Solutions of Non-electrolytes: Raoult’s Law, Henry’s Law and Colligative Properties
7 questions a year on average (42 in 2021–2026), in the physical block (about Q61–Q70). Mostly one-step numericals on Raoult’s law, Henry’s law, ΔTb, ΔTf and π.
Syllabus (Paper II, unit 7): Raoult's and Henry's laws, ideal and real solutions, colligative properties: lowering of vapour pressure, osmotic pressure, elevation of boiling point, depression of freezing point, van 't Hoff factor, solubility of gases.
7.1Concentration terms
| Term | Definition | Changes with temperature? |
|---|---|---|
| Mole fraction xB | nB/(nA + nB); Σx = 1 | no |
| Molality m | mol of solute per kg of solvent | no |
| Molarity c | mol of solute per litre of solution | yes (volume changes) |
| Mass or volume percent, ppm | g per 100 g (or mL); g per 10⁶ g | mass basis no |
- Colligative formulas use molality for ΔTb and ΔTf, molarity for osmotic pressure and mole fraction for vapour pressure. In dilute aqueous solution molality ≈ molarity, since 1 L of solution holds about 1 kg of water.
- For a dilute solution xB ≈ nB/nA = mMA (MA in kg mol⁻¹).
7.2Raoult’s law and ideal solutions
Raoult’s law: the partial vapour pressure of a component equals its mole fraction in the liquid times the vapour pressure of the pure component.
- The total pressure is a straight line in xA (liquid composition). In terms of vapour composition it is not: 1/p = yA/p°A + yB/p°B, so 1/p is linear in y.
- Vapour composition (Dalton): yA = pA/p = xAp°A/p. The vapour is richer in the more volatile component. With ratios only: if p°A : p°B = 1 : 6 and xA : xB = 1 : 4, then pA : pB = 1 : 24 and yB = 24/25 = 0.96.
- Ideal solution: obeys Raoult’s law at all compositions because A–B attractions equal the average of A–A and B–B. Then ΔmixH = 0, ΔmixV = 0, ΔmixS > 0 and ΔmixG < 0. Near-ideal pairs: benzene + toluene, hexane + heptane, bromoethane + chloroethane.
Non-volatile solute: relative lowering of vapour pressure
- Only the solvent evaporates, so the solution’s vapour pressure is p = xAp°. The relative lowering equals the mole fraction of solute. Papers usually expect the dilute form nB/nA; check whether the options were made with it.
7.3Real solutions: deviations from Raoult’s law
| Positive deviation | Negative deviation | |
|---|---|---|
| A–B attraction | weaker than A–A and B–B | stronger than A–A and B–B |
| ΔmixH, ΔmixV | both > 0 (heat absorbed, volume expands) | both < 0 (heat released, volume contracts) |
| Examples | ethanol + water, acetone + CS₂, ethanol + cyclohexane | acetone + chloroform, HNO₃ + water, HCl + water, phenol + aniline |
| Azeotrope | minimum-boiling (ethanol + water, 95.6% ethanol, 351 K) | maximum-boiling (HNO₃ + water, 68% HNO₃, 393.5 K) |
- In a dilute real solution the solvent follows Raoult’s law (pA → xAp°A as xA → 1), while the solute follows Henry’s law (pB = KHxB as xB → 0) with KH ≠ p°B. Such a solution is called ideal-dilute. On a plot of solute vapour pressure against its mole fraction: the line through p°B is Raoult’s ideal line, the tangent at xB = 0 is Henry’s line, and the curve between is the real solution.
- An azeotrope boils at constant composition; it cannot be separated by simple fractional distillation.
Prelims notes
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