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# The depletion of ozone involves the following steps: Step 1: ${{O}_{3}}\underset{k_1}{\overset{k_2}{\mathop{\rightleftharpoons }}}\,{{O}_{2}}+O$ (fast) Step 2: ${{O}_{3}}+O\underset{k}{\mathop{\to }}\,2{{O}_{2}}$(slow) The predicted order of reaction will be:

Last updated date: 29th May 2024
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Hint: The order of reaction can be defined as the power dependence of rate on the concentration of all reactants in the slowest step. Let’s consider, for example, the rate of a first-order reaction is dependent solely on the concentration of one species in the reaction.

Complete Step by step solution:
${{O}_{3}}\underset{k_1}{\overset{k_2}{\mathop{\rightleftharpoons }}}\,{{O}_{2}}+O$ Equation (1)
${{O}_{3}}+O\underset{k}{\mathop{\to }}\,2{{O}_{2}}$ Equation (2)
$Rate=k[{{O}_{3}}][O]$ Equation (3)
$k_1$ and $k_2$ are rate constants for equation (1),
$k_1[{{O}_{3}}]=k_2[{{O}_{2}}][O]$
$[O]=\dfrac{k_1}{k_2}\dfrac{[{{O}_{3}}]}{[{{O}_{2}}]}$
Putting the value of [O] in Equation (3)
$\begin{array}{*{35}{l}} Rate=\dfrac{k_1}{k_2}\dfrac{[{{O}_{3}}]}{[{{O}_{2}}]}k[{{O}_{3}}] \\ Rate=\dfrac{k_1k}{k_2}\dfrac{{{[{{O}_{3}}]}^{2}}}{[{{O}_{2}}]} \\ \end{array}$
Consider $\dfrac{k_1k}{k_2}$as a constant hence,
$Rate\propto {{[{{O}_{3}}]}^{2}}{{[{{O}_{2}}]}^{-1}}$

Order of reaction = 2-1=1