Acid-base titration is one of the oldest and most reliable techniques in analytical chemistry for determining an unknown concentration. By carefully adding a solution of known concentration to a measured volume of the unknown until the reaction is complete, a simple ratio calculation reveals the answer. This article walks through the equivalence point, the classic MₐVₐ = MᵦVᵦ relationship, why polyprotic acids and bases need a mole-ratio adjustment, and the practical sources of error that separate a good titration from a great one.
The equivalence point, not the color change
Every titration has two distinct moments that are easy to conflate: the equivalence point, where the moles of titrant added exactly balance the moles of analyte (adjusted for stoichiometry), and the endpoint, the moment the indicator visibly changes color. A well-chosen indicator changes color extremely close to the equivalence point, so in practice the measured endpoint volume is used as a stand-in for it. The calculation itself — Cₐ = Cₜ Vₜ × ratio / Vₐ — assumes you are reading the volume at true equivalence, which is why indicator selection (matching the indicator's color-change pH range to the expected pH at equivalence) matters so much for accuracy.
Where MₐVₐ = MᵦVᵦ comes from
For a simple monoprotic acid reacting with a monoprotic base (HA + BOH → BA + H₂O), one mole of acid reacts with exactly one mole of base. Since moles = concentration × volume, moles of acid = MₐVₐ and moles of base = MᵦVᵦ, and at equivalence these are equal: MₐVₐ = MᵦVᵦ. This is simply the ratio-adjusted equation above with ratio = 1. It works with any consistent volume unit — mL cancel against mL — as long as both volumes use the same unit and both concentrations use the same molarity scale.
When the mole ratio isn't 1:1
Many common acids and bases are polyprotic — they donate or accept more than one proton per molecule. Sulfuric acid (H₂SO₄) and oxalic acid (H₂C₂O₄) are diprotic; phosphoric acid (H₃PO₄) is triprotic. Titrating a diprotic acid with a monoprotic base means each mole of acid consumes two moles of base, so the naive 1:1 formula overstates the acid's concentration by a factor of two unless you build the ratio into the calculation. The Mole Ratio tab handles this by letting you enter the analyte:titrant ratio directly from the balanced equation — 0.5 for a diprotic acid analyte against a monoprotic base titrant, 2 for a diprotic base analyte against a monoprotic acid titrant, and so on for triprotic species.
Planning ahead: solving for titrant volume
Titration calculations aren't only run after the fact. A chemist preparing for a batch of titrations, or checking whether a burette holds enough titrant, often needs to go the other direction: given a known or expected analyte concentration and volume, how much titrant will it take to reach equivalence? Rearranging the equivalence equation to Vₜ = Cₐ Vₐ / (Cₜ × ratio) answers exactly that, and the Solve Volume tab performs this calculation directly so you don't have to rearrange the algebra by hand.
Sources of error in real titrations
The math is exact, but real titrations carry measurement uncertainty. The most common sources are: reading the burette meniscus imprecisely, overshooting the endpoint (adding titrant past the true color change), an indicator whose color-change range doesn't match the equivalence pH well, and imprecisely prepared titrant concentration. Good lab practice — standardizing the titrant against a primary standard, using a well-matched indicator, and titrating slowly near the expected endpoint — keeps the measured volume close enough to the true equivalence-point volume that this calculator's result is trustworthy.