Mechanism of a hypothetical reaction
`X_(2) + Y_(2) rarr 2XY` is given below:
(i) `X_(2) rarr X + X` (fast)
(ii) `X+Y_(2) hArr XY+Y` (slow)
(iii) `X + Y rarr XY` (fast)
The overall order of the reaction will be :

Options

A. 1
B. 2
C. 0
D. `1.5`

Answer

D

Explanation

As rate depends upon the slowest step,
Rate `=k[X]{Y_(2)]`
Taking step (i) to be reversible ( not given),
`K_(eq) = ([X]^(2))/([X_(2)]) or [X] = k_(eq)^(1//2) [X_(2)]^(1//2)`
Substituing in (i),
Rate `= k_(eq)^(1//2) [X_(2)]^(1//2) [Y_(2)] = k'[X_(2)]^(1//2)[Y_(2)]`
Overall order `= (1)/(2) + 1 = (3)/(2) = 1.5`