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^(@)C`. The `K_(a)(HA)` is

Options

A. `1 xx 10^(-4)`
B. `1 xx 10^(-5)`
C. `1 xx 10^(-6)`
D. `1 xx 10^(-6)`

Answer

A

Explanation

Rate w.r.t weak acid, `R_(1)=k[H^(+)]WA` ester
Rate w.r.t. strong acid, `R_(2)=k[H^(+)]WA` ester
`:. R_(1)//R_(2)=(|H^(+)|WA)/(|H^(+)|SA)=(1)/(100)`
`:. |H^(+)|_(WA)=(|H^(+)|SA)/(100)=(1)/(100)xx1M=0.01M`
`|H^(+)|_(WA)hArrH^(+)+A^(-)`
At eq `c-dalpha" "c alpha" "c alpha`
`= c(1- alpha)`
`|H^(+)|=calphaor 10^(-2)=1xxalpha oralpha=10^(-2)`
`ka=(calphacalpha)/(c(1-d))=(calpha^(2))/(1-alpha)=calpha^(2)`
`=1 xx (10^(-2))^(2)=10^(-6)`.