chapter 2 - solutions

Chapter 2 SOLUTIONS

Solutions are homogeneous mixtures of two or 

more than two components. 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.

1. Expressing Concentration of Solutions
   
   

(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 X 100

Total mass of the solution

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.

(ii) Volume percentage (v/v): The volume 

percentage is defined as:

Volume % of a component = 

 

Volume of the component X 100

Total volume of solution 

 

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.

3. Mass by volume percentage (w/v): Anotherunit 
   
   
   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.

4. 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 X 10⁶

Total number of parts of all components of the solution

5. Mole fraction: It is defined as: Mole fraction of a 
   component =
   
   
   Number of moles of the component

Total number of moles of all the components

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 x_A =        n_A

                                                                                          n_A + n_B

In a given solution sum of all the mole fractions is 

unity.

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

moles of solute dissolved in one litre (or one cubic 

decimetre) of solution, 

 

Molarity  =           Moles of solute

                                         Volume of solution in litre

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).

7. 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 

 

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.

2. Solubility

 Solubility of a substance is its maximum amount 

that can be dissolved in a specified amount of 

solvent. It depends upon the nature of solute and

 solvent as well as temperature and pressure.

Solubility of a Solid in a Liquid

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.

Effect of temperature

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.

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.

Solubility of a Gas in a Liquid

Many gases dissolve in water. Oxygen dissolves only 

to a small extent in water. It is this dissolved oxygen

 which sustains all aquatic life.

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

  pressure of the gas.

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_H x

Here K_H is the Henry’s law constant.

Different gases have different K_H values at the same temperature. This suggests that K_H is a function of the nature of the gas.

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.

3. Vapour Pressure of Liquid Solutions
   
   
   
   

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.

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.

Raoult’s law which states that for a solution of 

volatile liquids, the partial vapour pressure of 

each component in the solution is directly 

proportional to its mole fraction.

Thus, for component 1 p1 αx1

and p1 =p ⁰₁x1

where p ⁰₁ is the vapour pressure of pure component 1 at the same temperature.

Similarly, for component 2, p2 =p ⁰₂x2

where p ⁰₂ represents the vapour pressure of the pure component 2.

According to Dalton’s law of partial pressures, 

 ptotal = p1 + p2

Substituting the values of p1 and p2, we get, P _total = P₁⁰ + ( P₂⁰ – P₁⁰ ) X₂

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

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.

4. Vapour Pressure of Solutions of Solids in

 Liquids

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 . 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 , 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.

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.

5. Ideal and Nonideal Solutions

Liquid-liquid solutions can be classified into ideal and

 non-ideal solutions on the basis of Raoult’s law.

Ideal Solutions

The solutions which obey Raoult’s law over the 

entire  range of concentration are known as ideal 

solutions. ∆Hmix = 0, ∆Vmix = 0

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. Solution of 

n-hexane and n-heptane, bromoethane and 

chloroethane, benzene and toluene, etc. fall into this

 category.

Non-ideal Solutions

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 

.If it is higher, the solution exhibits positive

  deviation and if it is lower, it exhibits negative

 deviation from Raoult’s law.

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.

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.

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.

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.

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.

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. The solutions that show large negative 

deviation from Raoult’s law form maximum boiling azeotrope at a specific 

composition.

5. Colligative Properties and Determination of 
   
   
   Molar Mass

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.

These are: (1) relative lowering of vapour pressure

 of  the solvent (2) depression of freezing point the 

solvent (3) elevation of boiling point of the solvent

 and (4) osmotic pressure of the solution.

1. Relative Lowering of Vapour Pressure
   
   

Raoult established that the lowering of vapour 

pressure depends only on the concentration of the

 solute particles and it is independent of their 

identity.

p1 = x1 p1⁰

∆p1 = p1⁰ – p1 = p1⁰ – x1 p1⁰

               = p1⁰ (1 – x1)

p1⁰ – p1 = W₂ X M₁

  p1⁰              M₂ X W₁

2. Elevation of Boiling Point

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.

The vapour pressure of the solvent decreases in the 

presence of non-volatile solute. The boiling point of a

 solution is always higher than that of the boiling 

point of the pure solvent.

Let T ⁰ b be the boiling point of pure solvent and T b be the boiling point of 

solution. The increase in the boiling point 

  ∆T = Tb0 – Tb is known as elevation of boiling po

 int.

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 α m

or ∆Tb = Kb m

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 

(EbullioscopicConstant). The unit of Kb is K kg 

mol-1.

M2 = 1000 X W₂ X Kb

               ∆Tb X W₂

3. Depression of Freezing Point

The freezing point of a substance, the solid phase is 

in dynamic equilibrium with the liquid phase. The 

lowering of vapour pressure of a solution causes a 

lowering of the freezing point compared to that of

 the pure solvent. 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.

Let T ⁰ f be the freezing point of pure solvent and T f

  be its freezing point when non-volatile

solute is dissolved in it. The decrease in freezing 

point. ∆Tf  = Tf⁰ – Tf is known as depression in

  freezing point.

 

∆Tf α m

or ∆Tf = Kf m

Here m (molality) is the number of moles of solute 

dissolved in 1 kg of solvent and the constant of 

proportionality, Kf is called Freezing Point 

Depression Constant or Molal Depression

 Constant or Cryoscopic Constant.

The unit of Kf is K kg mol-1.

M2 = 1000 X W₂ X Kf

                ∆Tf X W₂

4. Osmosis and Osmotic Pressure
   
   

The flow of solvent through a semi permeable

 membrane from pure solvent to the solution is

 called osmosis.

The osmotic pressure of a solution is the excess 

pressure that must be applied on the solution to

 prevent osmosis.

π = C R T

π= n₂RT

            V

                   M₂ = W₂RT

                             π V

Two solutions having same osmotic pressure at 

a given temperature are called isotonic

 solutions.

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. Reverse osmosis is used in desalination of 

sea water.

6. Abnormal Molar Masses

A molar mass is either lower or higher than the 

expected or normal value is called as abnormal mass.

Ionic compounds when dissolved in water dissociate 

into cations and anions. When there is dissociation of

 solute into ions, the experimentally determined 

molar mass is always lower than the true value.

Molecules of acetic acid dimerise in benene due to 

hydrogen bonding. This normaly happens in solvents

 of low dielectric constant. Here the number of

 particles is reduce due to dimerisation. When there

 is association of solute, the experimentally 

determined molar mass is always higher than the 

true value.

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:

i  = 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 

association/dissociation