What is meant by the depression of freezing point? Explain it with a vapour pressure graph, and derive the formula for the molar mass of a solute from it.

1. 1 · Define. Depression of freezing point, ΔTf = Tf° − Tf, is the fall in the freezing point of a solvent when a non-volatile solute is dissolved in it.
2. 2 · Explain using vapour pressure. A liquid freezes when its vapour pressure equals that of its solid. The solution's vapour pressure is lower, so the two become equal at a lower temperature.
3. 3 · Draw the graph. Vapour pressure (y-axis) against temperature (x-axis): a steep curve for the solid solvent, a curve for the liquid solvent and a lower curve for the solution. Mark Tf° and Tf where they meet the solid curve, and label ΔTf.
4. 4 · Write the relation. For a dilute solution, ΔTf = Kf m, where Kf is the molal depression constant (K kg mol⁻¹).
5. 5 · Derive the molar mass.
   • m = (w₂ ÷ M₂) ÷ (w₁ ÷ 1000) = (w₂ × 1000) ÷ (M₂ × w₁)
   • ΔTf = Kf × (w₂ × 1000) ÷ (M₂ × w₁)
   • So, M₂ = (Kf × w₂ × 1000) ÷ (ΔTf × w₁)
6. 6 · Link to real life. Ethylene glycol antifreeze in car radiators works this way.
7. 7 · Close in one line. So measuring ΔTf for a known mass of solute gives its molar mass.

Scoring tip: Write the unit of Kf (K kg mol⁻¹), and keep w₁ in grams with the factor 1000. Mixing grams and kilograms is the commonest slip.