Vapour pressure and Raoult's law

Two volatile liquids in a closed vessel both evaporate until liquid and vapour are in equilibrium. By Dalton's law of partial pressures the total vapour pressure is p_total = p₁ + p₂.

Raoult's law: in a solution of volatile liquids, the partial vapour pressure of each component is directly proportional to its mole fraction in the liquid: p₁ = p₁° x₁ and p₂ = p₂° x₂, where p° is the vapour pressure of the pure liquid at the same temperature.

Combining the two, p_total = p₁° + (p₂° − p₁°) x₂: the total vapour pressure is a straight line in the mole fraction of either component, running from p₁° to p₂°.

The vapour's composition follows from Dalton's law: y_i = p_i / p_total. The vapour is always richer than the liquid in the more volatile component, the one with the larger p°.

Raoult's law is a special case of Henry's law: both say a volatile component's partial pressure is proportional to its mole fraction, and for Raoult's law the constant K_H equals p°.

When the solute is non-volatile, only the solvent contributes vapour: p₁ = x₁ p₁°. Solute particles occupy part of the surface, fewer solvent molecules escape, and the solution's vapour pressure falls below the pure solvent's.

This lowering depends on how much solute is present, not on what it is: 1.0 mol of sucrose and 1.0 mol of urea in 1 kg of water lower the vapour pressure by nearly the same amount.