Colligative Properties - Depression in Freezing Point

Freezing point of a substance is defined as the temperature at which the vapor pressure of the solid form is in equilibrium with liquid form of the substance. In other words, solid and liquid forms of the substance has same vapor pressure.

fig 3.10

The curves AB, BC, and A'B' are the vapor pressure curves of solid solvent (ice) liquid water and solution containing non volatile solute respectively. T^oK is the freezing point of pure solvent T₁K is the freezing point of the solution. The freezing point depression depends upon the molal concentration of the solute and does not depend upon the nature of solute. Therefore it is a colligative property.

denominator as compared to W_A/M_A.

Therefore,

If W_A is the mass of solvent in kg then nB/WA is the molality of the solution.

Or,

For, a given solvent M_A is fixed hence KMa is a constant (K_f).

DT_f = k_f m

Cryoscopic constant (k_f) is defined as the depression in the freezing point when one mole of non volatile solute is dissolved per kilogram of solvent.

Units of k_f are K kg mol^-1.

The molar mass of the unknown solute can be calculated by applying the formula

DT_f = k_f m ......(1)

But,

(where W_B is the weight of the solute in gms and M_B is molar mass of the solute and W_A is the weight of the solvent in gms in which W_B gms of solute is dissolved)

From equations (1) and (2)

Knowing all the other values on the right hand side MB can be calculated.

Depression in freezing point is used to lower the freezing temperature of water and clear roads during severe winters. Depression in freezing point is also useful in antifreeze, which is used in the radiators of cars to prevent the water in the radiators from freezing during extreme winters. Ethylene glycol is added as antifreeze.