Solutions
Solutions tests concentration units, Raoult's law, ideal and non-ideal behaviour, azeotropes, Henry's law and the four colligative properties - the most numerical part of the physical chemistry paper.
Concentration terms
- Molarity (M) = mol solute per litre of solution; it changes with temperature.
- Molality (m) = mol solute per kg of solvent; temperature-independent, and the unit used inside colligative formulae.
- Mole fraction, mass percentage, and ppm (mg per kg for dilute aqueous solutions).
Raoult's law and deviations
Each component's partial vapour pressure equals its mole fraction in the liquid times its pure vapour pressure. Ideal solutions have ΔH_mix = 0 and ΔV_mix = 0 (benzene–toluene). Positive deviation (ethanol–acetone) means A–B forces are weaker than A–A and B–B, giving a minimum-boiling azeotrope; negative deviation (chloroform–acetone, hydrogen bonding) gives a maximum-boiling azeotrope.
Colligative properties
Relative lowering of vapour pressure, ΔTb = i·Kb·m, ΔTf = i·Kf·m, and π = iCRT all depend on the number of solute particles, not their identity. The van't Hoff factor i > 1 for dissociation (NaCl → 2 ions) and i < 1 for association (benzoic acid dimerises in benzene, i ≈ 0.5).
Worked example
5.85 g of NaCl (M = 58.5 g mol⁻¹) is dissolved in 500 g of water; Kf = 1.86 K kg mol⁻¹. Moles = 5.85/58.5 = 0.100 mol, so m = 0.100/0.500 = 0.200 mol kg⁻¹. NaCl dissociates completely, so i = 2. ΔTf = 2 × 1.86 × 0.200 = 0.744 K, therefore the freezing point is −0.744 °C.
Traps that cost marks
- Substituting molarity into a formula that requires molality.
- Using i = 2 for a weak electrolyte such as acetic acid (i is only slightly above 1 there).
- Confusing the unit of Kf (K kg mol⁻¹) with the value of ΔTf itself.
- Reporting the freezing point as +0.744 °C instead of a depression below 0 °C.