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

JEE Advanced · 2013 · 02 Jun 2013 · Paper 1 · Equilibrium

The initial rate of hydrolysis of methyl acetate

(1 M)

by a weak acid

(H A, 1 M)

1/10 0^{th}

of that of a strong acid

(H X, 1 M)

, at 25 °C. The

K_{a}

H A

Answer: (A)

The hydrolysis of methyl acetate is acid-catalyzed:

C H_{3} C O O C H_{3} + H_{2} O H^{+} C H_{3} C O O H + C H_{3} O H

Rate

\propto [H^{+}]

For strong acid:

[H^{+}]_{S A} = 1

M

For weak acid:

\frac{r _{W A}}{r _{S A}} = \frac{[ H ^{+} ] _{W A}}{[ H ^{+} ] _{S A}} = \frac{1}{100}

Therefore:

[H^{+}]_{W A} = 0.01

M

For a weak acid:

[H^{+}] = K_{a} \cdot C

0.01 = K_{a} \times 1

K_{a} = (0.01)^{2} = 1 \times 1 0^{- 4}

JEE Advanced · 2013 · 02 Jun 2013 · Paper 1 · One or more correct options