Question

What is the order of reaction, $A_2+B_2⟶2AB$?
Mechanism:
$A_2\rightleftharpoons A+A$ (fast)
$A+B_2⟶AB+B$ (slow)
$A+B⟶AB$ (fast)

• A. $2$
• B. $1$
• C. $\frac{3}{2}$
• D. $\frac{1}{2}$

Answer 1

The correct option is C $\frac{3}{2}$

$A+B_2\underrightarrow{x_1}AB+B$ (slow)

Rate= $k_1\left[A\right]\left[B_2\right]$......(1)

$A_2\stackrel{k_{eq}}{\rightleftharpoons }A+A$

$k_{eq}=\frac{[A{]}^2}{\left[A_1\right]}=>\left[A\right]=k_{eq}^{1/2}[A_2{]}^{1/2}$....(2)

Rate =$k_1{k}_{eq}^{1/2}.\left[A{]}^{1/2}\right[B_2]$.....From (1) & (2)

$=k\left[A_2{]}^{1/2}\right[B_2]$

overall order =$\frac{1}{2}+1=3/2$