Buffers, pH curves and indicators (HL)

The big idea: A buffer is a solution that resists a change in pH when a small amount of acid or alkali is added.

It is made from a conjugate acid–base pair held together in solution:

- a weak acid + its conjugate base (e.g. ethanoic acid + sodium ethanoate) → an acidic buffer - a weak base + its conjugate acid (e.g. ammonia + ammonium chloride) → a basic (alkaline) buffer

Both members must be present in appreciable amounts, so there is a large reservoir of each.

Two equilibria mop up added H⁺ and OH⁻: Take the acidic buffer HA / A⁻. The added ions are removed by the two members of the pair:

- add H⁺ → it is mopped up by the conjugate base: A⁻ + H⁺ → HA - add OH⁻ → it is mopped up by the weak acid: HA + OH⁻ → A⁻ + H₂O

Because large reserves of both HA and A⁻ are present, the ratio [A⁻]/[HA] barely changes, so the pH barely changes. The buffer is consumed only when one member runs low.

A basic buffer works the same way with the pair NH₃ / NH₄⁺: NH₃ mops up added H⁺ (NH₃ + H⁺ → NH₄⁺) and NH₄⁺ mops up added OH⁻ (NH₄⁺ + OH⁻ → NH₃ + H₂O).

The pH of a buffer is set by the pK_{a} of the weak acid and the ratio of conjugate base to acid. Rearranging the K_a expression and taking −log of both sides gives a tidy equation.

pH = pKa at the half-equivalence point: Notice what the ratio does:

- if [A⁻] = [HA], the log term is log(1) = 0, so pH = pK_{a} - more conjugate base than acid → log > 0 → pH above pK_a - more acid than conjugate base → log < 0 → pH below pK_a

This is why a buffer is most effective near pH = pK_a, and why the pH at the half-equivalence point of a titration reads off the pK_a directly.

Adding base from a burette into an acid (or vice versa) and plotting pH against volume added gives a titration pH curve. Its shape depends on whether the acid and the base are strong or weak, and three features matter for every curve: the buffer region (a gentle slope), the vertical jump near the endpoint, and the equivalence point (where stoichiometrically equal amounts have reacted).

Equivalence-point pH is NOT always 7: At the equivalence point the salt formed governs the pH:

- strong acid + strong base → neutral salt → equivalence pH = 7 - weak acid + strong base → salt of a weak acid hydrolyses → equivalence pH > 7 (basic) - strong acid + weak base → salt of a weak base hydrolyses → equivalence pH < 7 (acidic) - weak acid + weak base → small, ill-defined jump → equivalence pH ≈ 7 but no sharp vertical (hard to titrate)

The buffer region appears with a weak partner: Whenever a weak acid (or weak base) is being titrated, a buffer region forms in the middle of the curve — the weak acid and the conjugate base it is being turned into coexist, so the pH rises only gently. The midpoint of that buffer region is the half-equivalence point, where pH = pK_{a}. A strong–strong titration has no buffer region (no weak conjugate pair).

Below is the shape of a weak acid titrated with a strong base (e.g. ethanoic acid with sodium hydroxide), read as pH at key volumes — note the buffer plateau, the half-equivalence point where pH = pK_a, and the vertical jump up to a basic equivalence point:

An indicator is itself a weak acid: An acid–base indicator is a weak acid, HIn, whose acid form and conjugate base have different colours:

HIn ⇌ H⁺ + In⁻ (one colour ⇌ another colour)

Adding H⁺ pushes it to the coloured HIn form; adding OH⁻ pulls it to the In⁻ form. The colour changes over a narrow pH window — its colour-change range, centred roughly on the indicator's pK_{a}(In).

The selection rule: Choose an indicator whose pK_{a}(In) — i.e. its colour-change range — falls within the vertical jump at the equivalence point of the titration.

The sharp vertical jump means a single drop of titrant sweeps the pH through several units, so any indicator that changes colour inside that jump flips sharply at (essentially) the equivalence point:

- weak acid + strong base (equivalence > 7) → phenolphthalein (8.3–10.0) ✓; methyl orange would change far too early - strong acid + weak base (equivalence < 7) → methyl orange (3.1–4.4) ✓; phenolphthalein would change too late - strong acid + strong base (equivalence 7, huge jump ≈ 3–11) → almost any indicator works - weak acid + weak base → no sharp jump, so no indicator gives a clean endpoint (use a pH meter)

The three common indicators and their colour-change ranges on the pH scale — pick the one whose range sits inside the titration's vertical jump: