Q. 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 the ratio of the concentration of the conjugate acid ($HIn$) and base ($In^{-}$) forms of the indicator given by the expression
Explanation
(d)
Acid indicators are generally weak acid. The dissociation of indicator $HIn$ takes place as follows
$HIn \rightleftharpoons H^{+} + In^{-}$
$K_{In} = \frac{\left\lbrack H^{+} \right\rbrack\left\lbrack In^{-} \right\rbrack}{\lbrack HIn\rbrack}$
or $\left\lbrack H^{+} \right\rbrack = K_{In}\frac{\lbrack HIn\rbrack}{\lbrack In^{-}\rbrack}$
$pH = - \log\left\lbrack H^{+} \right\rbrack$
$= - \log\left( K_{In}\frac{\lbrack HIn\rbrack}{\lbrack In^{-}\rbrack} \right)$
$= - \log{K_{In} + \log\frac{\left\lbrack In^{-} \right\rbrack}{\lbrack HIn\rbrack}}$
$\ = pK_{In} + \log\frac{\left\lbrack In^{-} \right\rbrack}{\lbrack HIn\rbrack}$
or $\log\frac{\left\lbrack In^{-} \right\rbrack}{\lbrack HIn\rbrack} = pH - pK_{In}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.