Titration at the equivalence point

The formula

• c_A · V_A · b = c_T · V_T · a

c_A and V_A are the concentration and volume of the analyte, the solution being titrated; c_T and V_T those of the titrant, the solution run in from the burette. a and b are the coefficients of the analyte and the titrant in the balanced equation. Each side is the moles of one substance times the other’s coefficient, and at the equivalence point the two are equal.

Holds when the reaction goes to completion and the end point found with the indicator is the equivalence point. A weak acid titrated with a weak base has neither, and the formula does not apply to it.

A worked example

25.0 cm³ of hydrochloric acid of unknown concentration needs 20.0 cm³ of 0.100 mol/dm³ sodium hydroxide to reach the end point. HCl + NaOH → NaCl + H₂O, so a = b = 1: c_A = 0.100 · 20.0 / 25.0 = 0.0800 mol/dm³.

With sulfuric acid, H₂SO₄ + 2 NaOH → Na₂SO₄ + 2 H₂O, a = 1 and b = 2. The same volumes give c_A = 0.100 · 20.0 · 1 / (25.0 · 2) = 0.0400 mol/dm³: each acid molecule takes two hydroxide ions, so half as much acid used the same base.

The 1 : 1 case

When the coefficients are equal they cancel and the formula is c₁V₁ = c₂V₂, the same shape as the dilution formula. The shape is the same because both say that an amount of substance, c · V, is conserved; the difference is that in a titration it is the amount of the other substance that matches.

Common mistakes

• Dropping the coefficients. Sulfuric acid against sodium hydroxide is the usual place to lose a factor of two.
• Mixing cm³ and dm³. Either unit works as long as both volumes use it.
• Reading the end point as exact. The indicator’s colour change is a little before or after the equivalence point, and a good indicator is chosen so that the gap is small.

Frequently asked questions