The relation at the equivalence point: n(acid) = n(base)

What exactly happens at the equivalence point

At the equivalence point, the reactants (the acid and the base) have been mixed in the stoichiometric proportions of the reaction: there is no longer an excess of either one. For a simple acid-base reaction, where an acid that releases only one H+ ion (a monoprotic acid) reacts with a base that captures only one (a monoprotic base), this translates into a very simple relation:

n(acid) = n(base)      (at the equivalence point)

How it's used

The amount of substance is calculated from the concentration C and the volume V:

n = C * V

If you titrate a volume Va of acid of unknown concentration Ca with a titrant base solution of known concentration Cb, added up to the volume at the equivalence point Veq, then:

Ca * Va = Cb * Veq
Ca = Cb * Veq / Va

Why this relation is so useful

It turns the initial problem (finding Ca, an invisible quantity) into a simple calculation, using three quantities measurable directly in the lab: Va (measured with a pipette), Cb (precisely prepared), and Veq (read off the burette). That is the whole power of titration: replacing a difficult chemical measurement with a volume measurement, much more accessible.

Common mistake

The relation n(acid) = n(base) is only valid for an acid and a base that each exchange a single H+ ion. For a diprotic acid (which releases 2 H+ ions, like sulfuric acid) or a diprotic base, the relation must be adjusted with the correct stoichiometric coefficients from the reaction equation, otherwise the final result is wrong.