Ionisation of water, pH, weak acids and weak bases

Water self-ionises: its ionic product Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 298 K, so pure water there has [H₃O⁺] = 1.0 × 10⁻⁷ M and pH 7.

Kw increases with temperature, so neutral water has pH below 7 when hot; neutrality means [H₃O⁺] = [OH⁻], not pH = 7.

pH = −log[H₃O⁺] and pH + pOH = pKw = 14 at 298 K.

For strong acids and bases, take complete dissociation and count all H⁺ or OH⁻ released: 0.05 M Ba(OH)₂ gives [OH⁻] = 0.10 M, pOH 1 and pH 13.

For a weak acid HA of concentration c and degree of ionisation α, Ka = cα²/(1 − α); when α is small, α ≈ √(Ka/c) and [H₃O⁺] ≈ √(Ka c).

pKa = −log Ka; a larger Ka (smaller pKa) means a stronger acid. Weak bases are treated the same way with Kb.

For a conjugate pair, Ka × Kb = Kw, so pKa + pKb = 14 at 298 K.

Polyprotic acids ionise in steps with Ka₁ > Ka₂ > Ka₃, because removing a proton from a negative ion is harder.

Acid strength of H–A: down a group, bond strength controls it (HF < HCl < HBr < HI); along a period, electronegativity of A controls it (CH₄ < NH₃ < H₂O < HF).