Depression of freezing point ~ Top Class Notes

Depression of freezing point

Freezing point of a substance is the temperature at which the vapour pressure
of the substance in its liquid phase is equal to the vapour pressure in the solid phase.
If the vapour pressure of the solution is equal to the vapour pressure of the pure solid solvent then the solution freezes.
According to Raoult’s law, addition of non-volatile solute decreases the vapour pressure of the solvent and would be equal to that of solid solvent at lower This decreases the freezing point of thesolvent.
The decrease in the freezing point = ΔTf = Tf – Tf0. This is known as depression in freezing point.

Tf0 = freezing point of pure solvent

Tf0 = freezing point when non-volatile solute is dissolved

In a dilute solution the depression of freezing point Tf is directly proportional to molality of the solution. Mathematically,

ΔTf ∝m

ΔTf = Kf m

Kf = Proportionality constant depending upon the nature of the solvent. This is known as Freezing Point Depression Constant or Molal Depression Constant or Cryoscopic Constant. The unit of Kf is K kg mol-1.

Let w2 and M2 = Masses and molar masses of solute

w1= Mass of solvent

Putting this value of molality in the equation ΔTf = Kf m

M2 can be determined by the equation

The values of Kf and Kb can be determined from the following relations.

R= gas constant

M1 = molar mass of the solvent

Δfus H= enthalpies for the fusion of the solvent.

Δvap H= enthalpies for the vaporization of the solvent.

Calculate the mass of ascorbic acid (Vitamin C, C6H8O6) to be dissolved in 75 g of acetic acid to lower its melting point by 1.5°C. Kf= 3.9 K kg mol-1.

Sol. Mass of acetic acid, w1= 75 g Molar mass of ascorbic acid (C6H8O6),

M2= 6 × 12 + 8 × 1 + 6 × 16 = 176 g mol - 1

Lowering of melting point, ΔTf = 1.5 K