Depression of freezing point: 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 T_f⁰ be the freezing point of pure solvent and T_f be its freezing point when non-volatile solute is dissolued in it. The decrease in freezing point

AT_f = T⁰_f - T_f is known as depression in freezing point.

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

ΔT_f ∝ m

or, ΔT_f ∝ k_fm

The proportionality constant k_f, which depends on the nature of the solvent is known as freezing point depression constant or molal depression constant or cryescopic constant.

If w₂ gram of the solute having molar mass of M₂, present in w₁ grain of solvent, produces the depression in freezing point ΔT_f of the solvent, then molality of the solute is given by

m = {(w₂/m₂)/(w₁/100)}

Substituting the values of molality in eq., we get

ΔT_f = {(k_f x w₂/M₂)/(W₁/1000)}

ΔT_f = {(k_f x w₂/1000)/(M₂ x W₁)}