Question

What is the relation between depression in freezing point and molar mass of the solute?

Hint:

Freezing point depression is a colligative property, depending only on the number of solute particles. The higher the molar mass, the smaller the depression for a fixed solute mass.

Answer 1

The depression in freezing point (\(\Delta T_f\)) is directly proportional to the molality of the solution. The relation is: \[ \Delta T_f = K_f \cdot m \] where \(K_f\) is the molal depression constant of the solvent and \(m\) is molality. Since molality \(m = \dfrac{w \times 1000}{M \times W}\), \[ \Delta T_f = K_f \cdot \frac{w \times 1000}{M \times W} \] where: - \(w\) = mass of solute (g),
- \(M\) = molar mass of solute (g mol\(^{-1}\)),
- \(W\) = mass of solvent (g).
Thus, molar mass of solute can be calculated as: \[ M = \frac{K_f \times w \times 1000}{\Delta T_f \times W} \]