A hypothetical reaction `A_(2) + B_(2) rarr 2AB` follows the mechanism as given below:
`A_(2) hArr A+A ("fast")`
`A+B_(2) rarr AB+B` (slow)
`A+B rarr AB` (fast)
The order of the overall reaction is

Options

A. 2
B. 1
C. `1 1/2`
D. 0

Explanation

From slow step, rate `=k[B]_2[A]`.
From 1st eqn. `k_(eq)=([A])^2/[A_2]`
or [A] `=sqrt(K_(eq)[A_2])=K_(eq)^(1/2)[A_2]^(1//2)` …….i)
from 2nd equation rate `=k[A] [B_2]`…….ii)
Hence from (i) and (ii)
rate `=k[B_2]k_(eq)^(1/2)[A_2]^(1/2)`
`=k'[A_2]^(1/2)[B_2]`
Hence, order `= 1 1/2`