Acid-Base Titration Curves and Indicators

For a strong acid–strong base titration in an ideal dilute solution at 25 °C, the initial pH is approximately −log[H₃O⁺]. Before equivalence, use excess acid moles divided by total volume; after equivalence, use excess base moles divided by total volume and convert pOH to pH. At equivalence the solution is neutral: pH = pK_w/2, or 7.00 at 25 °C.

This curve lacks a broad conjugate-pair buffer region. The size of the steep region depends on concentrations: very dilute titrations have a smaller jump than concentrated ones. A jump such as pH 3–11 is only an illustrative ordinary-concentration case. For extremely dilute solutions, water autoionization matters and the simple excess-concentration approximation must be revisited.

Region 1, before any base, is a weak acid ICE problem. Region 2 is a buffer, handled with Henderson-Hasselbalch on moles. Region 3, the half-equivalence point, has equal moles of acid and conjugate base, so pH = pK_a and the curve is at its flattest. Region 4, equivalence, is a solution of the conjugate base alone, so it is basic. Region 5 is governed by excess strong base.

For 25.00 mL of 0.100 M acetic acid, K_a = 1.80 × 10⁻⁵, titrated with 0.100 M NaOH at 25 °C, initial acid is 2.500 mmol and Veq = 25.00 mL:

At equivalence the original HA has been stoichiometrically converted, but the product A⁻ hydrolyzes; it is not a buffer containing equal prepared amounts. Just before or after equivalence, use the method whose species assumptions remain valid rather than forcing every point into Henderson–Hasselbalch.

An indicator is itself a weak acid whose two forms differ in colour, and it changes over roughly pK_a plus or minus 1. Phenolphthalein (range 8.3 to 10.0) suits a weak acid titration, methyl red (4.4 to 6.2) suits a weak base titration, and either works for strong-strong because the jump is so large.

Choose an indicator whose transition range lies within the steep part of the actual curve, so its color change requires little volume beyond or before equivalence. Merely knowing one equivalence-pH number is a useful first screen, not a full description of endpoint error. A weak acid–weak base titration often lacks a sharp jump and may need instrumental analysis. The endpoint is an observed signal; equivalence is the stoichiometric condition. They coincide only approximately in a well-designed indicator titration.

Polyprotic acids have successive stoichiometric equivalence amounts, but separate visible jumps require sufficiently separated acid strengths and suitable concentrations. Closely spaced pK_a values can merge regions, and a very weak final proton may have no useful visual endpoint. For a resolved diprotic system, the first half-equivalence volume estimates pK_a₁; the midpoint between the first and second equivalence volumes estimates pK_a₂. At the first equivalence, an amphiprotic intermediate may require both neighboring equilibria rather than a one-step weak-acid formula.

For a weak base titrated by strong acid, the pH falls and the equivalence solution contains its conjugate acid. At half-equivalence pH ≈ pK_a of that conjugate acid, equivalently pK_w − pK_b. Reverse the acid/base interpretation rather than copying the rising weak-acid curve.