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

For a weak acid, [H⁺] ≈ √(Ka × c). Ethanoic acid has Ka = 1.74 × 10⁻⁵ (pKa 4.76), so a 0.10 mol dm⁻³ solution gives pH ≈ 2.9. At half-equivalence in a weak acid titration, pH = pKa — that is how Ka is measured in required practical 9.

Buffers

A buffer resists pH change when small amounts of acid or base are added. You make one from a weak acid plus its salt, or by part-neutralising an excess of the weak acid.

Added H⁺ is removed by A⁻ → HA, while added OH⁻ is removed by HA → A⁻ + H₂O. Because the reservoirs of HA and A⁻ are large, their ratio — and hence the pH — stays nearly constant.

Choosing an indicator

The indicator's range must fall inside the vertical section of the curve. For strong–strong, either common indicator works. For weak acid–strong base pick phenolphthalein (8.3–10.0); for strong acid–weak base pick methyl orange (3.1–4.4). Weak–weak curves have no sharp section, so no indicator works — 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

SystemMethod
Strong acidpH = −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).
  1. First find [H⁺] = Ka × [HA]/[A⁻] = 1.74 × 10⁻⁵ × (0.10 ÷ 0.050) = 3.48 × 10⁻⁵.
  2. Then pH = −log(3.48 × 10⁻⁵) = 4.46.
Worked example — strong base. pH of 0.050 mol dm⁻³ NaOH at 298 K:
  1. Convert via Kw: [H⁺] = Kw ÷ [OH⁻] = 1.0 × 10⁻¹⁴ ÷ 0.050 = 2.0 × 10⁻¹³.
  2. That gives pH = 12.70.

3.1.12.5Reading titration curves

There are four shapes to recognise: strong–strong (vertical ~3–11), weak acid–strong base (starts ~3, vertical ~7–11), strong acid–weak base (vertical ~3–7, ends ~11) and weak–weak (no vertical section — no indicator works).

Strong (HCl) and weak (ethanoic) acid titrated with NaOH — same equivalence volume, different start pH and vertical region.
Strong (HCl) and weak (ethanoic) acid titrated with NaOH — same equivalence volume, different start pH and vertical region.Diagram: Roland.chem · Public domain · via Wikimedia Commons
Strong (NaOH) and weak (NH₃) base titrated with HCl — the mirror-image family.
Strong (NaOH) and weak (NH₃) base titrated with HCl — the mirror-image family.Diagram: Roland.chem · Public domain · via Wikimedia Commons

At half-equivalence, pH = pKa, and this is where buffering is strongest. The equivalence point 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.

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