Equilibrium
Chemical equilibrium, Kc and Kp, Le Chatelier, ionic equilibrium, pH, buffer, solubility product.
Chemical equilibrium and Kc/Kp
Equilibrium constant, units, relation Kp = Kc(RT)^Δn.
Le Chatelier's principle
Effect of concentration, temperature, pressure on equilibrium.
pH, buffers and solubility product
Acid-base equilibria, Henderson-Hasselbalch, Ksp.
pH measures the activity (effectively concentration) of H⁺ ions in solution:
pH = −log[H⁺]
Pure water at 25°C has [H⁺] = 10⁻⁷ M, so pH = 7. Acidic: pH < 7. Basic: pH > 7.
Water self-ionization: [H⁺][OH⁻] = K_w = 10⁻¹⁴ (at 25°C). So pH + pOH = 14.
Strong acids/bases dissociate completely:
- 0.01 M HCl → [H⁺] = 0.01 → pH = 2.
- 0.001 M NaOH → [OH⁻] = 0.001 → pOH = 3 → pH = 11.
Weak acids partially dissociate:
HA ⇌ H⁺ + A⁻, K_a = [H⁺][A⁻] / [HA]
For a weak acid with initial concentration C and small dissociation (α ≪ 1):
[H⁺] ≈ √(K_a · C), pH = ½ (pK_a − log C).
Buffer solutions resist pH change. They contain a weak acid + its conjugate base (or weak base + its conjugate acid).
Henderson-Hasselbalch equation:
pH = pK_a + log([A⁻] / [HA])
When [A⁻] = [HA], pH = pK_a — the maximum buffer capacity. Buffers work effectively within ±1 pH unit of pK_a.
Worked example. Acetic acid (pK_a = 4.74) and sodium acetate buffer with [HA] = 0.1 M, [A⁻] = 0.1 M:
pH = 4.74 + log(0.1/0.1) = 4.74 + 0 = 4.74.
If you add 0.01 mol of HCl per litre to this buffer, [HA] becomes 0.11, [A⁻] becomes 0.09:
pH = 4.74 + log(0.09/0.11) = 4.74 − 0.087 = 4.65.
Adding the same HCl to pure water (pH 7) would give pH 2 — buffer changed by 0.09 units vs pure water by 5 units. That's the buffering action.