Chemistry - Ionic Equilibrium Question with Solution | TestHub

${\text{CH}}_3{\text{COOCH}}_3+{\text{H}}_2\text{O}\stackrel{\left[{\text{H}}^{+}\right]}{\to }{\text{CH}}_3\text{COOH}+{\text{CH}}_3\text{OH }$
$\text{Rate Law}\Rightarrow \text{k}\left[\text{MA}\right]\left[{\text{H}}^{+}\right]$(as water is present in large excess)
$\left[\text{MA}\right]=\text{1 M}$in both cases
${\left[{\text{H}}^{+}\right]}_{\text{Strong}}=\text{1 M}$in presence of strong acid$\mathrm{HX}$.
${\left[{\text{H}}^{+}\right]}_{\text{weak}}=\sqrt{{\text{K}}_{\text{a}}\text{. c}}=\sqrt{{\text{K}}_{\text{a}}}$in the presence of weak acid$\mathrm{HA}$.
Initial rate (weak acid)$=\text{k}\left[1\right]\left[\sqrt{{\text{K}}_{\text{a}}}\right]......\; (I)$
Initial rate (strong acid)$= \text{k}\left[1\right]\left[1\right]......\; (II)$
$\frac{\text{I}}{\text{II}}=\sqrt{{\text{K}}_{\text{a}}}=\frac{1}{100}=10^{-2}$
${\text{K}}_{\text{a}}=1\times 10^{-4}$.