Solving a titration: a numerical example

The method, step by step

1. Identify the acid and the base, and check that they each exchange a single H+ ion.
2. Write down all the known quantities: titrated volume, titrant concentration, volume at the equivalence point.
3. Apply the relation at the equivalence point n(acid) = n(base).
4. Isolate the unknown, calculate, and check the order of magnitude.

Concrete example

You titrate a volume Va = 20.0 mL of a hydrochloric acid solution of unknown concentration Ca, with a sodium hydroxide solution of concentration Cb = 0.10 mol/L. The equivalence point is reached for a volume added Veq = 12.4 mL. What is the concentration Ca of the hydrochloric acid solution?

Hydrochloric acid (HCl) is a monoprotic acid and sodium hydroxide (NaOH) a monoprotic base, so at the equivalence point:

n(acid) = n(base)
Ca * Va = Cb * Veq
Ca = Cb * Veq / Va
Ca = (0.10 * 12.4) / 20.0
Ca = 0.062 mol/L

(the concentration of the hydrochloric acid solution is 0.062 mol/L)

Checking the order of magnitude

The volume added at the equivalence point (12.4 mL) is smaller than the titrated volume (20.0 mL): this means the titrant (base) is more concentrated than the titrated solution (acid), which is consistent with Cb = 0.10 mol/L being greater than the found Ca = 0.062 mol/L. The result is consistent.

A variant: titrating a base with an acid

The method is exactly the same if you titrate a base with an acid: the relation n(acid) = n(base) remains valid at the equivalence point, regardless of the direction of the titration.

Common mistake

Always pay attention to volume units: Va and Veq must be expressed in the same unit (milliliters or liters) for the calculation to be correct, otherwise the result is off by a factor of 1000.