Raoult's law and ideal solutions

When two volatile liquids are mixed, both evaporate, and each adds its own pressure to the vapour above the solution. Raoult's law says that the partial pressure of each liquid equals its mole fraction times the vapour pressure of the pure liquid:

p₁ = x₁p₁⁰ and p₂ = x₂p₂⁰, so p_total = x₁p₁⁰ + x₂p₂⁰

In questions, 'composition' means mole fraction. A smart step: since x₁ + x₂ = 1, write x₁ as (1 – x₂). Then the equation has only one unknown, and you can solve it in two lines.

The vapour has a different composition from the liquid. The mole fraction of a component in the vapour is its share of the pressure: y₁ = p₁ ÷ p_total. The vapour is always richer in the more volatile liquid, the one with the higher vapour pressure. This is what makes fractional distillation possible.

An ideal solution obeys Raoult's law at every composition. This happens when the A-B forces are the same as the A-A and B-B forces, so mixing gives no heat change (ΔmixH = 0) and no change in volume (ΔmixV = 0). Benzene and toluene come close.

Most real solutions deviate:

• Positive deviation: the A-B forces are weaker, so molecules escape more easily and the vapour pressure is higher than Raoult's law predicts. Mixing takes in heat (ΔmixH > 0). Example: ethanol and acetone.
• Negative deviation: the A-B forces are stronger (for example, hydrogen bonds form between acetone and chloroform), so the vapour pressure is lower than predicted and ΔmixH < 0.

Some mixtures boil at a fixed temperature with the same composition in the liquid and the vapour. These are azeotropes, and they cannot be separated by fractional distillation. About 95% ethanol in water is a minimum-boiling azeotrope; 68% nitric acid in water is a maximum-boiling one.