydrogen in palladium

Liquid Solid Amalgam of mercury with sodium

Solid Solid Copper dissolved in gold

Table 2.1: Types of Solutions

consisting of two components). Here each component may be solid,

liquid or in gaseous state and are summarised in Table 2.1.

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

Mass of the component in the solution

100

Total mass of the solution

(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 =

Volume of the component

100

Total volume of solution

(2.2)

2.22.2

2.2

ExpressingExpressing

Expressing

ConcentrationConcentration

Concentration

of Solutionsof Solutions

of Solutions

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37 Solutions

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 =

Number of parts of the component

×10

Total number of parts of all components of the solution

(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 (O

). Such a small

concentration is also expressed as 5.8 g per 10

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 =

Number of moles of the component

Total number of moles of all the compone

nts

(2.4)

For example, in a binary mixture, if the number of moles of A and

B are n

and n

respectively, the mole fraction of A will be

A B

n n

(2.5)

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

+ + +

1 2 i

.......

n n n

∑

(2.6)

It can be shown that in a given solution sum of all the mole

fractions is unity, i.e.

+ x

+ .................. + x

= 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.

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38Chemistry

Calculate the mole fraction of ethylene glycol (C

) in a solution

containing 20% of C

by mass.

Assume that we have 100 g of solution (one can start with any amount of

solution because the results obtained will be the same). Solution will

contain 20 g of ethylene glycol and 80 g of water.

Molar mass of C

= 12 × 2 + 1 × 6 + 16 × 2 = 62 g mol

–1

Moles of C

−

20 g

62 g mol

= 0.322 mol

Moles of water =

-1

80 g

18 g mol

= 4.444 mol

2 6 2

glycol

2 6 2 2

moles of C H O

moles of C H O moles of H O

0.322 mol

0.322 mol 4.444 mol

= 0.068

Similarly,

= =

water

4.444 mol

0.932

0.322 mol 4.444 mol

Mole fraction of water can also be calculated as: 1 – 0.068 = 0.932

Example 2.1Example 2.1

Example 2.1

(vi) Molarity: Molarity (M) is defined as number of moles of solute

dissolved in one litre (or one cubic decimetre) of solution,

Moles of solute

Molarity

Volume of solution in litre

(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).

Example 2.2Example 2.2

Example 2.2

Calculate the molarity of a solution containing 5 g of NaOH in 450 mL

solution.

Moles of NaOH =

-1

5 g

40 g mol

= 0.125 mol

Volume of the solution in litres = 450 mL / 1000 mL L

-1

Using equation (2.8),

Molarity =

–1

0.125 mol × 1000 mL L

450 mL

= 0.278 M

= 0.278 mol L

–1

= 0.278 mol dm

–3

SolutionSolution

Solution

SolutionSolution

Solution

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39 Solutions

Example 2.3Example 2.3

Example 2.3

SolutionSolution

Solution

(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) =

Moles of solute

Mass of solvent in kg

(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.

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 Solubility2.3 Solubility

2.3 Solubility

Calculate molality of 2.5 g of ethanoic acid (CH

COOH) in 75 g of benzene.

Molar mass of C

: 12 × 2 + 1 × 4 + 16 × 2 = 60 g mol

–1

Moles of C

2.5 g

60 g mol

−

= 0.0417 mol

Mass of benzene in kg = 75 g/1000 g kg

–1

= 75 × 10

–3

Molality of C

2 4 2

Moles of C H O

kg of benzene

0.0417 mol 1000 g kg

75 g

−

= 0.556 mol kg

–1

Intext QuestionsIntext Questions

Intext Questions

2.1 Calculate the mass percentage of benzene (C

) and carbon tetrachloride

(CCl

) if 22 g of benzene is dissolved in 122 g of carbon tetrachloride.

2.2 Calculate the mole fraction of benzene in solution containing 30% by

mass in carbon tetrachloride.

2.3 Calculate the molarity of each of the following solutions: (a) 30 g of

Co(NO

)

. 6H

O in 4.3 L of solution (b) 30 mL of 0.5 M H

diluted to

500 mL.

2.4 Calculate the mass of urea (NH

CONH

) required in making 2.5 kg of

0.25 molal aqueous solution.

2.5 Calculate (a) molality (b) molarity and (c) mole fraction of KI if the density

of 20% (mass/mass) aqueous KI is 1.202 g mL

-1

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40Chemistry

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.

When a solid solute is added to the solvent, some solute dissolves

and its concentration increases in solution. This process is known as

dissolution. Some solute particles in solution collide with the solid solute

particles and get separated out of solution. This process is known as

crystallisation. A stage is reached when the two processes occur at the

same rate. Under such conditions, number of solute particles going

into solution will be equal to the solute particles separating out and

a state of dynamic equilibrium is reached.

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.

Many gases dissolve in water. Oxygen dissolves only to a small extent

in water. It is this dissolved oxygen which sustains all aquatic life. On

the other hand, hydrogen chloride gas (HCl) is highly soluble in water.

Solubility of gases in liquids is greatly affected by pressure and

2.3.1 Solubility of

a Solid in a

Liquid

2.3.2 Solubility of

a Gas in a

Liquid

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41 Solutions

temperature. The solubility of gases increase with increase of pressure.

For solution of gases in a solvent, consider a system as shown in

Fig. 2.1 (a). The lower part is solution and the upper part is gaseous

system at pressure p and temperature T. Assume this system to be in

a state of dynamic equilibrium, i.e., under these conditions rate of

gaseous particles entering and leaving the solution phase is the same.

Now increase the pressure over the solution phase by compressing the

gas to a smaller volume [Fig. 2.1 (b)]. This will increase the number of

gaseous particles per unit volume over the solution and also the rate

at which the gaseous particles are striking the surface of solution to

enter it. The solubility of the gas will increase until a new equilibrium

is reached resulting in an increase in the pressure of a gas above the

solution and thus its solubility increases.

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 = K

x (2.11)

Here K

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.

Different gases have different K

values at the same

temperature (Table 2.2). This suggests that K

is a

function of the nature of the gas.

It is obvious from equation (2.11) that higher the

value of K

at a given pressure, the lower is the solubility

of the gas in the liquid. It can be seen from Table 2.2

that K

values for both N

and O

increase with increase

of temperature indicating that the solubility of gases

Fig. 2.1: Effect of pressure on the solubility of a gas. The

concentration of dissolved gas is proportional to the

pressure on the gas above the solution.

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, K

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42Chemistry

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 CO

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.

If N

gas is bubbled through water at 293 K, how many millimoles of N

gas would dissolve in 1 litre of water? Assume that N

exerts a partial

pressure of 0.987 bar. Given that Henry’s law constant for N

at 293 K is

76.48 kbar.

The solubility of gas is related to the mole fraction in aqueous solution.

The mole fraction of the gas in the solution is calculated by applying

Henry’s law. Thus:

x (Nitrogen) =

(nitrogen)

0.987bar

76,480 bar

= 1.29 × 10

–5

As 1 litre of water contains 55.5 mol of it, therefore if n represents

number of moles of N

in solution,

x (Nitrogen) =

mol

mol 55.5 mol

55.5

= 1.29 × 10

–5

(n in denominator is neglected as it is < < 55.5)

Thus n = 1.29 × 10

–5

× 55.5 mol = 7.16 × 10

–4

mol

−4

7.16×10 mol × 1000 mmol

1 mol

= 0.716 mmol

Example 2.4Example 2.4

Example 2.4

SolutionSolution

Solution

Gas Temperature/K K

/kbar Gas Temperature/K K

/kbar

He 293 144.97

293 69.16

293 76.48

303 88.84

293 34.86

303 46.82

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

Argon 298 40.3

298 1.67

Formaldehyde 298 1.83×10

-5

Methane 298 0.413

Vinyl chloride 298 0.611

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43 Solutions

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

Solubility of gases in liquids decreases with rise in temperature. When

dissolved, the gas molecules are present in liquid phase and the process

of dissolution can be considered similar to condensation and heat

is evolved in this process. We have learnt in the last Section that

dissolution process involves dynamic equilibrium and thus must follow

Le Chatelier’s Principle. As dissolution is an exothermic process, the

solubility should decrease with increase of temperature.

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.

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 p

total

and p

be the partial

vapour pressures of the two components 1 and 2 respectively. These

partial pressures are related to the mole fractions x

and x

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,

2.42.4

2.4

VapourVapour

Vapour

Pressure of

Pressure ofPressure of

Pressure of

LiquidLiquid

Liquid

SolutionsSolutions

Solutions

Intext QuestionsIntext Questions

Intext Questions

2.6 H

S, a toxic gas with rotten egg like smell, is used for the qualitative analysis. If

the solubility of H

S in water at STP is 0.195 m, calculate Henry’s law constant.

2.7 Henry’s law constant for CO

in water is 1.67x10

Pa at 298 K. Calculate

the quantity of CO

in 500 mL of soda water when packed under 2.5 atm

pressure at 298 K.

2.4.1 Vapour

Pressure of

Liquid-

Liquid

Solutions

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44Chemistry

the partial vapour pressure of each component of the solution

is directly proportional to its mole fraction present in solution.

Thus, for component 1

∝ x

and p

(2.12)

where

is the vapour pressure of pure component 1 at the same

temperature.

Similarly, for component 2

= p

(2.13)

where p

represents the vapour pressure of the pure component 2.

According to

Dalton’s law of partial pressures, the total pressure

(

total

) 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:

total

= p

+ p

(2.14)

Substituting the values of p

and p

, we get

total

= x

+ x

= (1 – x

) p

+ x

(2.15)

= p

+ (p

– p

) x

(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 p

or p

versus the mole

fractions x

and x

for a solution gives a

linear plot as shown in Fig. 2.3. These

lines (I and II) pass through the points

for which x

and x

are equal to unity.

Similarly the plot (line III) of p

total

versus

is also linear (Fig. 2.3). The minimum

value of p

total

is p

and the maximum value

is p

, assuming that component 1 is less

volatile than component 2, i.e., p

< p

The composition of vapour phase in

equilibrium with the solution is determined

by the partial pressures of the components.

If y

and y

are the mole fractions of the

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 p

and p

are directly

proportional to x

and x

, respectively). The

total vapour pressure is given by line marked

III in the figure.

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45 Solutions

components 1 and 2 respectively in the vapour phase then, using Dalton’s

law of partial pressures:

= y

total

(2.17)

= y

total

(2.18)

In general

= y

total

(2.19)

Vapour pressure of chlor

oform (CHCl

) and dichloromethane (CH

)

at 298 K are 200 mm Hg and 415 mm Hg respectively. (i) Calculate

the vapour pressure of the solution prepared by mixing 25.5 g of

CHCl

and 40 g of CH

at 298 K and, (ii) mole fractions of each

component in vapour phase.

(i) Molar mass of CH

= 12×1+1×2+35.5×2=85 g mol

–1

Molar mass of CHCl

= 12×1+1×1+35.5×3=119.5 g mol

-1

Moles of CH

40 g

85 g mol

−

= 0.47 mol

Moles of CHCl

25.5 g

119.5 g mol

−

= 0.213 mol

Total number of moles = 0.47 + 0.213 = 0.683 mol

2 2

CH Cl

0.47 mol

0.683 mol

= 0.688

CHCl

= 1.00 – 0.688 = 0.312

Using equation (2.16),

total

= p

+ (p

– p

) x

= 200 + (415 – 200) × 0.688

= 200 + 147.9 = 347.9 mm Hg

(ii) Using the relation (2.19), y

= p

total

, we can calculate the mole

fraction of the components in gas phase (y

2 2

CH Cl

= 0.688 × 415 mm Hg = 285.5 mm Hg

CHCl

= 0.312 × 200 mm Hg = 62.4 mm Hg

2 2

CH Cl

= 285.5 mm Hg/347.9 mm Hg = 0.82

CHCl

= 62.4 mm Hg/347.9 mm Hg = 0.18

Note: Since, CH

is a more volatile component than CHCl

, [

2 2

CH Cl

415 mm Hg and

CHCl

= 200 mm Hg] and the vapour phase is also richer

in CH

[

2 2

CH Cl

= 0.82 and

CHCl

= 0.18], it may thus be concluded

that at equilibrium, vapour phase will be always rich in the component

which is more volatile.

Example 2.5Example 2.5

Example 2.5

SolutionSolution

Solution

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46Chemistry

According to Raoult’s law, the vapour pressure of a volatile component

in a given solution is given by p

= x

. In the solution of a gas in a

liquid, one of the components is so volatile that it exists as a gas and

we have already seen that its solubility is given by Henry’s law which

states that

p = K

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 K

differs from p

. Thus, Raoult’s law becomes

a special case of Henry’s law in which K

becomes equal to p

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.

The decrease in the vapour pressure of solvent depends on the

quantity of non-volatile solute present in the solution, irrespective of

its nature. For example, decrease in the vapour pressure of water by

adding 1.0 mol of sucrose to one kg of water is nearly similar to that

produced by adding 1.0 mol of urea to the same quantity of water at

the same temperature.

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 p

2.4.2 Raoult’s

Law as a

special case

of Henry’s

Law

2.4.3 Vapour

Pressure of

Solutions of

Solids in

Liquids

Fig. 2.4: Decrease in the vapour pressure of the

solvent on account of the presence of

solute in the solvent (a) evaporation of the

molecules of the solvent from its surface

is denoted by , (b) in a solution, solute

particles have been denoted by and they

also occupy part of the surface area.

2020-21

47 Solutions

the vapour pressure of the solvent, x

its mole fraction, p

be its vapour pressure

in the pure state. Then according to

Raoult’s law

∝

and p

= x

(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).

Liquid-liquid solutions can be classified into ideal and non-ideal

solutions on the basis of Raoult’s law.

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.,

∆

mix

H = 0, ∆

mix

V = 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.

When a solution does not obey Raoult’s law over the entire range of

concentration, then it is called non-ideal solution. The vapour pressure

of such a solution is either higher or lower than that predicted by

Raoult’s law (equation 2.16). If it is higher, the solution exhibits positive

deviation and if it is lower, it exhibits negative deviation from Raoult’s

law. The plots of vapour pressure as a function of mole fractions

for such solutions are shown in Fig. 2.6.

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

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 and Non-

Ideal and Non-

ideal Solutionsideal Solutions

ideal Solutions

2.5.1 Ideal

Solutions

2.5.2 Non-ideal

Solutions

2020-21

48Chemistry

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.

In case of negative deviations from Raoult’s law, the intermolecular

attractive forces between A-A and B-B are weaker than those between

A-B and leads to decrease in vapour pressure resulting in negative

deviations. An example of this type is a mixture of phenol and aniline.

In this case the intermolecular hydrogen bonding between phenolic

proton and lone pair on nitrogen atom of aniline is stronger than the

respective intermolecular hydrogen bonding between similar

molecules. Similarly, a mixture of chloroform and acetone forms a

solution with negative deviation from Raoult’s law. This is because

chloroform molecule is able to form hydrogen bond with acetone

molecule as shown.

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.

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.

2020-21

49 Solutions

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.

2.62.6

2.6

ColligativeColligative

Colligative

Properties andProperties and

Properties and

DeterminationDetermination

Determination

of Molar Massof Molar Mass

of Molar Mass

We have learnt in Section 2.4.3 that the vapour pressure of solution

decreases when a non-volatile solute is added to a volatile solvent.

There are many properties of solutions which are connected with this

decrease of vapour pressure. These are: (1) relative lowering of vapour

pressure of the solvent (2) depression of freezing point of the solvent

(3) elevation of boiling point of the solvent and (4) osmotic pressure of

the solution. All these properties depend on the number of solute

particles irrespective of their nature relative to the total number

of particles present in the solution. Such properties are called

colligative properties (colligative: from Latin: co means together, ligare

means to bind). In the following Sections we will discuss these properties

one by one.

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.,

= x

(2.22)

The reduction in the vapour pressure of solvent (∆p

) is given as:

∆p

= p

– p

= p

- p

= p

(1 – x

) (2.23)

Knowing that x

= 1 – x

, equation (2.23) reduces to

∆p

= x

(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

∆

1 1

−

p p

= x

(2.25)

Intext QuestionIntext Question

Intext Question

2.8 The vapour pressure of pure liquids A and B are 450 and 700 mm Hg

respectively, at 350 K . Find out the composition of the liquid mixture if total

vapour pressure is 600 mm Hg. Also find the composition of the vapour phase.

2.6.1 Relative

Lowering of

Vapour

Pressure

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50Chemistry

The expression on the left hand side of the equation as mentioned

earlier is called relative lowering of vapour pressure and is equal to

the mole fraction of the solute. The above equation can be written as:

1 1

p – p

1 2

n n

1 2

since

 

 

 

n n

(2.26)

Here n

and n

are the number of moles of solvent and solute

respectively present in the solution. For dilute solutions n

< < n

hence neglecting n

in the denominator we have

1 1

p p

−

(2.27)

1 1

p p

2 1

w ×

× w

(2.28)

Here w

and w

are the masses and

and

are the molar masses

of the solvent and solute respectively.

From this equation (2.28), knowing all other quantities, the molar

mass of solute (

) can be calculated.

Example 2.6Example 2.6

Example 2.6

The vapour pressure of pure benzene at a certain temperature is 0.850

bar. A non-volatile, non-electrolyte solid weighing 0.5 g when added to

39.0 g of benzene (molar mass 78 g mol

-1

). Vapour pressure of the solution,

then, is 0.845 bar. What is the molar mass of the solid substance?

The various quantities known to us are as follows:

= 0.850 bar; p = 0.845 bar; M

= 78 g mol

–1

; w

= 0.5 g; w

= 39 g

Substituting these values in equation (2.28), we get

0.850 bar – 0.845 bar

0.850 bar

–1

0.5 g × 78 g mol

× 39 gM

Therefore, M

= 170 g mol

–1

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

2.6.2 Elevation of

Boiling Point

SolutionSolution

Solution

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51 Solutions

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.

Let

be the boiling point of pure solvent and

be the boiling point of solution. The increase in

the boiling point

b b b

∆ = −

T T T

is known as

elevation of boiling point.

Experiments have shown that for dilute

solutions

the elevation of boiling point (∆T

) is

directly proportional to the molal concentration of

the solute in a solution. Thus

∆T

∝ m (2.29)

or ∆T

= K

m (2.30)

Here m (molality) is the number of moles of solute dissolved in 1 kg

of solvent and the constant of proportionality, K

is called Boiling Point

Elevation Constant or Molal Elevation Constant (Ebullioscopic

Constant). The unit of K

is K kg mol

-1

. Values of K

for some common

solvents are given in Table 2.3. If w

gram of solute of molar mass

is dissolved in w

gram of solvent, then molality, m of the solution is

given by the expression:

m =

2 2

/1000

2 1

1000 ×

× M

(2.31)

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

∆T

b 2

2 1

× 1000 ×

(2.32)

2 b

b 1

1000 × ×

× ∆

(2.33)

Thus, in order to determine M

, molar mass of the solute, known

mass of solute in a known mass of the solvent is taken and ∆T

determined experimentally for a known solvent whose K

value is known.

18 g of glucose, C

, is dissolved in 1 kg of water in a saucepan.

At what temperature will water boil at 1.013 bar? K

for water is 0.52

K kg mol

-1

Moles of glucose = 18 g/ 180 g mol

–1

= 0.1 mol

Number of kilograms of solvent = 1 kg

Thus molality of glucose solution = 0.1 mol kg

-1

For water, change in boiling point

Example 2.7Example 2.7

Example 2.7

SolutionSolution

Solution

Fig. 2.7: The vapour pressure curve for

solution lies below the curve for pure

water. The diagram shows that ∆T

denotes the elevation of boiling

point of a solvent in solution.

1.013 bar

2020-21

52Chemistry

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.

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.

f f f

∆ = −

T T T

is known as depression in

freezing point.

Similar to elevation of boiling point, depression of freezing point (∆T

)

for dilute solution (ideal solution) is directly proportional to molality,

m of the solution. Thus,

∆T

∝ m

or ∆T

= K

m (2.34)

The proportionality constant, K

, which depends on the nature of the

solvent is known as Freezing Point Depression Constant or Molal

Example 2.8Example 2.8

Example 2.8

∆T

= K

× m = 0.52 K kg mol

–1

× 0.1 mol kg

–1

= 0.052 K

Since water boils at 373.15 K at 1.013 bar pressure, therefore, the

boiling point of solution will be 373.15 + 0.052 = 373.202 K.

The boiling point of benzene is 353.23 K. When 1.80 g of a non-volatile

solute was dissolved in 90 g of benzene, the boiling point is raised to

354.11 K. Calculate the molar mass of the solute. K

for benzene is 2.53

K kg mol

–1

The elevation

(∆T

) in the boiling point = 354.11 K – 353. 23 K = 0.88 K

Substituting these values in expression (2.33) we get

–1 –1

2.53 K kg mol × 1.8 g × 1000 g kg

0.88 K × 90 g

= 58 g mol

–1

Therefore, molar mass of the solute, M

= 58 g mol

–1

Fig. 2.8: Diagram showing ∆T

, depression

of the freezing point of a solvent in

a solution.

SolutionSolution

Solution

2.6.3 Depression

of Freezing

Point

2020-21

53 Solutions

Depression Constant or Cryoscopic Constant. The unit of K

is K kg

mol

-1

. Values of K

for some common solvents are listed in Table 2.3.

If w

gram of the solute having molar mass as M

, present in w

gram of solvent, produces the depression in freezing point ∆T

of the

solvent then molality of the solute is given by the equation (2.31).

m =

2 2

/1000

(2.31)

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

∆T

f 2 2

/1000

K M

∆T

f 2

2 1

× × 1000

(2.35)

f 2

f 1

× × 1000

× ∆

(2.36)

Thus for determining the molar mass of the solute we should know

the quantities w

, w

, ∆T

, along with the molal freezing point depression

constant.

The values of K

and K

, which depend upon the nature of the

solvent, can be ascertained from the following relations.

1 f

fus

× ×

1000 × ∆

R M T

(2.37)

1 b

vap

× ×

1000 × ∆

R M T

(2.38)

Here the symbols R and M

stand for the gas constant and molar

mass of the solvent, respectively and T

and T

denote the freezing point

and the boiling point of the pure solvent respectively in kelvin. Further,

∆

fus

H and ∆

vap

H represent the enthalpies for the fusion and vapourisation

of the solvent, respectively.

Solvent b. p./K K

/K kg mol

-1

f. p./K K

/K kg mol

-1

Water 373.15 0.52 273.0 1.86

Ethanol 351.5 1.20 155.7 1.99

Cyclohexane 353.74 2.79 279.55 20.00

Benzene 353.3 2.53 278.6 5.12

Chloroform 334.4 3.63 209.6 4.79

Carbon tetrachloride 350.0 5.03 250.5 31.8

Carbon disulphide 319.4 2.34 164.2 3.83

Diethyl ether 307.8 2.02 156.9 1.79

Acetic acid 391.1 2.93 290.0 3.90

Table 2.3: Molal Boiling Point Elevation and Freezing Point

Depression Constants for Some Solvents

2020-21

54Chemistry

Fig. 2.9

Level of solution

rises in the thistle

funnel due to

osmosis of solvent.

45 g of ethylene glycol (C

) is mixed with 600 g of water. Calculate

(a) the freezing point depression and (b) the freezing point of the solution.

Depression in freezing point is related to the molality, therefore, the molality

of the solution with respect to ethylene glycol =

moles of ethylene glycol

mass of water in kilogram

Moles of ethylene glycol =

45 g

62 g mol

−

= 0.73 mol

Mass of water in kg =

600g

1000g kg

−

= 0.6 kg

Hence molality of ethylene glycol =

0.73 mol

0.60 kg

= 1.2 mol kg

–1

Therefore freezing point depression,

ÄT

= 1.86 K kg mol

–1

× 1.2 mol kg

–1

= 2.2 K

Freezing point of the aqueous solution = 273.15 K – 2.2 K = 270.95 K

1.00 g of a non-electrolyte solute dissolved in 50 g of benzene lowered the

freezing point of benzene by 0.40 K. The freezing point depression constant

of benzene is 5.12 K kg mol

–1

. Find the molar mass of the solute.

Substituting the values of various terms involved in equation (2.36) we get,

1 1

5.12 K kg mol × 1.00 g × 1000 g kg

0.40 × 50 g

− −

= 256 g mol

-1

Thus, molar mass of the solute = 256 g mol

-1

Example 2.9Example 2.9

Example 2.9

Example 2.10Example 2.10

Example 2.10

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

SolutionSolution

Solution

SolutionSolution

Solution

2.6.4 Osmosis and

Osmotic

Pressure

2020-21

55 Solutions

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 = (n

/V) R T (2.40)

Here V is volume of a solution in litres containing n

moles of solute.

If w

grams of solute, of molar mass, M

is present in the solution, then

= w

/ M

and we can write,

Π V =

R T

(2.41)

or M

∏

R T

(2.42)

Thus, knowing the quantities w

, 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

Fig. 2.10: The excess pressure equal to the

osmotic pressure must be applied on

the solution side to prevent osmosis.

2020-21

56Chemistry

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.

200 cm

of an aqueous solution of a protein contains 1.26 g of the

protein. The osmotic pressure of such a solution at 300 K is found to

be 2.57 × 10

-3

bar. Calculate the molar mass of the protein.

The various quantities known to us are as follows: Π = 2.57 × 10

–3

bar,

V = 200 cm

= 0.200 litre

T = 300 K

R = 0.083 L bar mol

-1

Substituting these values in equation (2.42) we get

1 1

1.26 g × 0.083 L bar K mol × 300 K

2.57×10 bar × 0.200 L

− −

−

= 61,022 g mol

-1

Example 2.11Example 2.11

Example 2.11

SolutionSolution

Solution

The phenomena mentioned in the beginning of this section can be

explained on the basis of osmosis. A raw mango placed in concentrated

salt solution loses water via osmosis and shrivel into pickle. Wilted

flowers revive when placed in fresh water. A carrot that has become

limp because of water loss into the atmosphere can be placed into the

water making it firm once again. Water will move into its cells through

osmosis. When placed in water containing less than 0.9% (mass/

volume) salt, blood cells swell due to flow of water in them by osmosis.

People taking a lot of salt or salty food experience water retention in

tissue cells and intercellular spaces because of osmosis. The resulting

2020-21

57 Solutions

puffiness or swelling is called edema. Water movement from soil into

plant roots and subsequently into upper portion of the plant is partly

due to osmosis. The preservation of meat by salting and of fruits by

adding sugar protects against bacterial action. Through the process

of osmosis, a bacterium on salted meat or candid fruit loses water,

shrivels and dies.

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.

2.6.5 Reverse

Osmosis and

Water

Purification

Intext QuestionsIntext Questions

Intext Questions

2.9 Vapour pressure of pure water at 298 K is 23.8 mm Hg. 50 g of urea

(NH

CONH

) is dissolved in 850 g of water. Calculate the vapour pressure

of water for this solution and its relative lowering.

2.10 Boiling point of water at 750 mm Hg is 99.63°C. How much sucrose is to

be added to 500 g of water such that it boils at 100°C.

2.11 Calculate the mass of ascorbic acid (Vitamin C, C

) to be dissolved in

75 g of acetic acid to lower its melting point by 1.5°C. K

= 3.9 K kg mol

-1

2.12 Calculate the osmotic pressure in pascals exerted by a solution prepared

by dissolving 1.0 g of polymer of molar mass 185,000 in 450 mL of water

at 37°C.

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

2.72.7

2.7

AbnormalAbnormal

Abnormal

MolarMolar

Molar

MassesMasses

Masses

Fig. 2.11: Reverse osmosis occurs when a

pressure larger than the osmotic

pressure is applied to the solution.

2020-21

58Chemistry

2 CH

COOH



(CH

COOH)

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 ∆T

or ∆T

for ethanoic acid will be half

of the normal value. The molar mass calculated on the basis of this ∆T

or ∆T

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

In 1880 van’t Hoff introduced a factor

i, known as the van’t Hoff

factor, to account for the extent of dissociation or association. This

factor i is defined as:

Normal molar mass

Abnormal molar mass

Observed colligative property

Calculated colligative property

Total number of moles of particles after

association/dissociation

Number of moles of particles before asso

ciation/dissociation

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,

1 1 2

–

p p n

Elevation of Boiling point, ∆T

= i K

Depression of Freezing point, ∆T

= i K

Osmotic pressure of solution, Π = i n

R T / V

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59 Solutions

2 g of benzoic acid (C

COOH) dissolved in 25 g of benzene shows a

depression in freezing point equal to 1.62 K. Molal depression constant

for benzene is 4.9 K kg mol

–1

. What is the percentage association of acid

if it forms dimer in solution?

The given quantities are: w

= 2 g; K

= 4.9 K kg mol

–1

; w

= 25 g,

∆T

= 1.62 K

Substituting these values in equation (2.36) we get:

–1 –1

4.9 K kg mol × 2 g × 1000 g kg

25 g × 1.62 K

= 241.98 g mol

–1

Thus, experimental molar mass of benzoic acid in benzene is

= 241.98 g mol

–1

Now consider the following equilibrium for the acid:

2 C

COOH



COOH)

If x represents the degree of association of the solute then we would

have (1 – x) mol of benzoic acid left in unassociated form and

correspondingly

as associated moles of benzoic acid at equilibrium.

Therefore, total number of moles of particles at equilibrium is:

1 1

2 2

− + = −

x x

Thus, total number of moles of particles at equilibrium equals van’t Hoff

factor i.

But

Normal molar mass

Abnormal molar mass

Example 2.12Example 2.12

Example 2.12

SolutionSolution

Solution

Table 2.4 depicts values of the factor, i for several strong electrolytes.

For KCl, NaCl and MgSO

, i values approach 2 as the solution becomes

very dilute. As expected, the value of i gets close to 3 for K

Salt

Values of i van’t Hoff Factor i for complete

0.1 m 0.01 m 0.001 m

dissociation of solute

NaCl 1.87 1.94

1.97 2.00

KCl 1.85

1.94

1.98 2.00

MgSO

1.21

1.53

1.82 2.00

2.32

2.70

2.84 3.00

* represent i values for incomplete dissociation.

Table 2.4: Values of van’t Hoff factor, i, at Various Concentrations

for NaCl, KCl, MgSO

and K

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60Chemistry

Example 2.13Example 2.13

Example 2.13

122 g mol

241.98 g mol

−

122

1 1 0.504 0.496

241.98

− = − =

or x = 2 × 0 .496 = 0.992

Therefore, degree of association of benzoic acid in benzene is 99.2 %.

0.6 mL of acetic acid (CH

COOH), having density 1.06 g mL

–1

, is

dissolved in 1 litre of water. The depression in freezing point

observed for this strength of acid was 0.0205°C. Calculate the van’t

Hoff factor and the dissociation constant of acid.

Number of moles of acetic acid =

0.6 mL 1.06 g mL

60 g mol

−

= 0.0106 mol = n

Molality =

0.0106 mol

1000 mL 1 g mL

−

= 0.0106 mol kg

–1

Using equation (2.35)

∆T

= 1.86 K kg mol

–1

× 0.0106 mol kg

–1

= 0.0197 K

van’t Hoff Factor (i) =

Observed freezing point

Calculated freezing point

0.0205 K

0.0197 K

= 1.041

Acetic acid is a weak electrolyte and will dissociate into two ions:

acetate and hydrogen ions per molecule of acetic acid. If x is the

degree of dissociation of acetic acid, then we would have n (1 – x)

moles of undissociated acetic acid, nx moles of CH

COO

–

and nx

moles of H

ions,

( )

+ −

−



3 3

CH COOH H CH COO

mol 0 0

mol mol

n nx nx

Thus total moles of particles are: n(1 – x + x + x) = n(1 + x)

(

)

1 1.041

= = + =

i x

Thus degree of dissociation of acetic acid = x = 1.041– 1.000 = 0.041

Then [CH

COOH] = n(1 – x) = 0.0106 (1 – 0.041),

[CH

COO

–

] = nx = 0.0106 × 0.041, [H

] = nx = 0.0106 × 0.041.

[ ][ ]

[ ]

− +

CH COO H

CH COOH

0.0106 × 0.041 × 0.0106 × 0.041

0.0106 (1.00 0.041)−

= 1.86 × 10

–5

SolutionSolution

Solution

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61 Solutions

SummarySummary

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:

0 0

total 1 2 2

= +p p x p x

. 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.

2.1 Define the term solution. How many types of solutions are formed? Write briefly

about each type with an example.

2.2 Give an example of a solid solution in which the solute is a gas.

2.3 Define the following terms:

(i) Mole fraction (ii) Molality (iii) Molarity (iv) Mass percentage.

2.4 Concentrated nitric acid used in laboratory work is 68% nitric acid by mass in

aqueous solution. What should be the molarity of such a sample of the acid if

the density of the solution is 1.504 g mL

–1

ExercisesExercises

Exercises

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62Chemistry

2.5 A solution of glucose in water is labelled as 10% w/w, what would be the

molality and mole fraction of each component in the solution? If the density of

solution is 1.2 g mL

–1

, then what shall be the molarity of the solution?

2.6 How many mL of 0.1 M HCl are required to react completely with 1 g mixture

of Na

and NaHCO

containing equimolar amounts of both?

2.7 A solution is obtained by mixing 300 g of 25% solution and 400 g of 40%

solution by mass. Calculate the mass percentage of the resulting solution.

2.8 An antifreeze solution is prepared from 222.6 g of ethylene glycol (C

) and

200 g of water. Calculate the molality of the solution. If the density of the

solution is 1.072 g mL

–1

, then what shall be the molarity of the solution?

2.9 A sample of drinking water was found to be severely contaminated with

chloroform (CHCl

) supposed to be a carcinogen. The level of contamination

was 15 ppm (by mass):

(i) express this in percent by mass

(ii) determine the molality of chloroform in the water sample.

2.10 What role does the molecular interaction play in a solution of alcohol and water?

2.11 Why do gases always tend to be less soluble in liquids as the temperature

is raised?

2.12 State Henry’s law and mention some important applications.

2.13 The partial pressure of ethane over a solution containing 6.56 × 10

–3

g of

ethane is 1 bar. If the solution contains 5.00 × 10

–2

g of ethane, then what

shall be the partial pressure of the gas?

2.14 What is meant by positive and negative deviations from Raoult's law and how is

the sign of ∆

mix

H related to positive and negative deviations from Raoult's law?

2.15 An aqueous solution of 2% non-volatile solute exerts a pressure of 1.004 bar

at the normal boiling point of the solvent. What is the molar mass of the solute?

2.16 Heptane and octane form an ideal solution. At 373 K, the vapour pressures of

the two liquid components are 105.2 kPa and 46.8 kPa respectively. What will

be the vapour pressure of a mixture of 26.0 g of heptane and 35 g of octane?

2.17 The vapour pressure of water is 12.3 kPa at 300 K. Calculate vapour pressure

of 1 molal solution of a non-volatile solute in it.

2.18 Calculate the mass of a non-volatile solute (molar mass 40 g mol

–1

) which

should be dissolved in 114 g octane to reduce its vapour pressure to 80%.

2.19 A solution containing 30 g of non-volatile solute exactly in 90 g of water has a

vapour pressure of 2.8 kPa at 298 K. Further, 18 g of water is then added to

the solution and the new vapour pressure becomes 2.9 kPa at 298 K. Calculate:

(i) molar mass of the solute (ii) vapour pressure of water at 298 K.

2.20 A 5% solution (by mass) of cane sugar in water has freezing point of 271K.

Calculate the freezing point of 5% glucose in water if freezing point of pure

water is 273.15 K.

2.21 Two elements A and B form compounds having formula AB

and AB

. When

dissolved in 20 g of benzene (C

), 1 g of AB

lowers the freezing point by

2.3 K whereas 1.0 g of AB

lowers it by 1.3 K. The molar depression constant

for benzene is 5.1 K kg mol

–1

. Calculate atomic masses of A and B.

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63 Solutions

2.22 At 300 K, 36 g of glucose present in a litre of its solution has an osmotic pressure

of 4.98 bar. If the osmotic pressure of the solution is 1.52 bars at the same

temperature, what would be its concentration?

2.23 Suggest the most important type of intermolecular attractive interaction in

the following pairs.

(i) n-hexane and n-octane

(ii) I

and CCl

(iii) NaClO

and water

(iv) methanol and acetone

(v) acetonitrile (CH

CN) and acetone (C

O).

2.24 Based on solute-solvent interactions, arrange the following in order of increasing

solubility in n-octane and explain. Cyclohexane, KCl, CH

OH, CH

CN.

2.25 Amongst the following compounds, identify which are insoluble, partially

soluble and highly soluble in water?

(i) phenol (ii) toluene (iii) formic acid

(iv) ethylene glycol (v) chloroform (vi) pentanol.

2.26 If the density of some lake water is 1.25g mL

–1

and contains 92 g of Na

ions per

kg of water, calculate the molarity of Na

ions in the lake.

2.27 If the solubility product of CuS is 6 × 10

–16

, calculate the maximum molarity of

CuS in aqueous solution.

2.28 Calculate the mass percentage of aspirin (C

) in acetonitrile (CH

CN) when

6.5 g of C

is dissolved in 450 g of CH

CN.

2.29 Nalorphene (C

), similar to morphine, is used to combat withdrawal

symptoms in narcotic users. Dose of nalorphene generally given is 1.5 mg.

Calculate the mass of 1.5 × 10

–3

m aqueous solution required for the above dose.

2.30 Calculate the amount of benzoic acid (C

COOH) required for preparing 250

mL of 0.15 M solution in methanol.

2.31 The depression in freezing point of water observed for the same amount of

acetic acid, trichloroacetic acid and trifluoroacetic acid increases in the order

given above. Explain briefly.

2.32 Calculate the depression in the freezing point of water when 10 g of

CHClCOOH is added to 250 g of water. K

= 1.4 × 10

–3

, K

= 1.86

K kg mol

–1

2.33 19.5 g of CH

FCOOH is dissolved in 500 g of water. The depression in the freezing

point of water observed is 1.0

C. Calculate the van’t Hoff factor and dissociation

constant of fluoroacetic acid.

2.34 Vapour pressure of water at 293 K is 17.535 mm Hg. Calculate the vapour

pressure of water at 293 K when 25 g of glucose is dissolved in 450 g of water.

2.35 Henry’s law constant for the molality of methane in benzene at 298 K is

4.27 × 10

mm Hg. Calculate the solubility of methane in benzene at 298 K

under 760 mm Hg.

2.36 100 g of liquid A (molar mass 140 g mol

–1

) was dissolved in 1000 g of liquid B

(molar mass 180 g mol

–1

). The vapour pressure of pure liquid B was found to be

500 torr. Calculate the vapour pressure of pure liquid A and its vapour pressure

in the solution if the total vapour pressure of the solution is 475 Torr.

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64Chemistry

2.37 Vapour pressures of pure acetone and chloroform at 328 K are 741.8 mm

Hg and 632.8 mm Hg respectively. Assuming that they form ideal solution

over the entire range of composition, plot p

total

, p

chloroform

, and p

acetone

as a

function of x

acetone

. The experimental data observed for different compositions

of mixture is:

100 x x

acetone

0 11.8 23.4 36.0 50.8 58.2 64.5 72.1

acetone

/mm Hg 0 54.9 110.1 202.4 322.7 405.9

454.1 521.1

chloroform

/mm Hg 632.8 548.1 469.4 359.7 257.7 193.6 161.2 120.7

Plot this data also on the same graph paper. Indicate whether it has positive

deviation or negative deviation from the ideal solution.

2.38 Benzene and toluene form ideal solution over the entire range of composition.

The vapour pressure of pure benzene and toluene at 300 K are 50.71 mm Hg

and 32.06 mm Hg respectively. Calculate the mole fraction of benzene in vapour

phase if 80 g of benzene is mixed with 100 g of toluene.

2.39 The air is a mixture of a number of gases. The major components are oxygen

and nitrogen with approximate proportion of 20% is to 79% by volume at 298

K. The water is in equilibrium with air at a pressure of 10 atm. At 298 K if the

Henry’s law constants for oxygen and nitrogen at 298 K are 3.30 × 10

mm and

6.51 × 10

mm respectively, calculate the composition of these gases in water.

2.40 Determine the amount of CaCl

(i = 2.47) dissolved in 2.5 litre of water such

that its osmotic pressure is 0.75 atm at 27° C.

2.41 Determine the osmotic pressure of a solution prepared by dissolving 25 mg of

in 2 litre of water at 25° C, assuming that it is completely dissociated.

Answers to Some Intext Questions

2.1 C

= 15.28%, CCl

= 84.72%

2.2 0.459, 0.541

2.3 0.024 M, 0.03 M

2.4 36.946 g

2.5 1.5 mol kg

–1

, 1.45 mol L

–1

0.0263

2.9 23.4 mm Hg

2.10 121.67 g

2.11 5.077 g

2.12 30.96 Pa

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