Question

A hypothetical reaction, $A_2+B_2 \longrightarrow 2 A B$ follows the mechanism as given below;

$A 2 \rightleftharpoons A+A \ldots . . \text { (fast) } $

$A+B_2 \longrightarrow A B+B \ldots . . . \text { (slow) } $

$A+B \longrightarrow A B \ldots . . . \text { (fast) }$

The order of the overall reaction is

(A) 2

(B) 1

(C) $1 \frac{1}{2}$

(D) zero.

Answer 1

Correct Option : (C)

Explanation—

For slow step,

$r=k[A]\left[B_2\right]$

$K_c=\frac{[A][A]}{\left[A_2\right]} \text { or }[A]=K_c^{1 / 2}\left[A_2\right]^{1 / 2}$

$\text { Thus, } \quad r=k \cdot K_c^{1 / 2}\left[A_2\right]^{1 / 2}\left[B_2\right]$

$=k_1\left[A_2\right]^{1 / 2}\left[B_2\right] \quad\left\{k_1=k \cdot K_c^{1 / 2}\right\}$

and

Hence, order is $\frac{3}{2}$.