Solutions
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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.