An acid-base indicator which is a weak acid has a $p^{H}$ value = 5.5. At what concentration ratio of sodium acetate to acetic acid would the indicator show a colour, half-way between those of its acid and conjugate base forms ? ${pK}_{a}$ of acetic acid = 4.75

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4.93 : 1

6.3 : 1

5.62 : 1

2.37 : 1

answer is C.

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Detailed Solution

At Half way $[HIn] = {In}^{-}$

$pH = P^{ka} + \frac{[salt]}{[acid]}, 5.5 = 4.75 + \log \frac{[salt]}{[acid]} \log \frac{[salt]}{[acid]} = 0.75 \Rightarrow \frac{[salt]}{[acid]} = 5.62$

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