The initial rate of hydrolysis of methyl acetate (1M) by a weak...

{\text{CH}_{3} {\text{COOCH}_{3} + {\text{H}_{2} \text{O} \overset{\left[{\text{H}}^{+}\right]}{\to} {\text{CH}_{3} \text{COOH} + {\text{CH}_{3} \text{OH }$<br />$\text{Rate Law} ⇒ \text{k} \left[\text{MA}\right] \left[{\text{H}}^{+}\right]$(as water is present in large excess)<br />\left[\text{MA}\right] = \text{1 M}$ in both cases
${\left[{\text{H}}^{+}\right]}_{\text{Strong}} = \text{1 M}$ in presence of strong acid $HX$.
${\left[{\text{H}}^{+}\right]}_{\text{weak}} = \sqrt{{\text{K}}_{\text{a}} \text{. c}} = \sqrt{{\text{K}}_{\text{a}}}$ in the presence of weak acid $HA$.
Initial rate (weak acid) $= \text{k} \left[1\right] \left[\sqrt{{\text{K}}_{\text{a}}}\right] ...... (I)$
Initial rate (strong acid) $= \text{k} \left[1\right] \left[1\right] ...... (II)$
$\dfrac{\text{I}}{\text{II}} = \sqrt{{\text{K}}_{\text{a}}} = \dfrac{1}{1 0 0} = 1 {0}^{- 2}$
${\text{K}}_{\text{a}} = 1 \times 1 {0}^{- 4}$.