Neutralisation Titration Calculation

At neutralisation the moles of H⁺ from the acid equal the moles of OH⁻ from the base. Equating valence × concentration × volume gives the volume of base needed.

Explanation

Neutralisation is the point where the $\mathrm{H^+}$ released by an acid exactly matches the $\mathrm{OH^-}$ released by a base, with nothing left over. The two amounts, in moles, are equal.

a \, c_a V_a = b \, c_b V_b

$a$ and $b$ — the valences, the number of $\mathrm{H^+}$ or $\mathrm{OH^-}$ one molecule can give up
$c$ — the molar concentrations
$V$ — the volumes in litres

Example

Neutralise 10 mL of 0.05 mol/L sulfuric acid, $\mathrm{H_2SO_4}$ , which is diprotic, with 0.1 mol/L sodium hydroxide, $\mathrm{NaOH}$ , which is monoprotic.

The acid supplies

2 \times 0.05 \times 0.010 = 0.001\ \text{mol of } \mathrm{H^+}

and the volume of base that supplies the same amount of $\mathrm{OH^-}$ is

V_b = \dfrac{0.001}{1 \times 0.1} = 0.010\ \text{L} = 10\ \text{mL}

Never forget the valence

The commonest error by far is leaving out the valence.

Sulfuric acid gives up two hydrogen ions per molecule, so at equal concentration and volume it demands twice as much base as hydrochloric acid does.

Monoprotic acids — $\mathrm{HCl}$ , $\mathrm{HNO_3}$ , $\mathrm{CH_3COOH}$
Diprotic acid — $\mathrm{H_2SO_4}$
Monobasic — $\mathrm{NaOH}$
Dibasic — $\mathrm{Ca(OH)_2}$

Watch out

The equivalence point is not always pH 7. Neutralising a strong acid with a weak base leaves a salt that makes the solution slightly acidic, so the equivalence point falls below 7. This is exactly why titrations choose between methyl orange and phenolphthalein as the indicator.

Note also that the equation cares nothing for whether the acid is strong or weak. A weak acid such as acetic acid reacts completely in the end, so the amount of base it needs is unchanged.