Vapour pressure and Raoult’s law

The essentials

In a closed vessel, a liquid evaporates until its vapour exerts a constant pressure called its vapour pressure. For a solution of two volatile liquids, Raoult's law states that the partial vapour pressure of each component is proportional to its mole fraction in the solution: p₁ = x₁p₁°, p₂ = x₂p₂°. Total pressure p = p₁ + p₂ (Dalton's law). If the solute is non-volatile, only the solvent contributes and the vapour pressure is lowered.

Key points

• Ideal solution: obeys Raoult's law at all concentrations; ΔmixH = 0 and ΔmixV = 0. A–B interactions are similar to A–A and B–B. Examples: n-hexane + n-heptane, benzene + toluene.
• Positive deviation: A–B interactions are weaker; vapour pressure is higher than predicted; ΔmixH > 0, ΔmixV > 0. Example: ethanol + acetone, carbon disulphide + acetone.
• Negative deviation: A–B interactions are stronger; vapour pressure is lower; ΔmixH < 0, ΔmixV < 0. Example: chloroform + acetone (hydrogen bonding), phenol + aniline, nitric acid + water.
• Azeotropes boil at constant temperature with the same composition in liquid and vapour, so they cannot be separated by fractional distillation.
• Minimum boiling azeotropes come from large positive deviation (ethanol–water, about 95% ethanol). Maximum boiling azeotropes come from large negative deviation (nitric acid–water, about 68% nitric acid).

Exam tips

• The vapour is richer in the more volatile component. Mole fraction in vapour y₁ = p₁ ÷ p_total.
• Example: p_A° = 400 mm Hg, p_B° = 200 mm Hg, x_A = 0.25 gives p = 100 + 150 = 250 mm Hg.

Common mistakes

• Mixing up which deviation gives a minimum boiling azeotrope; higher vapour pressure means a lower boiling point.