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

Answer

A

Explanation

Rate law is given as r = k [A] `[B_(2)]`
From 1st eqn. `K=([A][A])/([A_(2)])`
`therefore" "[A]=[K[A_(2)]]^(1//2)=D^(1//2)[A_(2)]^(1//2)`
Thus, rate law becomes
`r=k[B_(2)][K]^(1//2)[A_(2)]^(1//2)`
`=k[K]^(1//2)[A_(2)]^(1//2)[B_(2)]`
`=k'[A_(2)]^(1//2)[B_(2)]"where", k'=[K]^(1//2)`
`therefore" order"=(1)/(2)+1=1(1)/(2)`