Solutions

Concept overview

A solution is a homogeneous mixture of two or more components. The 'solvent' is typically the component in largest amount and 'solute' the smaller one — but the rules of solution chemistry treat them symmetrically. Concentration units (molarity, molality, mole fraction, mass %, ppm) each have their preferred use case: molarity for stoichiometry at fixed temperature; molality when temperature varies (as in colligative properties); mole fraction in Raoult's-law contexts.

Raoult's law states that for an ideal solution, the vapour pressure of a solvent above the solution is p = x_solvent × p°, where p° is the pure solvent's vapour pressure. Adding a non-volatile solute lowers the solvent's vapour pressure proportionally to its mole fraction — the origin of the colligative properties (properties that depend on the number of solute particles but not their identity).

The four colligative properties are: (1) relative lowering of vapour pressure, Δp/p° = x_solute; (2) boiling-point elevation, ΔT_b = K_b × m; (3) freezing-point depression, ΔT_f = K_f × m; (4) osmotic pressure, π = CRT (with C in mol/L and T in K). For ionic solutes that dissociate, multiply the colligative expression by the van't Hoff factor i — typically 2 for NaCl, 3 for CaCl₂, and something less than the ideal value when ion pairing is significant.

Non-ideal solutions deviate from Raoult's law. Positive deviations (like ethanol + water) mean the vapour pressure is higher than predicted, arising from weaker A-B interactions than A-A and B-B. Negative deviations (like HCl + water) mean the opposite — stronger A-B interactions and lower vapour pressure. Azeotropes form at compositions where the vapour is compositionally identical to the liquid.

Key formulas & concepts

• Molarity: M = n_solute / V_solution (L)
• Molality: m = n_solute / m_solvent (kg)
• Mole fraction: x_i = n_i / n_total
• Raoult's law: p = x_solvent × p°_solvent
• Relative lowering: Δp / p° = x_solute
• Boiling-point elevation: ΔT_b = i × K_b × m
• Freezing-point depression: ΔT_f = i × K_f × m
• Osmotic pressure: π = i × M × R × T

Common mistakes to avoid

• Using molarity in colligative-property formulas — they all use molality (except osmotic pressure, which uses molarity).
• Ignoring the van't Hoff factor i for ionic solutes — NaCl has i ≈ 2, not 1.
• Applying Raoult's law to a highly concentrated solution — it holds in the dilute limit; non-ideal behaviour kicks in beyond a few percent.
• Confusing K_b (molal boiling-point elevation constant) with the equilibrium constant K_b for a weak base — different chapters, same symbol.

JEE Main relevance

JEE Main asks 2 solution problems every paper — one Raoult's-law or colligative-property calculation and one concentration-conversion numerical (molarity → molality → mole fraction). Both are formula-driven with predictable setups.

JEE Advanced relevance

Advanced solutions problems test non-ideal behaviour — computing i for a partial-dissociation problem, or deriving the vapour pressure of a two-component non-ideal mixture from given deviations. Osmotic-pressure problems combined with molar-mass determination of an unknown polymer are also Advanced staples.

Previous-year questions (PYQ)

800+ questions in the JEETutorAI bank. Filter by colligative properties for the first pass — the four formulas repeat with different numerical values year after year.