Chemistry

Chemistry

Problem

A solution of 0.643 g of an organic compound in 50 mL of benzene (density 0.879 g/mL) lowered its freezing point from 5.51∘C5.51^\circ\text{C} to 5.03∘C5.03^\circ\text{C}. Calculate the molar mass of solid. KfK_f for benzene is 5.12 K mol−1 kg5.12 \text{ K mol}^{-1} \text{ kg}. (IIT 1992)
Intuitive explanation

Freezing point depression is a colligative property that depends only on how many solute particles dissolve, not what they are—so it's a powerful way to find molar mass when you know the mass dissolved. The key is converting the temperature drop into molality using the freezing point depression equation ΔTf=Kf⋅m\Delta T_f = K_f \cdot m, then using molality and the known mass of solute to back-calculate the molar mass. Don't forget that molality uses kilograms of solvent, not solution volume.

Intuitive explanation

Freezing point depression is a colligative property that depends only on how many solute particles dissolve, not what they are—so it's a powerful way to find molar mass when you know the mass dissolved. The key is converting the temperature drop into molality using the freezing point depression equation ΔTf=Kf⋅m\Delta T_f = K_f \cdot m, then using molality and the known mass of solute to back-calculate the molar mass. Don't forget that molality uses kilograms of solvent, not solution volume.

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