A titration finds an unknown concentration by reacting it, drop by drop, with a solution of known concentration until the reaction is exactly complete — the equivalence point. At that moment the moles of acid and base are balanced by the reaction's mole ratio, which gives the working equation Ca·Va·b = Cb·Vb·a. For the common 1:1 case it simplifies to Ca·Va = Cb·Vb, the same relationship written as N₁V₁ = N₂V₂ when you use normality. Rearrange it to solve for whichever of the four quantities you didn't measure.
Reviewed: June 19, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: stoichiometric equivalence at the titration endpoint.
The titration equations
The coefficients a and b come straight from the balanced neutralisation equation: they are the moles of acid and base that react together. When a = b the equation collapses to a simple cross-multiplication. Because volume sits on both sides, its unit cancels — millilitres are fine. To report the moles that actually reacted, convert a volume to litres and multiply by its molar concentration.
Worked example — standardising an acid
Scenario: A 25 mL sample of hydrochloric acid is titrated with 0.1 M sodium hydroxide. The indicator changes colour after 20 mL of base. The reaction HCl + NaOH is 1:1. What is the acid concentration?
The acid is 0.08 M. Both half-reactions supply 0.002 mol, confirming the balance. Had this been sulfuric acid (a = 1, b = 2), the same 20 mL of base would only neutralise half as much acid per millilitre, so the calculated Ca would be 0.04 M instead — which is exactly why the mole ratio must be set correctly before reading the answer.
Frequently Asked Questions
Ca = Cb·Vb·a/(Va·b). For 1:1, Ca·Va = Cb·Vb. e.g. 0.1 M × 20 mL ÷ 25 mL = 0.08 M.
The normality form — equivalents already include the proton/electron count, so coefficients vanish. Use normality, not molarity.
Equivalence = moles exactly matched (what we calculate). Endpoint = the indicator colour change you watch for.
Diprotic acids like H₂SO₄ need 2 NaOH per acid (a=1, b=2). Ignoring it gives an answer off by 2×.
No — the unit cancels. Use mL on both sides. Litres are only needed if you want the moles reacted.