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Q. At what concentration of $CH _{3} COOH$ will the $\left[ H ^{+}\right]$ obtained will be same as that obtained from $10^{-2} M$ $HCOOH ,\left( Ka \left( CH _{3} COOH \right)=10^{-5}, Ka ( HCOOH )=10^{-4}\right)$

Equilibrium

Solution:

$C _{1} \alpha_{1}= C _{2} \alpha_{2}$
$\Rightarrow C _{1} \sqrt{\frac{ Ka _{1}}{ C _{1}}}= C _{2} \times \sqrt{\frac{ Ka _{2}}{ C _{2}}}$
$\Rightarrow \sqrt{ C _{1} Ka _{1}}=\sqrt{ C _{2} Ka _{2}} $
$\Rightarrow C _{1} Ka _{1}= C _{2} Ka _{2}$
$\Rightarrow C _{1} \times 10^{-5}=10^{-2} \times 10^{-4}$
$\Rightarrow C _{1}=10^{-1} M$