The reaction $2 O_{3} \to 3 O_{2}$ Proceeds through the mechanism as below
$\begin{array}{l} O_{3} ⇌ O_{2} + O (f a s t) \\ O_{3} + O \to 2 O_{2} (s l o w) \end{array}$
The rate law is given as

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$r = k {[o_{3}]}^{2}$

$r = k {[o_{3}]}^{2} [o_{2}]$

$r = k {[o_{3}]}^{2} {[o_{2}]}^{- 1}$

$r = k [o_{3}] [o_{2}]$

answer is A.

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Detailed Solution

$\begin{array}{l} K = \frac{[O_{2}] [O]}{O_{3}} \\ [O] = K \frac{[O_{3}]}{[O_{2}]} \\ R a t e = K [O_{3}] [O] \\ R a t e = K_{1} \frac{[O_{3}] [O_{3}]}{[O_{2}]} = K {[O_{3}]}^{2} {[O_{2}]}^{- 1} \end{array}$

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