The rapid change of pH near the stoichiometric point of an acid base titration is the basis of indicator detection, pH of the solution is related to ratio of the concentration of the conjugate acid (Hln) and base ( In ⁻ ) forms of the indicator by the expression:

Step-by-step solution

Let us consider the formation of a salt of a weak acid and a strong base. aligned In ⁻+ H ₂ O & HIn + OH ⁻ K _h & = [ HIn ] [ OH ⁻ ] [ In ⁻ ] aligned aligned & HIn H ⁺+ In ⁻ & H ₂ O H ⁺+ OH ⁻ & K _ ln = [ H ⁺ ] [ In ⁻ ] [ HIn ] & K _ w = [ H ⁺ ] [ OH ⁻ ] aligned From (ii) and (iii), aligned & K _ w K _ In = [ HIn ] [ OH ⁻ ] [ In ⁻ ] & [ OH ⁻ ] = K _ w K _ In [ In ⁻ ] [ HIn ] & [ OH ⁻ ]= logK _ w - _ ln + & [ In ⁻ ] [ HIn ] aligned aligned & - pOH =- pK _w+ pK _ ln + & [ In ⁻ ] [ HIn ] & pK _w- pOH = pK _ + [ In ⁻ ]