Question

A hypothetical reaction $A_2+B_2\to 2AB$ follows the mechanism as given below,
$A_2\rightleftharpoons A+A\text{ (fast ) }$
$A+B_2⟶AB+B\text{ (slow) }$
$A+B⟶AB\text{ (fast) }$
The order of the overall reaction is

• A. 2
• B. 1
• C. $1\frac{1}{2}$
• D. 0

Answer 1

Answer: (C)

From slow step, rate $=k\left[B_2\right][A]$
From 1st equation $K_{eq}=\frac{[A{]}^2}{\left[A_2\right]}$
or $[A]=\sqrt{K_{eq}\left[A_2\right]}=K_{eq}^{1/2}{A}_2^{1/2}$
Hence, rate $=k\left[B_2\right]K_{eq}^{1/2}{\left[A_2\right]}^{1/2}$
$=k^{\prime }{\left[A_2\right]}^{1/2}\left[B_2\right]$
Hence, order $=1\frac{1}{2}$