Question

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

• A. $1\times {10}^{-4}$
• B. $1\times {10}^{-5}$
• C. $1\times {10}^{-6}$
• D. $1\times {10}^{-3}$

Answer 1

The correct option is A $1\times {10}^{-4}$

Rate in weak = $\frac{1}{100}$ (rate in strong acid)
$\therefore [H^{\oplus }{]}_{weakacid}=\frac{1}{100}=[H^{\oplus }{]}_{strongacid}$
$\therefore [H^{\oplus }{]}_{weakacid}=\frac{1}{100}M={10}^{-2}M$
$\therefore C\alpha ={10}^{-2}=1\times \alpha ={10}^{-2}$
$\therefore \alpha ={10}^{-2}$
$K_a=C{\alpha }^2$ (C = 1M)
$=1\times ({10}^{-2}{)}^2$
$K_a={10}^{-4}$
Option (a) is correct.