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Question

A hypothetical reaction, $$A_{2} + B_{2}\rightarrow 2AB$$ follows the mechanism as given below:
$$A_{2}\rightleftharpoons A + A ....(fast)$$
$$A + B_{2} \rightarrow AB + B .... (slow)$$
$$A + B \rightarrow AB .... (fast)$$
The order of the overall reaction is ?


A
2
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B
1
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C
3/2
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D
Zero
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Solution

The correct option is A $$3/2$$
As rate depends upon the slow step,
$$Rate = k[A][B_{2}]$$
For the equilibrium, $$A_{2}\rightleftharpoons 2A, K_{c} = \dfrac {[A]^{2}}{[A_{2}]}$$

or $$[A] = \sqrt {K_{c}[A_{2}]}$$

$$\therefore Rate = k K_{c}^{1/2} [A_{2}]^{1/2} [B_{2}] = k^{f}[A_{2}]^{1/2} [B_{2}]$$

Hence, $$order = \dfrac {1}{2} + 1 = \dfrac {3}{2}$$.

Chemistry

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