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


A
1 x 104
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B
1 x 105
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C
1 x 106
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D
1 x 103
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Solution

The correct option is A 1 x 10$$^{-4}$$
The rate of the hydrolysis of methyl acetate is directly proportional to the hydrogen ion concentration.
In case of weak acid, the equilibrium constant is given by the expression $$K_a=\dfrac {[H^+][A^-]}{[HA]}=\dfrac {[H^+]^2}{[HA]}$$
Hence, $$[H^+]=\sqrt {K_a[HA]}$$

Hence, the expression for the ratio of the rate of the hydrolysis of methyl acetate in presence of weak acid and strong acid becomes $$\dfrac {r_{weak  acid}} {r_{strong  acid}}=\dfrac {\sqrt {K_a[HA]}}{[HA]}=\dfrac {1} {100}$$

Substitute $$[HA]=1  M$$

Hence, $$\dfrac {\sqrt {K_a \times 1}}{1}=\dfrac {1} {100}$$
$$K_a=1 \times 10^{-4}$$

Chemistry

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