The initial rate of hydrolysis of methyl acetate (1M) by a weak acid (HA, 1M) is $1 / 100^{t h}$ of that of a strong acid (HX, 1M), at $25^{\circ} C .$ The $K_{a}$ of HA is

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$1 \times 10^{- 4}$

$1 \times 10^{- 6}$

$1 \times 10^{- 5}$

$1 \times 10^{- 3}$

answer is A.

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Detailed Solution

$r = K [C H_{3} C O O C H_{3}] [H_{2} O] [H^{+}]$

$\frac{r_{H A}}{r_{M X}} = \frac{[H^{+}] from H A}{[H^{+}] from H X}$

$\frac{1}{100} = \frac{[H^{+}] from H A}{1} \Rightarrow [H^{+}] from H A = 10^{- 2} M$

$\underset{1 - 10^{- 2} ≃ 1}{H A (a q)} ⇌_{}^{} \underset{10^{- 2}}{H^{+} (a q)} + \underset{10^{- 2}}{A^{-} (a q)}$

$k_{a} = \frac{10^{- 2} \times 10^{- 2}}{1} = 10^{- 4}$

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