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Reaction between $C O$ and $C l_{2}$ takes place as
I. $C l_{2} ⇌_{K_{- 1}}^{K_{1}} 2 C l$ (fast equilibrium)
II. $C l + C O ⇌_{K_{- 2}}^{K_{2}} C O C l$ (fast equilibrium)
III. $C O C l + C l_{2} \overset{K_{3}}{\to} C O C l_{2} + C l$ (slow)
Thus the rate law with overall rate constant K is.

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$K {[C l_{2}]}^{3 / 2} [C O]$

$K [C l_{2}] {[C O]}^{3 / 2}$

$K [C l] [C O]$

$K [C l_{2}] {[C O]}^{1 / 2}$

answer is B.

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Detailed Solution

$r = K_{3} [C o C l] [C l_{2}] K_{e q 2} = \frac{[C o C l]}{[C l] [C o]} ∴ r = K_{3} K_{e q} [C l] [C o] [C l_{2}] = K_{e q 1} = \frac{{[C l]}^{2}}{[C l_{2}]} C l = {[k_{e q 1} [C l_{2}]]}^{1 / 2} ∴ r = K [C o] {[C l_{2}]}^{3 / 2}$

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