Depression of freezing point

At the freezing point, solid and liquid are in dynamic equilibrium, which means their vapour pressures are equal. A solution freezes when its vapour pressure equals that of the pure solid solvent.

A non-volatile solute lowers the liquid's vapour pressure, so it meets the solid's vapour-pressure curve at a lower temperature: the freezing point drops.

For dilute solutions the depression ΔTf = Tf° − Tf is directly proportional to molality: ΔTf = Kf m.

Kf, the molal depression (cryoscopic) constant, has units K kg mol⁻¹ and depends only on the solvent: 1.86 for water, 5.12 for benzene, 20.00 for cyclohexane and 31.8 for carbon tetrachloride.

Molar mass from freezing point: M₂ = (Kf × w₂ × 1000)/(ΔTf × w₁).

Kf = R × M₁ × Tf² / (1000 × ΔfusH), with Tf the solvent's freezing point in kelvin and ΔfusH its enthalpy of fusion.

For water Kf (1.86) is much larger than Kb (0.52), so the same solution lowers the freezing point more than it raises the boiling point. Ethylene glycol in car radiators uses this as antifreeze.