Ostwald's Dilution LawJEE Main

Concept

A weak electrolyte HA ⇌ H⁺ + A⁻ obeys $K_a = \frac{C\alpha^2}{1-\alpha}$. Since $K_a$ is fixed, diluting (smaller C) forces α up — Ostwald's dilution law. At infinite dilution even a weak acid is fully dissociated, yet its solution grows LESS acidic because there's less of it per litre.

Key formula

Derivation

Set up the ICE table: HA starts at C; at equilibrium HA = C(1−α), H⁺ = A⁻ = Cα.

$$K_a = \frac{(C\alpha)^2}{C(1-\alpha)} = \frac{C\alpha^2}{1-\alpha}$$

For α < 5% drop the (1−α): α = √(Ka/C) — halve C, α grows √2×. But [H⁺] = √(KaC) FALLS on dilution.

Scenarios to explore

• Ostwald's Dilution Law — Dilute a weak acid — α climbs while pH still rises.

Real-world applications

• Weak-acid pH calculations (vinegar, formic acid).
• Conductivity of weak electrolytes rising on dilution (Λ ∝ α).
• Buffer design begins from Ka and α.

JEE exam tips

• [H⁺] = √(KaC) — the single most-used weak-acid formula.
• Molar conductivity: α = Λ/Λ° connects this to Kohlrausch.
• pH of weak acid = ½(pKa − log C).

Common mistakes

• Applying the law to STRONG electrolytes (α ≈ 1 always; law fails).
• Thinking dilution raises acidity — α rises but [H⁺] falls.
• Using the √ approximation when α > 5% (small Ka·large dilution).

Exam traps to avoid

• At extreme dilution (C → 10⁻⁷), water's own H⁺ matters — pH never crosses 7 for an acid.
• α doubles when C drops 4× (square-root scaling), not 2×.