Ideal and Non-Ideal Solutions: Raoult, Henry and Azeotropes

Raoult's law and what ideality requires

The partial vapour pressure of a component equals its mole fraction times its pure vapour pressure. For this to hold across all compositions, a molecule must experience the same environment in the mixture as in the pure liquid — which means A–B interactions must equal the average of A–A and B–B interactions.

Consequently, for an ideal solution the enthalpy of mixing is zero and the volume change on mixing is zero. Mixing is driven entirely by entropy. Those two zeros are the standard test of ideality, and questions frequently supply one of them as the clue.

Deviations, and why they happen

A classic case of negative deviation is a mixture whose components hydrogen-bond to each other more strongly than to themselves. Positive deviation typically arises where mixing disrupts hydrogen bonding present in one pure component.

Azeotropes

An azeotrope is a composition at which the liquid and its vapour have the same composition. Because distillation works by exploiting a difference between those compositions, an azeotrope cannot be separated by simple fractional distillation — the distillate has the same composition as the pot.

That is why certain mixtures cannot be purified beyond a fixed composition by distillation alone, and why other methods are required. Explaining why distillation fails at the azeotropic composition is the standard question.

Henry's law

Henry's law describes a dilute solute rather than the solvent: its partial pressure is proportional to its mole fraction, with a constant that is not the pure vapour pressure.

The two laws are limiting cases of the same behaviour. As a component's mole fraction approaches one it obeys Raoult's law; as it approaches zero it obeys Henry's law. Both are exact in their respective limits and approximate in between, which is a useful way to present the relationship.

Applications worth knowing include the temperature dependence of gas solubility — the constant increases with temperature, so gases are less soluble in warm water — and the pressure dependence that explains why dissolved gas comes out of solution when pressure is released.

Colligative properties in this framework

Adding a non-volatile solute lowers the solvent's vapour pressure according to Raoult's law. Every colligative property follows from that single lowering: boiling point elevation, freezing point depression and osmotic pressure are all consequences of it.

They are called colligative because they depend on the number of solute particles, not their identity. That is why an electrolyte producing several ions per formula unit has a larger effect than its molar concentration suggests, and the van't Hoff factor accounts for the difference.

Frequently asked questions

Why can an azeotrope not be separated by distillation?

Because at that composition the vapour has the same composition as the liquid, so condensing it changes nothing. Distillation depends on that difference existing.

Why is enthalpy of mixing zero for an ideal solution?

Because unlike interactions match like ones, so no net energy change accompanies replacing a neighbour of one type with the other.

How are Raoult and Henry related?

They are the limiting behaviours of the same component at opposite ends of the composition range — Raoult as mole fraction approaches one, Henry as it approaches zero.

Why does the van't Hoff factor matter?

Because colligative properties count particles. An electrolyte dissociating into several ions produces more particles than its formula concentration implies, and the factor corrects for that — including for incomplete dissociation or association.