Question

A hypothetical reaction $A_{2}+B_{2} \rightarrow 2 A B$ follows the mechanism as given below,
$A_{2} \rightleftharpoons A+A \text { (fast ) } $
$A+B_{2} \longrightarrow A B+B \text { (slow) } $
$A+B \longrightarrow A B \text { (fast) }$
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_{e q}^{1 / 2}\left[A_{2}\right]^{1 / 2} $
$=k'\left[A_{2}\right]^{1 / 2}\left[B_{2}\right]$
Hence, order $=1 \frac{1}{2}$