When an indicator changes colour, this is described as the 'end point' of a reaction.
The equivalence point is when the acid and base have reacted together in the exact proportions dictated by the stoichiometric equation.
When titrating a an aqueous solution of a MONOBASIC acid with an aqueous solution of a MONOACIDIC base, 25cm^3 of acid will react with exactly 25cm^3 of base.
The pH at the equivalence point depends on the combination of acid and base used. E.g. dilute NaOH (aq) titrated with dilute HCl (aq) will give a pH of 7.00 at the equivalence point, because of the strong acid and strong base.
If ethanoic acid (weak acid) and sodium hydroxide (strong base) were titrated together, the pH of the solution at the equivalence point would be greater than 7 (more alkaline solution).
If hydrochloric acid (strong acid) is titrated against aqueous ammonia (weak base), the solution at the equivalence point will have a pH less than 7 (more acidic).
pH titration curves are used to plot the pH of a solution against the volume of acid added (titrated) against the base. They show how the pH changes across an acid-base reaction.
When an acid and base react, a neutralisation (equivalence) point is reached, whereby the graph has a large vertical section.
To obtain a pH titration curve, alkali is added slowly to an acid (or vice versa) and the pH is regularly measured with a pH probe. The smaller the added volumes, the more accurate the curve produced.
For a strong acid-base reaction, the neutralisation point occurs at around pH 7. Other combinations of strong and weak acids and bases result in different neutralisation points.
The vertical region of a titration curve is the equivalence point. At the half-equivalence point, pH = pKa.
The half-equivalence point is when half the volume of acid/base at the equivalence point is added.
By reading the pH at the half-equivalence point, Ka can be easily calculated from pKa.