Question

Describe cryoscopic method to determine the molecular mass of a non-volatile solute.

Answer 1

The freezing point of a liquid is the temperature at which the solid and the liquid are in equilibrium. The depression in freezing point by addition of solute can be used for the determination of molecular mass.
The molality of a solution containing $W_2$ grams of solute of molar mass $M_2$ dissolved in $W_1$ gram of solvent is :
Molality $\left(m\right)=\frac{Massofsolute\left(W_2\right)}{Molecularmassofsolute\left(M_2\right)\times Massofsolvent\left(W_1\right)}$
$\therefore m=\frac{W_2}{M_2\times W_1}$ ....(i)
Depression in freezing point of the solution is directly proportional to molality of the solution.
$\Delta T_f\propto m$
$\Delta T_f=K_{f}m$
From equation (i), we get,
$\Delta T_f=K_f\frac{W_2}{M_2\times W_1}$
The molar mass of solutes from freezing point depressions can be calculated using the following equation :
$M_2=\frac{K_f}{\Delta T_f}\times \frac{W_2}{W_1}$
Where,
$W_1$ - mass of solvent
$W_2$ - mass of solute
$M_2$ - molecular mass of solute
$K_f$ - molal freezing point depression (cryoscopic constant)
$\Delta T_f$ - observed freezing point depression
The experimental method to determine the molecular mass of non-volatile solute by determining freezing points of pure solvent and solution of known concentration is called cryoscopy.