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Solutions

Concentration terms, Raoult's law, and the four colligative properties with the van 't Hoff factor for electrolytes.

Questions in the bank
110
q/paper in 2025–26
1.09
Calculation
65%
Notes pages
6

Strand: Calculate

When you’ll see it

A gas dissolving under pressure, the vapour pressure of a mixture, or a solute changing a boiling point, freezing point or osmotic pressure.

How this chapter is tested

Almost every question is a single formula with new numbers: Henry's law, Raoult's law, ΔT = iK·m or π = iCRT. The van 't Hoff factor multiplies each colligative effect for a salt, a weak acid or an associating solute, and finding i or α from a measured shift is where much of the chapter sits.

What decides the marks is the concentration each formula wants: a mole fraction for vapour pressure, moles per kilogram of solvent for boiling and freezing points, and moles per litre of solution for osmotic pressure. A large share are numeric-answer questions, so a slip in grams against kilograms or in R against the pressure unit cannot be rescued by the options.

The recall is narrow: what the Henry constant depends on, which mixtures deviate from Raoult's law and which azeotrope each gives, which way solvent flows in osmosis, and that only pure solvent freezes out.

The sub-skills

The distinct skills inside the chapter, in the order to learn them.

  • Henry's law

    p = KH·x with the gas's partial pressure; a larger KH means a less soluble gas; 1 L of water is 55.56 mol.

  • Raoult's law for volatile liquids

    P = x_A p°_A + x_B p°_B; vapour y_A = x_A p°_A/P; positive deviation gives a minimum-boiling azeotrope, negative a maximum-boiling one.

  • Relative lowering of vapour pressure

    (p° − p)/p° = x₂ ≈ n₂/n₁; reachable from ΔTb because both depend on the same moles of solute.

  • Boiling and freezing points

    ΔTb = iKb·m and ΔTf = iKf·m with m per kg of solvent; M₂ = 1000Kw₂/(ΔT·W₁); water's Kf 1.86 exceeds its Kb 0.52.

  • Osmotic pressure

    π = iCRT with C per litre of solution and R matched to the pressure unit; isotonic solutions have equal iC.

  • Van 't Hoff factor

    i = 1 + (n − 1)α for dissociation, i = 1 − α/2 for a dimer; rank solutions by i × m.

Traps to expect

Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.

  • Total pressure in Henry's law

    A gas that is one-fifth of the air at 5 atm has p = 1 atm. Putting 5 atm into p = KH·x gives a mole fraction five times too large.

  • Forgetting i, or dividing by n

    0.1 M NaCl is not isotonic with 0.1 M glucose. And α = (i − 1)/(n − 1): for MX₃ with i = 1.9, α = 0.3, not 0.9/4.

  • Molality against molarity

    ΔT uses kilograms of solvent; π uses litres of solution. Kilograms for molality, grams for moles of solvent; mixing them is a factor of 1000.

  • Mole fractions swapped

    With 1 mol A and 3 mol B, x_A = 0.25 multiplies p°_A. The relative lowering is the solute's mole fraction, p/p° the solvent's.

  • Azeotropes swapped

    Ethanol + water deviates positively and boils at a minimum; chloroform + acetone forms a new hydrogen bond, deviates negatively and boils at a maximum.

Learn it before you drill it

This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each page. Read the notes once, then drill page by page below.

Solutions notes

Drill every Solutions question

110 questions from the bank, across 6 subtopics.

Drill the 110 questions

Drill one subtopic at a time

The 6 subtopics, in teaching order.

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