The rate constant for the reaction
`A rarr B` is `2 xx 10^(-4) mol^(-1)`. The concentration of `A` at which rate of the reaction is `(1//2) xx 10^(-5) M sec^(-1)` is -

Options

A. `0.25 M`
B. `(1//20) sqrt(5//3) M`
C. `0.5 M`
D. None of these

Answer

B

Explanation

Order of reaction is `2` (from unit of `K`)
`:. rate = K C_(A)^(2)`
`C_(A) = sqrt((1//12 xx 10^(-5))/(2 xx 10^(-4))) = sqrt((1)/(24) xx 10^(-1)) = sqrt((1)/(240))`
`= sqrt((5)/(1200)) = (1)/(20) sqrt((5)/(3))`