What is the concentration of $C H_{3} C O O H$ which can be added to 0.5 M HCOOH solution so that dissociation of both is same.
[Given that : $K_{C H_{3} C O O H} = 1.8 \times 10^{- 5}, K_{H C O O H} = 2.4 \times 10^{- 4}$ ]
(as nearest integer)

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Solution

$H C O O H ⇌ H^{\oplus} + H C C O O^{⊝}$
$C H_{3} C O O H ⇌ H^{\oplus} + C H_{3} C O O^{⊝}$
Since both are present in a mixture and as per question,
$[H C O O^{⊝}]$ by $H C O O H = [C H_{3} C O O^{⊝}]$ by $C H_{3} C O O H$
$C_{1} α_{1} = C_{2} α_{2}$
$\sqrt{(K_{a_{1}} C_{1})} = \sqrt{(K_{a_{2}} C_{2})}$
$∴ \sqrt{(2.4 \times 10^{- 4} \times 0.5)} = \sqrt{(1.8 \times 10^{- 5} \times C)}$

$∴ C_{C H_{3} C O O H} = 6.66 M \approx 7 M$

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