Abnormal molar masses and van't Hoff factor

Ionic solutes dissociate in water and give more particles than formula units: 1 mol of KCl gives 1 mol of K⁺ and 1 mol of Cl⁻, so, ignoring interionic attraction, 1 mol of KCl in 1 kg of water would raise the boiling point by 2 × 0.52 = 1.04 K.

Dissociation therefore makes the molar mass found from a colligative property lower than the true value.

Association does the reverse: ethanoic acid forms hydrogen-bonded dimers in benzene, a solvent of low dielectric constant. If every molecule paired up, ΔTb and ΔTf would be half the normal value and the apparent molar mass twice the true one.

A molar mass found this way that is lower or higher than expected is called an abnormal molar mass.

van't Hoff factor: i = normal molar mass / abnormal molar mass = observed colligative property / calculated colligative property = total moles of particles after association or dissociation / moles before.

i > 1 for dissociation and i < 1 for association: i is close to 2 for aqueous KCl and nearly 0.5 for ethanoic acid in benzene.

With the factor included: relative lowering = i n₂/n₁, ΔTb = i Kb m, ΔTf = i Kf m and π = i n₂RT/V.

For strong electrolytes i approaches the full value only on dilution because ions attract each other: NaCl gives i = 1.87 at 0.1 m, 1.94 at 0.01 m and 1.97 at 0.001 m, and K₂SO₄ approaches 3.

For a weak electrolyte splitting into two ions with degree of dissociation α, i = 1 + α; for dimerisation with degree of association x, i = 1 − x/2.