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# 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 conjugated acid(HIn) and base (In) form of the indicator by the expression

(a) $log \frac{[In^-]}{[HIn]} = pH - pK_{In}$

(b) $log \frac{[In^-]}{[HIn]} = pH_{In} - pH$

(c) $log \frac{[HIn]}{[In^-]} = pK_{In} - pH$

(d) $log \frac{[HIn]}{[In^-]} = pH - pK_{In}$

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A)
Answer: $log \frac{[In^-]}{[HIn]} = pH - pK_{In}$
$HIn \rightleftharpoons H^+ + In^-$
$K_{In} = \frac{[H^+][In^-]}{[HIn]}$
$-log K_{In} = -log [H^+] - log \frac{[In^-]}{[HIn]}$
$\Rightarrow pK_{In} = pK_a - log \frac{[In^-]}{[HIn]}$
$\Rightarrow$ $log \frac{[In^-]}{[HIn]} = pH - pK_{In}$