Titration Curve of a Weak Acid

The stoichiometric balance tells you the volume at which reactants have been consumed in stoichiometric amounts. The titration curve instead shows how pH changes throughout titrant addition. A weak acid titrated with strong base has an initial acid region, a buffer region, an equivalence point and excess base afterward. For 25.0 mL of 0.100 M acetic acid titrated with 0.100 M NaOH, equivalence occurs at 25.0 mL. The equivalence pH is about 8.73 rather than 7 because acetate reacts with water. The pH curve therefore adds acid equilibrium to the reaction balance; the two views answer different experimental questions.

By half the equivalence volume, half of the initial HA has been neutralized. The remaining acid and its conjugate base A⁻ therefore have equal amounts. In pH=pKa+log10(nA⁻/nHA), the ratio is one and its logarithm is zero. For the acetic acid example, the half-equivalence point occurs at 12.5 mL NaOH and pH≈4.76. This is a buffer-region approximation; close to the initial state or equivalence point, use the corresponding acid or hydrolysis equilibrium instead. The ratio uses amounts actually neutralized, not necessarily equal volumes when the solutions have different concentrations.

At equivalence, the weak acid has been consumed stoichiometrically, but its conjugate base A⁻ remains in solution. Acetate, for example, accepts protons from water and produces OH⁻. This hydrolysis makes the solution basic. In the example, dilution gives an acetate concentration of 0.0500 mol/L; with pKa=4.76, the approximation at 25 °C gives pH≈8.73. The value depends on concentration and temperature. A strong-acid/strong-base titration has no comparable base hydrolysis, so its equivalence pH is near 7. This follows from the basicity of the anion and is not a measurement error at the correctly determined stoichiometric endpoint.

The indicator transition range should fall within the steep pH jump around equivalence. In a weak-acid/strong-base titration, equivalence pH is above 7, so phenolphthalein may fit while an indicator with an acidic transition range could change too early. The actual curve matters more than the phrase “equivalence point.” The endpoint is the observed color change; equivalence is the stoichiometric condition. Good analysis selects an indicator whose endpoint volume lies as close as possible to the equivalence volume. Choose an indicator whose transition falls in the steep section, keeping the observed endpoint close to equivalence.

The shortcut assumes a monoprotic weak acid, strong base, dilute solution and roughly constant temperature. It approximates activities by concentrations. Polyprotic acids can have several buffer regions and equivalence points, so their stages must be handled separately. In very dilute solutions, water autoprotolysis affects pH more strongly. Nonideal solutions, electrode potentials and volume changes can also shift results. For precise analysis, use activities and complete equilibrium balances rather than extending the Henderson–Hasselbalch approximation across the entire curve. For quantitative work, use a full equilibrium calculation or measured curve and report the associated uncertainty.