The initial rate of hydrolysis of methyl acet | vedclass

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(A) The rate of acid-catalyzed hydrolysis of an ester is directly proportional to the concentration of $H^+$ ions,i.e.,$Rate \propto [H^+]$.For a stro

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$1 	imes 10^{-4}$

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(A) The rate of acid-catalyzed hydrolysis of an ester is directly proportional to the concentration of $H^+$ ions,i.e.,$Rate \propto [H^+]$.For a strong acid $(HX, 1 \ M)$,$[H^+]_{HX} = 1 \ M$.Given that the rate with $HA$ is $1/100$th of the rate with $HX$,we have:$\frac{Rate_{HA}}{Rate_{HX}} = \frac{[H^+]_{HA}}{[H^+]_{HX}} = \frac{1}{100}$Since $[H^+]_{HX} = 1 \ M$,then $[H^+]_{HA} = 0.01 \ M$.For the weak acid dissociation: $HA \rightleftharpoons H^+ + A^-$.At equilibrium,$[H^+] = [A^-] = 0.01 \ M$ and $[HA] = 1 - 0.01 \approx 1 \ M$.The acid dissociation constant $K_a$ is given by:$K_a = \frac{[H^+][A^-]}{[HA]} = \frac{(0.01)(0.01)}{1} = 10^{-4}$.

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

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