Abnormal molar masses

Colligative properties count particles. So when a solute breaks up or joins up in solution, the measured effect changes, and the molar mass worked out from it looks wrong.

• Dissociation: salts and other electrolytes split into ions. NaCl gives Na⁺ and Cl⁻, two particles, so the effect is about double. Salt does this in water even if the question does not say so.
• Association: some molecules pair up. Acids such as ethanoic or benzoic acid form dimers in benzene through hydrogen bonds, so there are fewer particles and the effect is smaller.

The van't Hoff factor i measures this:

i = normal molar mass ÷ observed molar mass = observed colligative effect ÷ calculated effect

Every formula then gets an i: ΔT_b = iK_b m, ΔT_f = iK_f m, Π = iCRT. Use i only when the solute breaks or joins; otherwise i = 1 and you leave it out.

To find i from the degree of breaking or joining, α. If a question gives a percentage, α = percentage ÷ 100; 'complete' means 100%, so α = 1.

• Dissociation into n ions: i = 1 + (n – 1)α. Fully dissociated NaCl: i = 1 + (2 – 1) × 1 = 2.
• Association into groups of n: i = 1 + (1/n – 1)α. For a dimer (n = 2) this is i = 1 – α/2.

Sometimes α is what the question asks for ('what fraction has dimerised?'). Then work the other way: find i from the measured ΔT, put it into the formula for i, and solve for α. Multiply by 100 for a percentage.

For a weak acid HA that only partly ionises, i = 1 + α, and its dissociation constant is K_a = cα² ÷ (1 – α).