Abnormal molar mass and van’t Hoff factor

The essentials

Colligative properties count particles. If a solute dissociates (like NaCl into Na⁺ and Cl⁻) the number of particles increases, and if it associates (like ethanoic acid forming dimers in benzene) the number decreases. The molar mass calculated from such measurements is then "abnormal": lower than the true value for dissociation and higher for association.

Key points

• van't Hoff factor i = normal molar mass ÷ abnormal molar mass = observed colligative property ÷ calculated colligative property = total moles of particles after association/dissociation ÷ moles of particles before.
• Modified equations: ΔTb = iKbm, ΔTf = iKfm, π = iCRT, relative lowering of vapour pressure = i × x₂ (dilute solutions).
• For complete dissociation: NaCl, KCl i = 2; K₂SO₄, CaCl₂ i = 3; K₃[Fe(CN)₆] i = 4.
• For complete dimerisation (2A → A₂), i = ½.
• Degree of dissociation for an electrolyte giving n ions: α = (i − 1) ÷ (n − 1).
• Degree of association for nA → Aₙ: α = (1 − i) ÷ (1 − 1/n).

Exam tips

• When comparing solutions of equal molality, the one with the larger i has the larger ΔTf and ΔTb and the lower freezing point.
• Example: 0.1 m NaCl in water, i = 2: ΔTf = 2 × 1.86 × 0.1 = 0.372 K.

Common mistakes

• Using i = 1 for strong electrolytes.
• Forgetting that association makes i less than 1, so the apparent molar mass is larger.