Question

Mechanism of a hypothetical reaction $X_2+Y_2\to 2XY$ is given below:

(i) $X_2\rightleftharpoons X+X$ (fast)
(ii) $X+Y_2\rightleftharpoons XY+Y$ ( slow )
(iii) $X+Y\rightleftharpoons XY$ (fast)
The overall order of the reaction will be

• A. 1.5
• B. 0
• C. 2
• D. 1

Answer 1

The correct option is A 1.5

Overall rate = Rate of slowest step (ii)

$=k\left[X\right]\left[Y_2\right]...\left(1\right)$

k= rate constant of step (ii)

Equilibrium constant of equation (i)

$k_{eq}=\frac{[X{]}^2}{\left[X_2\right]}\Rightarrow \left[X\right]=k_{eq}^{1/2}[X_2{]}^{1/2}...(2)$

Put (2) in (1)

Rate =$k{k}_{eq}^{1/2}\left[X_2{]}^{1/2}\right[Y_2]$

Overall order =$\frac{1}{2}+1=\frac{3}{2}$

Hence, option (c) is correct.