An acid-base titration finds an unknown concentration by reacting a measured sample with a titrant of known strength until neutralisation is complete. The volume of titrant needed, the titre, is the single measurement that unlocks the answer. This calculator turns that titre into a concentration and tells you what to expect at the endpoint.
How it works
Neutralisation is complete when the reactive equivalents of acid and base are equal. In normality form:
Ca x Va x za = Cb x Vb x zbwhere C is molarity, V is volume, and z is the number of reactive protons or hydroxides per molecule. Rearranging for the analyte concentration:
Ca = (Cb x Vb x zb) / (za x Va)The valence terms za and zb matter for polyprotic acids such as sulfuric acid (z = 2) and polyhydroxide bases such as calcium hydroxide. For a simple monoprotic-monohydroxide reaction both are 1 and the formula collapses to the familiar Ca·Va = Cb·Vb.
Equivalence pH and indicator choice
The pH at the equivalence point depends on the salt that forms. A strong acid neutralised by a strong base leaves a neutral salt, so the pH is 7. A weak acid neutralised by a strong base leaves a conjugate base, pushing the equivalence pH above 7, while a strong acid neutralised by a weak base leaves a conjugate acid and an equivalence pH below 7. Pick an indicator whose transition range brackets that pH so the colour change marks true neutralisation.
Common indicators and their transition ranges:
| Indicator | Transition range | Suitable for |
|---|---|---|
| Methyl orange | pH 3.1–4.4 | Strong acid / weak base |
| Methyl red | pH 4.4–6.2 | Strong acid / weak base |
| Bromothymol blue | pH 6.0–7.6 | Strong acid / strong base |
| Phenolphthalein | pH 8.2–10.0 | Weak acid / strong base |
| Alizarin yellow | pH 10.1–12.0 | Very weak acid / strong base |
Worked example
Titrating 25.0 mL of an unknown acid against 0.100 mol/L NaOH that requires a 25.0 mL titre, with both valences 1:
Ca = (0.100 × 0.025 × 1) / (1 × 0.025) = 0.100 mol/LThe equivalence point falls at approximately pH 7, so bromothymol blue is the appropriate indicator for a clean colour change.
Now consider a diprotic case: titrating 20.0 mL of sulfuric acid (za = 2) against 0.100 mol/L NaOH, requiring a 40.0 mL titre:
Ca = (0.100 × 0.040 × 1) / (2 × 0.020) = 0.100 mol/LBoth protons are accounted for through the za term. Setting za = 1 for sulfuric acid would incorrectly halve the result.
Sources of experimental error to watch for
- Indicator over-shoot. Adding titrant too fast near the endpoint means you may reach the indicator colour change slightly beyond the true equivalence point. Add dropwise as you approach the endpoint.
- CO2 absorption. NaOH solutions absorb atmospheric carbon dioxide over time, lowering the effective concentration. Use freshly standardised titrant and keep solutions stoppered.
- Temperature effects. Molarity is defined at a specific temperature, and most solutions expand slightly when warm. Titrations performed at significantly different temperatures from standardisation can introduce small systematic errors.
- Burette parallax. Read the burette meniscus at eye level to avoid parallax error, particularly at the curved bottom of the meniscus for colourless solutions.
The equivalence pH and indicator suggestion produced by this calculator are idealised guides based on the reaction type; for exact endpoint pH in buffers or with weak electrolytes you must include the salt concentration and the relevant Ka or Kb.