Question

A hypothetical reaction, $X_2+Y_2\to 2XY$ follows the following mechanism:

$X_2\rightleftharpoons X+X.....fast$
$X+Y_2\to XY+Y.....slow$
$X+Y\to XY.....fast$

The order of the overall reaction is :

• A. $2$
• B. $3/2$
• C. $1$
• D. $0$

Answer 1

The correct option is B $3/2$

$X+Y_2\to XY+Y$ ..... slow

$rate=k\left[X\right]\left[Y_2\right]$......(1)
$X_2\rightleftharpoons X+X$ ..... fast

$K=\frac{\left[X\right]\left[X\right]}{\left[X_2\right]}$
$\left[X\right]=\sqrt{K\left[X_2\right]}$ .......(2)
Substitute (2) in (1)
$rate=k\sqrt{K\left[X_2\right]}\left[Y_2\right]$
Hence, the reaction is of 0.5 order with respect to $X_2$ and first order with respect to $Y_2$. The overall order of the reaction is $0.5+1=\frac{3}{2}$