Solutions

Ways to express concentration

Molarity (M), molality (m), mole fraction (χ), ppm, mass percent — know which uses mass of solvent vs volume of solution. Molality is preferred when temperature swings matter for colligative properties.

For dilution: M₁V₁ = M₂V₂ only when the solute amount is conserved and you are not mixing chemically. Mixing acids or ethanol and water needs care — volumes are not always additive.

Raoult’s law

For a volatile component in an ideal solution: pᵢ = χᵢ pᵢ° (partial pressure = mole fraction × vapour pressure of pure liquid).

Ideal solution: ΔH_mix = 0, ΔV_mix = 0, obeys Raoult over the whole range. Non-ideal: positive deviation (A–B weaker than A–A, B–B — e.g. ethanol–water) or negative deviation (stronger A–B).

Azetropes: constant-boiling mixtures; composition of vapour equals liquid at that point — fractional distillation cannot split them beyond the azeotropic composition.

Colligative properties

Depend on number of solute particles, not identity: relative lowering of vapour pressure, elevation of boiling point ΔT_b = K_b m, depression of freezing point ΔT_f = K_f m, osmotic pressure π = MRT (dilute solutions).

Van’t Hoff factor i accounts for dissociation or association: observed colligative property = i × value for non-electrolyte. NaCl → i ≈ 2 for dilute complete dissociation; weak electrolytes and association (carboxylic acids) give i < calculated from formula.

Solubility and Henry’s law

Like dissolves like: polar solutes in polar solvents; non-polar in non-polar. Hydration enthalpy vs lattice enthalpy decides ionic salt solubility trends — Na salts often soluble; some carbonates and sulphates less so.

Henry’s law: p = K_H × x (gas in liquid). Higher K_H or lower solubility for a given gas depends on wording in your text — use the form your NCERT uses. Temperature usually lowers gas solubility in water.