Acid-Base Titration Calculator

Background.

Three numbers come off the bench at the end of a titration: the concentration of the solution in the burette, the volume of it you delivered before the indicator turned, and the volume of unknown you pipetted into the flask. A fourth number never appears on any glassware, and it is the one most likely to be wrong — how many moles of the unknown react with each mole of titrant.

For hydrochloric or acetic acid against sodium hydroxide that ratio is 1 and the arithmetic is almost trivial. Sulfuric acid is different. Each H2SO4 gives up two protons, so neutralising it takes two NaOH: H2SO4 + 2 NaOH → Na2SO4 + 2 H2O. Work it out as though the reaction were 1:1 and the acid concentration comes out exactly twice the true value, a clean and plausible figure with nothing about it to raise suspicion. Sodium carbonate titrated with hydrochloric acid to its second endpoint has the same trap in reverse. That is why the ratio is a field you fill in from your own balanced equation rather than an assumption baked into the arithmetic.

The rest depends on the titrant really being the strength you type in. A bottle marked 0.1 M NaOH is approximate: solid sodium hydroxide picks up water and carbon dioxide from the air, so its solutions are standardised against a weighed primary standard such as potassium hydrogen phthalate (KHP) before any quantitative use. NIST certifies reference lots of KHP, benzoic acid, boric acid and sodium carbonate for exactly this purpose, which lets a carefully standardised titrant trace its strength back to a national measurement laboratory.

The same calculation serves an acidity check on wine or vinegar, a water-alkalinity test, a pharmaceutical assay or a first-year lab report.

What is acid-base titration calculator?

Titration measures how much of a substance a solution contains by adding a reagent of known concentration until the reaction between them is exactly complete. IUPAC calls that moment the equivalence point: titrant and analyte have reacted in the proportions of the balanced equation, with neither left over. What you actually observe is the endpoint, an indicator's colour change or the steepest stretch of a pH curve, and the small gap between endpoint and equivalence point is the titration error. The result here is the molar concentration of the analyte in the aliquot you titrated, in moles per litre.

How to use this calculator.

1. 01Write the balanced equation and divide the analyte's coefficient by the titrant's. Acetic acid with NaOH gives 1; sulfuric acid taken to its second endpoint with NaOH gives 1 ÷ 2 = 0.5; hydrochloric acid neutralised by barium hydroxide, Ba(OH)2, gives 2 ÷ 1 = 2. Enter that as the stoichiometric ratio.
2. 02Enter the titrant concentration from your own standardisation, in mol/L, rather than the nominal strength printed on the bottle.
3. 03Enter the titrant volume as the final burette reading minus the initial one, in millilitres. After a rough first run, use the mean of the trials that agree closely.
4. 04Enter the volume of unknown you pipetted into the flask. Water used to rinse the flask walls or wash down the tip does not change the moles present, so leave it out.
5. 05Read the concentration and copy the two mole figures into your notebook. If the sample was diluted before you took the aliquot, multiply the concentration by the dilution factor to get back to the original.

The formula.

The result chains two definitions. Molarity is moles per litre, so the titrant delivered amounts to nt = Ct × Vt, with Vt in litres. A balanced equation of the form a·analyte + b·titrant → products says every b moles of titrant consume a moles of analyte, so the analyte present is nx = nt × r, where r = a/b. Dividing by the aliquot volume gives Cx = nx ÷ Vx, and putting the steps together, Cx = (Ct × Vt × r) ÷ Vx.

Both volumes are entered in millilitres and divided by 1,000 before the moles are found. In the combined equation the two factors of 1,000 cancel, which is why chemists often do the whole calculation in millilitres without converting.

The answer is directly proportional to Ct, Vt and r and inversely proportional to Vx, so a 1% error in any of them becomes a 1% error in the concentration. A single burette drop is about 0.05 mL; overshooting a 27.50 mL endpoint by one drop moves the result by roughly 0.18%. The equation assumes one direct titration in which the titrant reacted with the analyte and nothing else, so back-titrations and mixtures of two acids need extra steps.

A worked example.

Frequently asked questions.

References& sources.

1. [1]NIST — 'Evaluation of Independent High-Precision Assay Procedures for a High-Purity Primary Standard Reagent.' Describes NIST's certified acidimetric and alkalimetric primary-standard SRMs (potassium hydrogen phthalate, benzoic acid, boric acid, sodium carbonate) used to standardise titrants before use. National Institute of Standards and Technology.
2. [2]Harvey, D.T. Analytical Chemistry 2.1, §9.2 'Acid-Base Titrations' — derives the stoichiometric relationship between moles of titrant and moles of analyte, including polyprotic acid/base cases with equivalence-point ratios other than 1:1. LibreTexts / DePauw University.
3. [3]IUPAC Gold Book, 'titration' (T06387) — formal IUPAC definition of titration as the process of determining a substance's quantity by measured addition of a reacting titrant. International Union of Pure and Applied Chemistry.
4. [4]IUPAC Gold Book, 'equivalence point' (E02188) — formal definition of the equivalence point as the stage of titration at which titrant has completely reacted with titrand according to reaction stoichiometry, distinguished from the observed endpoint. International Union of Pure and Applied Chemistry.
5. [5]Skoog, D.A., West, D.M., Holler, F.J. & Crouch, S.R. (2013). Fundamentals of Analytical Chemistry, 9th ed. Cengage. Chapters on titrimetric methods, primary standards, and polyprotic acid-base equilibria. ISBN 978-0495558286.