Raoult's law, ideal and non-ideal solutions

Chemistry · Solutions. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Raoult's law says that the vapour pressure of a solvent above a solution equals the vapour pressure of the pure solvent multiplied by its mole fraction in the solution. A dissolved solute therefore lowers the vapour pressure of the solvent.

An ideal solution obeys Raoult's law at all concentrations. The attractions between unlike molecules are the same as those between like molecules. Non-ideal solutions show positive or negative deviations and can form an azeotropic mixture, which boils at a constant temperature without changing composition.

A solubility curve is a graph of solubility against temperature. Most curves rise smoothly; a few show a sudden break.

Rules to remember

Raoult's law: p = p° × X₁, where X₁ is the mole fraction of the solvent. Relative lowering of vapour pressure: Δp ÷ p° = X₂, the mole fraction of the solute.
Two volatile liquids: total vapour pressure P = p°_AX_A + p°_BX_B. The vapour is richer in the more volatile component.
Ideal (nearly): benzene and toluene; no heat change and no volume change on mixing.
Positive deviation: A−B attractions are weaker, vapour pressure is higher than predicted, e.g. ethanol and water. They form a minimum-boiling azeotrope with about 95.6% ethanol.
Negative deviation: A−B attractions are stronger, vapour pressure is lower than predicted, e.g. acetone and chloroform, or HCl and water (maximum-boiling azeotrope).
An azeotrope cannot be separated by fractional distillation, because the liquid and the vapour have the same composition.
Solubility rises with temperature if dissolving absorbs heat (e.g. KNO₃); NaCl changes very little; Na₂SO₄·10H₂O shows a break at 32.4 °C.

Common mistake

Students mix up the two deviations. Positive deviation means a higher vapour pressure than Raoult's law predicts, so a lower boiling point (minimum-boiling azeotrope). Negative deviation is the opposite.

Worked example

At a certain temperature p° of liquid A is 100 torr and p° of liquid B is 40 torr. They form an ideal solution with mole fraction of A = 0.25. Find the total vapour pressure and the mole fraction of A in the vapour.

X_B = 1 − 0.25 = 0.75
p_A = 100 × 0.25 = 25 torr and p_B = 40 × 0.75 = 30 torr
Total vapour pressure = 25 + 30 = 55 torr
Mole fraction of A in the vapour = 25 ÷ 55 = 0.45, which is more than 0.25 in the liquid.

Answer: Total vapour pressure = 55 torr; the vapour contains A with mole fraction 0.45, so it is richer in the more volatile liquid A.

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Chapter 9: Solutions

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