The reaction follows the mechanism The overall order of the reaction is: [2025]

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Solution

Q.
The reaction $A_{2} + B_{2} \to 2 A B$ follows the mechanism

$A_{2} \underset{k_{- 1}}{\overset{k_{1}}{⇌}} A + A (fast)$

$A + B_{2} \overset{k_{2}}{\to} A B + B (slow)$

$A + B \to A B (fast)$

The overall order of the reaction is: [2025]

1 2

2 1.5

3 2.5

4 3

Ans.
(2)

$Rate of reaction = rate of slow step = k_{2} [A] [B_{2}] - (I)$

$[A] cannot be kept in the final rate expression as it is an intermediate.$

$A_{2} ⇌ A + A$

$K_{e q} = \frac{{[A]}^{2}}{[A_{2}]} \Rightarrow [A] = \sqrt{K_{e q} [A_{2}]} - (II)$

$Put [A] from (II) in (I):$

$Rate of reaction = k_{2} \sqrt{K_{e q} [A_{2}]} [B_{2}] = k {[A_{2}]}^{1 / 2} [B_{2}]$

$Order = \frac{1}{2} + 1 = \frac{3}{2}$

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