Titration Curve Calculator

How it works

equivalence volume V_e = C_a V_a ÷ C_t · pH from the charge balance [H⁺] + [cations] = [OH⁻] + [anions], with [A⁻] = C_HA·Ka ÷ (Ka + [H⁺]) for a weak acid and [BH⁺] = C_B·[H⁺] ÷ (Ka(BH⁺) + [H⁺]) for a weak base · Kw = 1.0 × 10⁻¹⁴ (25 °C) · half-equivalence: pH = pKa

Instead of switching between textbook shortcuts (initial pH, Henderson–Hasselbalch buffer region, hydrolysis at equivalence, excess titrant), this calculator solves the exact charge balance of the mixture at every point, so it stays correct near the start and the equivalence point where the shortcuts break down. Dilution by the added titrant is included. It assumes 25 °C, monoprotic acids or bases and ideal behaviour (concentrations instead of activities), which is accurate to a few hundredths of a pH unit for dilute solutions.

Worked example

Titrating 25 mL of 0.1 mol/L acetic acid (pKa 4.76) with 0.1 mol/L NaOH, the equivalence volume is 0.1 × 25 ÷ 0.1 = 25.00 mL. After 12.5 mL — the half-equivalence point — half the acid has become acetate and pH = 4.76, equal to the pKa. At the equivalence point the acetate solution is basic, pH 8.73.

Sources: LibreTexts Chemistry — Acid–base titrations · Harris — Quantitative Chemical Analysis (charge balance)

Frequently asked questions