Colligative Properties

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Certain properties of solutions depend only on the number of particles of the solute (molecule or ions) present in definite volume of the solution and do not depend on the nature of solute. Such properties are called colligative properties.

A few colligative properties are:

(i) Relative lowering of vapor pressure

(ii) Elevation of boiling point

(iii) Depression in freezing point

(iv) Osmotic pressure.

Relative Lowering of Vapor Pressure

The relative lowering of vapor pressure is a colligative property as it depends only on the concentration of the solute and it is independent of its nature.

Consider a binary solution consisting of non volatile solute in a volatile solvent. The vapor pressure of the solution (P) is equal to vapor pressure of solvent (P_A) in the solution, which in turn is directly proportional to its mole fraction in solution.

= P^o_A c_A ...(i)

where c_A = mole fraction of solvent.

If mole fraction of solute is c_B then

c_A + c_B = 1 or c_A = 1-c_B ...(ii)

From eq (i) and (ii) PA = P^o_A (1-c_B) = P^o_A-P^o_Ac_B

P^o_A - PA = P^o_Ac_B

is called the relative lowering of vapor pressure and is equal to the mole fraction of the solute.

Calculation of molecular mass from relative lowering of vapor pressure

A known mass W_B of the non-volatile solute is dissolved in a known mass (W_A) of the volatile solvent to prepare a dilute solution and relative lowering of vapor pressure is determined experimentally. Knowing the molecular mass (M_A) of the solvent, molecular mass (M_B) of the solute can be determined as follows:

Relative lowering of vapor pressure is given by:

For dilute solutions W_B/M_B << W_A/M_A and hence in the above expression W_B/M_B may be neglected in the denominator as compared with W_A/M_A.

In this expression all the parameters are known except M_B and hence M_B can be calculated.

Elevation of Boiling Point

The boiling point of a liquid may be defined as the temperature at which the vapor pressure of the liquid becomes equal to the atmospheric pressure.

fig 3.9

The vapor pressure curves for the pure solvent and solution consisting of a nonvolatile solute is represented diagrammatically. AB is the vapor pressure curve for pure solvent and CD is vapor pressure curve for the solution. T₀ represents the boiling point of pure solvent and T₁ represents the boiling point of solution. In the presence of a non-volatile solute the solution has to be heated to a slightly higher temperature so that the vapor of the solution becomes equal to atmospheric pressure and solution begins to boil. The differences in the boiling points are represented as DT_b, which is the elevation in boiling point. The elevation in boiling point is proportional to the solute concentration.

in the denominator.

If W_A is the mass of the solvent in kg, then n_B/W_A is equal to the molality ('m' of the solution)

Tb = kM_Am

where kM_A is replaced by a constant k_b where k_b is called ebulloiscopic constant defined as elevation in boiling point caused by one mole of nonvolatile solute dissolved per kilogram (1000g) of the solvent. The units of k_b are K.kg mol^-1. The value of k_b depends upon the solvent and is independent of the nature of the solute and concentration of the solution.

Calculation of molecular mass of the solute from elivation in boiling point

DT_b = k_b m ……(1)

If W_B gms of the solute is dissolved in W_A gms of the solvent then

(where M_B is the molar mass of the solute)

From (1) and (2)