# Solutions

> Henry's law, Raoult's law, azeotropes, colligative properties and van't Hoff factor — NCERT Class 12 NEET-UG Chemistry notes with a worked example.

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- Exam / course: NEET-UG · Subject: Chemistry
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- First published: 2026-10-02
- Last updated: 2026-10-02
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## Direct answer

Raoult's law ties a solution's vapour pressure to composition: the partial pressure of each volatile component equals its pure vapour pressure times its mole fraction, and deviations from this define ideal versus non-ideal solutions. Colligative properties — relative lowering of vapour pressure, boiling point elevation (ΔTb = Kb m), freezing point depression (ΔTf = Kf m) and osmotic pressure (π = CRT) — depend only on the number of solute particles, which is why they measure molar mass. Water's constants, Kb = 0.52 K kg per mol and Kf = 1.86 K kg per mol, anchor most numericals, and the van't Hoff factor i corrects for dissociation (KCl, i ≈ 2) and association (benzoic acid dimerising in benzene, i ≈ 0.5).

## What you must remember

- Henry's law p = KH x: higher KH means lower solubility, and KH rises with temperature, which is why aquatic life suffers in warm water.
- Soda bottles are bottled under high pressure; scuba tanks dilute air with helium to avoid nitrogen narcosis and the bends.
- Positive deviation gives a minimum-boiling azeotrope (ethanol 95 per cent by volume with water); negative deviation gives maximum-boiling (nitric acid 68 per cent by mass with water).
- Ideal solution: obeys Raoult's law throughout, ΔHmix = 0, ΔVmix = 0 — benzene with toluene is the textbook pair.
- Osmotic pressure uses the ideal gas form π = (n/V)RT; solutions of equal π are isotonic, and 0.9 per cent saline matches blood.
- Reverse osmosis needs external pressure exceeding osmotic pressure and desalinates sea water.
- Abnormal molar mass: i = observed colligative effect ÷ calculated effect, and observed molar mass = normal molar mass / i.

## From a freezing-point dip to a molar mass

An NCERT-style question: 1.0 g of a non-electrolyte dissolved in 50 g of benzene lowers the freezing point by 0.40 K; Kf of benzene is 5.12 K kg per mol. Find the molar mass. Start from ΔTf = Kf × m, so the molality is 0.40/5.12 = 0.078 mol per kg of solvent. The solvent mass is 0.050 kg, so moles of solute = 0.078 × 0.050 = 0.0039 mol. Molar mass = 1.0 g / 0.0039 mol ≈ 256 g per mol. Two habits make this automatic: convert solvent grams to kilograms before using Kf, and resist computing molarity — colligative laws speak molality, not molarity, because they must not depend on temperature. If the question added "the solute dimerises in benzene", divide by i = 0.5 to get the true molar mass of 512 g per mol; the 256 you first computed is the apparent (abnormal) value NCERT warns about.

## Where the marks leak

Kb and Kf belong to the solvent, not the solute — a question that quietly hands you ethanol's constants while you mentally use water's is testing exactly that attention. Second, the azeotrope pairs get swapped: ethanol–water is minimum boiling because the deviation is positive (A–B repulsions), nitric acid–water is maximum boiling because the deviation is negative (A–B attraction); the words "95 per cent" and "68 per cent" make regular appearances in the options. Third, gas solubility: students say solubility rises with temperature; for gases it falls, since Henry's constant KH increases — the fact behind boiled-water tasting flat and rivers holding less oxygen in summer. Finally, in osmotic problems remember π = CRT uses molarity (a volume-based term), the one colligative property where temperature sits explicitly in the formula and the measurement happens at room temperature.

## Frequently asked questions

### What happens to the solubility of a gas as temperature rises?

It decreases, because KH increases with temperature; this is why fizzy drinks go flat faster when warm.

### Why does benzoic acid show roughly half its expected molar mass in benzene?

It dimerises through hydrogen bonding, so the particle count halves (i ≈ 0.5) and the apparent molar mass doubles from the colligative measurement's viewpoint.

### What is the difference between minimum- and maximum-boiling azeotropes?

Minimum-boiling types arise from positive deviation (ethanol–water, 95 per cent), maximum-boiling from negative deviation (HNO3–water, 68 per cent); both boil at constant composition.

### Which colligative property is best for measuring polymer molar masses?

Osmotic pressure, because it gives measurable magnitudes at room temperature for very low solute mole fractions.

### What pressure is needed for reverse osmosis?

External pressure larger than the osmotic pressure of the solution, pushing solvent from the concentrated side through the semipermeable membrane.