Colligative properties

The essentials

Colligative properties depend on the number of solute particles in a given amount of solvent, not on their identity. For dilute solutions of non-volatile, non-electrolyte solutes there are four such properties.

Key points

• Relative lowering of vapour pressure: (p₁° − p₁) ÷ p₁° = x₂, the mole fraction of solute.
• Elevation of boiling point: ΔTb = Kb × m, where Kb is the ebullioscopic constant (for water, 0.52 K kg mol⁻¹).
• Depression of freezing point: ΔTf = Kf × m, where Kf is the cryoscopic constant (for water, 1.86 K kg mol⁻¹).
• Osmotic pressure: π = CRT, where C is molarity, R the gas constant and T the temperature in kelvin.
• Molar mass of solute can be found from each: for example M₂ = (Kb × w₂ × 1000) ÷ (ΔTb × w₁) with masses in grams.
• Osmotic pressure is preferred for proteins and polymers because it is measured at room temperature and gives large values even for very dilute solutions.
• Isotonic solutions have equal osmotic pressure. Blood cells swell in a hypotonic solution and shrink in a hypertonic one; 0.9% saline is isotonic with blood.
• Reverse osmosis: applying a pressure larger than the osmotic pressure forces pure solvent out of the solution through a semipermeable membrane; used in desalination of seawater.

Exam tips

• Use molality for ΔTb and ΔTf, and molarity for π.
• Equal molal solutions of non-electrolytes give equal ΔTb in the same solvent.

Common mistakes

• Using °C directly in π = CRT instead of kelvin.
• Forgetting that the solute must be non-volatile for vapour pressure lowering formulae.