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Titration Curve Calculator

Calculate and plot the titration curve of a strong, weak or polyprotic acid with a strong base, with equivalence volumes, equivalence and half-equivalence pH.

Formula

Veq=CaVaCbV_{\mathrm{eq}} = \dfrac{C_a V_a}{C_b}
[H+]+[Na+]=[OH−]+∑(charge of the ionised forms of the acid)[\mathrm{H}^+] + [\mathrm{Na}^+] = [\mathrm{OH}^-] + \sum (\text{charge of the ionised forms of the acid})
at half-equivalence, pH=pKa (monoprotic)\text{at half-equivalence, } \mathrm{pH} = \mathrm{p}K_{\mathrm{a}}\ (\text{monoprotic})
Ca, VaC_a,\ V_a
acid concentration and volume
CbC_b
base (titrant) concentration

How it works

In a titration, strong base is added to an acid and the pH is followed. For a strong acid the curve is flat until just before the equivalence point, rises steeply through pH 7, and flattens again. A weak acid starts at a higher pH, buffers around its pKa, and has an equivalence point above 7, because the conjugate base is itself basic.

Each pH is found exactly for an ideal solution from the charge balance, without the approximations used to sketch the curve by hand. At half-equivalence the acid and its conjugate base are present in equal amounts, so the pH equals the pKa: that is how pKa values are read from titration data. A polyprotic acid gives one step for each proton, well resolved when the pKa values are far apart.

Worked example

50 mL of 0.1 M acetic acid (pKa 4.76) titrated with 0.1 M NaOH.

  1. Equivalence volume = 0.1 × 50 / 0.1 = 50 mL.
  2. At the start the pH is 2.88; at 25 mL (half-equivalence) it equals the pKa, 4.76.
  3. At 50 mL the solution is sodium acetate, and the pH is 8.73.

An equivalence point at 50 mL and pH 8.73, with the half-equivalence pH of 4.76 equal to the pKa.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • An ideal solution at 25 °C with activity coefficients of one.
  • Complete mixing at each point, and no CO₂ absorption, which lowers the pH of a real alkaline solution.
  • A strong base titrant; weak base titrants are not modelled.

Common mistakes

  • Choosing an indicator whose colour change is far from the equivalence pH.
  • Reading a pKa from a titration of a dilute acid, where water's own ionisation distorts the half-equivalence point.
  • Expecting sharp steps for a polyprotic acid whose pKa values are close together.

Related tools

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Related equipment

Service documentation, failure modes and parts for the instruments this calculation is used with.