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.
The four colligative properties
| Property | Relation |
|---|---|
| Relative lowering of vapour pressure | (p° − p) / p° = xsolute |
| Elevation of boiling point | ΔTb = i Kb m |
| Depression of freezing point | ΔTf = i Kf 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.
ΔTf = i Kf 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.
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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