A-level chemistry · Chapter 7
Acids, bases & buffers
pH, Ka, titration curves, indicators
Brønsted–Lowry: an acid is a proton donor; a base is a proton acceptor.
pH = −log₁₀[H⁺] · Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ at 298 K
Ka = [H⁺][A⁻]/[HA] · pKa = −log₁₀ Ka
- Weak acid pH: [H⁺] ≈ √(Ka × c). Ethanoic acid Ka = 1.74 × 10⁻⁵ (pKa 4.76); 0.10 mol dm⁻³ gives pH ≈ 2.9.
- At half-equivalence in a weak acid titration, pH = pKa — how Ka is measured (required practical 9).
Buffers
- A buffer resists pH change on adding small amounts of acid or base: weak acid + its salt (or excess weak acid part-neutralised).
- Added H⁺ is removed by A⁻ → HA; added OH⁻ is removed by HA → A⁻ + H₂O. The large reservoirs of HA and A⁻ keep the ratio, and hence pH, nearly constant.
Choosing an indicator
- The indicator's range must fall inside the vertical section of the curve. Strong–strong: either works. Weak acid–strong base: phenolphthalein (8.3–10.0). Strong acid–weak base: methyl orange (3.1–4.4). Weak–weak: no sharp section — use a pH meter.
The titration simulation lets you test all of this live.
3.1.12.3The four pH calculations you must do on demand
| System | Method |
|---|---|
| Strong acid | pH = −log[HA] (fully dissociated) |
| Strong base | [OH⁻] → [H⁺] = Kw ÷ [OH⁻] → pH |
| Weak acid | [H⁺] = √(Ka × c) → pH |
| Buffer | [H⁺] = Ka × [HA]/[A⁻] → pH |
Worked example — buffer. A buffer contains 0.10 mol ethanoic acid and 0.050 mol sodium ethanoate in 1 dm³ (Ka = 1.74 × 10⁻⁵).
- [H⁺] = Ka × [HA]/[A⁻] = 1.74 × 10⁻⁵ × (0.10 ÷ 0.050) = 3.48 × 10⁻⁵
- pH = −log(3.48 × 10⁻⁵) = 4.46
Worked example — strong base. pH of 0.050 mol dm⁻³ NaOH at 298 K:
- [H⁺] = Kw ÷ [OH⁻] = 1.0 × 10⁻¹⁴ ÷ 0.050 = 2.0 × 10⁻¹³
- pH = 12.70
3.1.12.5Reading titration curves
- Four shapes: strong–strong (vertical ~3–11), weak acid–strong base (starts ~3, vertical ~7–11), strong acid–weak base (vertical ~3–7, ends ~11), weak–weak (no vertical section — no indicator works).
- Half-equivalence: pH = pKa (biggest buffering). Equivalence for weak acid–strong base sits above 7 because the salt's anion is a base.
- Diprotic acids show two vertical sections — two equivalence points, at V and 2V.
Exam tip. Always quote pH to 2 decimal places, and check sanity: a weak acid's pH must sit between the strong-acid value and 7.
Extended🎓 Beyond the standard course
- When √(Ka·c) fails: the approximation assumes dissociation is small. If x is more than ~5% of c (very dilute, or Ka not so weak), solve the quadratic x² + Ka·x − Ka·c = 0 properly.
- Ultra-dilute traps: 10⁻⁸ mol dm⁻³ HCl is NOT pH 8 — water's own ionisation dominates and the answer is just under 7. Charge balance beats formulas.
- Polyprotic acids: H₂SO₄'s first proton is fully dissociated, the second only partially (Ka2 ≈ 0.01). For most polyprotic calculations the first ionisation dominates the pH.
- Your blood is a buffer (pH 7.35–7.45): CO₂/HCO₃⁻ with the lungs controlling [CO₂] and kidneys [HCO₃⁻]. Hyperventilation expels CO₂ → pH rises → alkalosis — Le Chatelier in your bloodstream.
- Indicators are acids too: colour changes when [HInd] ≈ [Ind⁻], i.e. around pH = pKind. That's why an indicator's range is ~2 units centred on its pKind, and why you pick pKind ≈ equivalence pH.
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