Question

How molar mass of a non-volatile solute is related to the depression in freezing point?

Derive an equation.

Answer 1

According to Raoul'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 $T_f^o$ be freezing point of pure solvent

$T_f$ be freezing point of solution

Then, increase in freezing point

$\Delta T_f=T_f-T_f^o$

known as depression of freezing point.

By experiments we know

$\Delta T_f\propto m$ where, $m=$ molar conc. of solute in solution.

$\Rightarrow \Delta T_f=K_{f}m$

$T_f-T_f^o=K_{f}m$

where, $K_f=$ freezing point depression constant.