Solutions and Colligative Properties (Class 12): Formulas Plus Solved Numericals

Raoult's law, the four colligative properties, and the van't Hoff factor that decides whether your answer is right or half right.

Class 12 · Physical Chemistry · Concept · Updated 24 August 2026

The core idea: A colligative property depends on the number of solute particles, not their identity. Everything in this chapter follows from that one sentence — including why NaCl depresses freezing point roughly twice as much as glucose at the same molality.

The four colligative properties

Property	Relation
Relative lowering of vapour pressure	(p° − p) / p° = x_solute
Elevation of boiling point	ΔT_b = i K_b m
Depression of freezing point	ΔT_f = i K_f m
Osmotic pressure	π = i C R T

The van't Hoff factor is where marks are won

The factor i accounts for particles produced or removed in solution. Ignore it and every electrolyte numerical in the chapter comes out wrong.

Non-electrolyte such as glucose or urea: i = 1.
NaCl dissociating completely: i = 2. K₂SO₄: i = 3.
Association, as with benzoic acid dimerising in benzene: i < 1.
For partial dissociation into n particles with degree α: i = 1 + (n − 1)α.

Worked: ΔT_f for 0.1 m NaCl in water, K_f = 1.86 K kg mol⁻¹
ΔT_f = i K_f m = 2 × 1.86 × 0.1 = 0.372 K → freezing point = −0.372 °C

Molality, not molarity

Boiling-point elevation and freezing-point depression both use molality (mol of solute per kg of solvent), not molarity. Molality is chosen because it does not change with temperature, whereas molarity does — volume expands when heated.

A very common error is dividing by the mass of the solution rather than the mass of the solvent. Read the question twice on this point.

Exam tip: When a numerical gives you an observed ΔT_f and a calculated one, it is asking for i — and usually then for the degree of dissociation or association. Spotting that pattern saves a minute.

FAQs

Why is molality used instead of molarity?

Molality is based on mass, which does not change with temperature. Molarity is based on volume, which does.

Why does NaCl depress freezing point more than glucose?

NaCl gives two particles per formula unit in solution (i = 2) while glucose gives one. Colligative properties count particles.

Can the van't Hoff factor be less than 1?

Yes, when solute molecules associate — for example carboxylic acids dimerising in benzene.

What is an ideal solution?

One that obeys Raoult's law across all compositions, with ΔH of mixing and ΔV of mixing both zero.

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