Colligative Properties
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Direct answer
Colligative properties — relative lowering of vapour pressure, boiling point elevation, freezing point depression and osmotic pressure — depend on the number of solute particles, not their identity. Each follows a counting law: delta p/p° = x(solute), delta T_b = K_b m, delta T_f = K_f m and pi = C R T. Where solutes dissociate or associate, the van't Hoff factor i corrects the particle count: i = observed colligative effect / calculated effect.
What you must remember
- Raoult's law: p = p° x for a volatile component; for an ideal pair, total vapour pressure p = pA° xA + pB° xB across all proportions.
- Positive deviation (weaker interactions) gives minimum-boiling azeotropes like ethanol-water; negative deviation gives maximum-boiling azeotropes like nitric acid-water (about 68 per cent HNO3).
- delta T_b = K_b × m and delta T_f = K_f × m on molality; for water K_b = 0.52 and K_f = 1.86 K kg mol^-1.
- Osmotic pressure pi = C R T; osmosis is solvent flow across a semipermeable membrane towards the concentrated side; equal pi means isotonic.
- van't Hoff factor: i = 1 + alpha(n - 1) for dissociation into n particles, i below 1 on association; observed molar mass M(observed) = M(normal)/i. Counts: NaCl 2, CaCl2 3, K4[Fe(CN)6] and Al2(SO4)3 5 each; benzoic acid dimerising in benzene gives about 0.5.
- Henry's law p = K_H x: K_H rises with temperature, so gas solubility in water falls on heating — the physics behind the bends in scuba diving and fizz escaping warm drinks.
- Osmotic pressure is the preferred route to macromolecular molar masses: measurable at room temperature with molarity.
Common confusion
The classic error is sign logic for association versus dissociation: dissociation creates more particles, so effects grow, i exceeds 1 and apparent molar mass falls below true; association does the reverse. Students plug molarity into delta T_b or delta T_f (they need molality) or molality into pi (it needs molarity), and read azeotropes as pure compounds — an azeotrope is a mixture whose vapour matches its liquid composition, resisting distillation.
Exam-focused takeaway
JEE Main tests the four laws as direct numericals — compute delta T_f or pi, find molar mass from a depression, pick i for a named electrolyte. JEE Advanced layers concepts: Raoult with Dalton's law over an ideal pair, vapour-composition diagrams read for deviation type, molar mass anomalies from i (dimerising benzoic acid, ionising KCl), and isotonic-condition problems. Write the concentration unit each formula wants before substituting.
Frequently asked questions
Why are colligative properties called colligative?
They depend on the collective number of solute particles, not their nature — equal moles of any non-volatile solute lower the freezing point equally.
What is the van't Hoff factor?
The ratio of actual to nominal particle count: 2 for NaCl, about 0.5 for a dimerising acid in benzene; it multiplies every colligative effect.
What is an azeotrope?
A mixture boiling at constant composition — minimum-boiling ethanol-water, maximum-boiling nitric acid-water — that simple distillation cannot separate.
Why is osmotic pressure preferred for polymer masses?
It is measurable at room temperature on dilute solutions and avoids the heat and tiny effects that damage macromolecules.
How does Henry's law explain the bends?
Rapid ascent lowers pressure, dissolved nitrogen's solubility drops and it bubbles out of blood — hence staged decompression.
Does delta T_f use molality or molarity?
Molality: delta T_f = K_f × m, because solvent mass, unlike volume, does not change with temperature.