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. 2
B. 0
C. 1.5
D. 1

Answer

C

Explanation

The overall reaction rate depends on the rate of the slowest step
i.e., Overall rate=Rate of slowest step (ii) `=k[X][Y_(2)]` ... (1)
k=rate constant
Assuming step (i) to be reversible, its equilibrium constant,
`k_(eq)=([X]^(2))/([X_(2)])implies [X]^(2)=k_(eq)[X_(2)]`,
`[X]=k_(eq)^((1)/(2))[X_(2)]^((1)/(2))` ...(2)
From eq (1) and (2)
`"Rate"=k k_(eq)^((1)/(2))[X_(2)]^((1)/(2))[Y_(2)]`
`"Overall order"=(1)/(2)+1=(3)/(2)=1.5`