Solutions
Solutions is a short, high-yield domain: concentration terms, Raoult's law, deviation behaviour, and one colligative-property calculation. Bihar Board papers usually pair a conceptual part (why does a mixture show positive deviation?) with a numerical on molar mass or van't Hoff factor.
Core rules
- Molality (mol per kg solvent) is temperature-independent; molarity (mol per litre solution) is not. Colligative formulae use molality: ΔTb = Kb·m, ΔTf = Kf·m, π = CRT.
- Raoult's law: p_A = p°_A·x_A. An ideal solution obeys it at every composition with ΔH_mix = 0 and ΔV_mix = 0, meaning A–B interactions match A–A and B–B.
- Positive deviation (ΔH > 0, ΔV > 0): A–B attraction weaker than in the pure liquids - ethanol + acetone, ethanol + water. Negative deviation: chloroform + acetone, where new hydrogen bonding lowers vapour pressure.
- Azeotropes: minimum-boiling from positive deviation (ethanol–water, about 95% ethanol); maximum-boiling from negative deviation (HNO₃–water).
- Henry's law p = K_H·x; K_H increases with temperature, so gases are less soluble in warm water.
- van't Hoff factor i: i > 1 for dissociation, i < 1 for association. Benzoic acid dimerising in benzene approaches i = 0.5.
Worked example
1.00 g of a non-volatile solute in 100 g water raises the boiling point by 0.052 K (Kb = 0.52 K kg mol⁻¹). ΔTb = Kb·m gives m = 0.052 ÷ 0.52 = 0.100 mol kg⁻¹. So 0.100 kg of water holds 0.0100 mol, and M = 1.00 ÷ 0.0100 = 100 g mol⁻¹. The reasoning step that carries the marks is converting solvent mass to kg; using 100 g directly gives an answer 1000 times too small.
Traps that cost marks
- Substituting molarity where molality is required.
- Ignoring i for electrolytes (NaCl ≈ 2, K₂SO₄ ≈ 3).
- Claiming colligative properties depend on the nature of the solute - only particle number matters.
- Reporting ΔTf as a negative number instead of stating the magnitude of depression.