A secondary alkyl halide `(A)` hydrolyzes with alkali `(B)` in aqueous medium ismultaneously via `S_(N)1` and `S_(N)2` pathways with rate constants `k_(1)` and `k_(2)`, respectively. form kinetic data, it was found that a plot of `= (-1)/([A])(d[A])/(dt)` vs `[B]` is straight line with a slope equal to `2.7 xx 10^(-4) L mol^(-1) min^(-1)` and intercept equal to `1.02 xx 10^(-3)`. Minimum initial concentration of `[A] = 0.2 M` and `[B]`, i.e., `[overset(ɵ)(OH)] = 0.5 M`.
The initial rate of consumption is isopropyl chloride (in `M min^(-1))` is

Options

A. `a. 0.2 xx 10^(-3)`
B. `b. 3 xx 10^(-5)`
C. `c 2.31 xx 10^(-4)`
D. `d. 2.31 xx 10^(-3)`

Answer

C

Explanation

`[RX]_(0) = [A]_(0) = 0.2 M, [B]_(0) = [overset(ɵ)(OH)] = 0.5 M`
form Eq. (iii),
`(-d[A])/(dt) = [A][k_(1) + k_(2)[B]]`
`= 0.2[1.02 xx 10^(-3) +0.27 + 10^(-3) xx 0.5]`
`= 0.2 xx 10^(-3)[1.02+0.135]`
`= 0.2 xx 10^(-3) xx 1.155`
`= 2.31 xx 10^(-4)M min^(-1)`