The rapid change of pH near the stoichiometric point of an acid-base titration is the basis of indic

Question

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 concentrations of the conjugate acid (HIn) and base $\left(\mathrm{In}^{-}ight)$forms of the indicator by the expression\

Professor PC Thomas Classes · Answer

(d) : Let us consider the formation of a salt of a weak acid and a strong base.\ $\mathrm{In}^{-}+\mathrm{H}_{2} \mathrm{O} ightleftharpoons \mathrm{HIn}+\mathrm{OH}^{-}$\ $K_{h}=\frac{[\mathrm{HIn}]\left[\mathrm{OH}^{-}ight]}{\left[\mathrm{In}^{-}ight]}$\ Other equations present in the solution are\ $\mathrm{HIn} ightleftharpoons \mathrm{H}^{+}+\mathrm{In}^{-}$\ $\mathrm{H}_{2} \mathrm{O} ightleftharpoons \mathrm{H}^{+}+\mathrm{OH}^{-}$\ $K_{	ext {In }}=\frac{\left[\mathrm{H}^{+}ight]\left[\mathrm{In}^{-}ight]}{[\mathrm{HIn}]}$\ $K_{w}=\left[\mathrm{H}^{+}ight]\left[\mathrm{OH}^{-}ight]$\ From (ii) and (iii),\ $\frac{K_{w}}{K_{\mathrm{In}}}=\frac{[\mathrm{HIn}]\left[\mathrm{OH}^{-}ight]}{\left[\mathrm{In}^{-}ight]}=K_{h}$\ $\left[\mathrm{OH}^{-}ight]=\frac{K_{w}}{K_{	ext {In }}} \frac{\left[\mathrm{In}^{-}ight]}{[\mathrm{HIn}]}$\ $\log \left[\mathrm{OH}^{-}ight]=\log K_{w}-\log K_{\mathrm{In}}+\log \frac{\left[\mathrm{In}^{-}ight]}{[\mathrm{HIn}]}$\ $-\mathrm{pOH}=-\mathrm{p} K_{w}+\mathrm{p} K_{\mathrm{In}}+\log \frac{\left[\mathrm{In}^{-}ight]}{[\mathrm{HIn}]}$\ $\mathrm{p} K_{w}-\mathrm{pOH}=\mathrm{p} K_{\mathrm{In}}+\log \frac{\left[\mathrm{In}^{-}ight]}{[\mathrm{HIn}]}$ or, $\mathrm{pH}=\mathrm{p} K_{\mathrm{In}}+\log \frac{\left[\mathrm{In}^{-}ight]}{[\mathrm{HIn}]}$\ i.e. $\log \frac{\left[\mathrm{In}^{-}ight]}{[\mathrm{HIn}]}=\mathrm{pH}-\mathrm{p} K_{	ext {In }}$