Mechanism of Ozone Destruction Ozone decomposes thermally to...

Mechanism of Ozone Destruction Ozone decomposes thermally to oxygen in the following reaction: $$ 2 \mathrm{O}_{3}(g) \rightarrow 3 \mathrm{O}_{2}(g) $$ The following mechanism has been proposed: $$ \begin{array}{l} \quad \mathrm{O}_{3}(g) \rightarrow \mathrm{O}(g)+\mathrm{O}_{2}(g) \\ \mathrm{O}(g)+\mathrm{O}_{3}(g) \rightarrow 2 \mathrm{O}_{2}(g) \end{array} $$ The reaction is second order in ozone. What properties of the two elementary steps (specifically, relative rate and reversibility) are consistent with this mechanism?

Mechanism of Ozone Destruction Ozone decomposes thermally to oxygen in the following reaction:
$$
2 \mathrm{O}_{3}(g) \rightarrow 3 \mathrm{O}_{2}(g)
$$
The following mechanism has been proposed:
$$
\begin{array}{l}
\quad \mathrm{O}_{3}(g) \rightarrow \mathrm{O}(g)+\mathrm{O}_{2}(g) \\
\mathrm{O}(g)+\mathrm{O}_{3}(g) \rightarrow 2 \mathrm{O}_{2}(g)
\end{array}
$$
The reaction is second order in ozone. What properties of the two elementary steps (specifically, relative rate and reversibility) are consistent with this mechanism?

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Key Concepts

Pre-Equilibrium Approximation

This concept involves a fast, reversible initial step that rapidly reaches equilibrium, producing an intermediate species. Because equilibrium is established rapidly, the concentration of the intermediate can be written in terms of the initial reactants, allowing the overall rate law to be determined without directly measuring the intermediate.

Rate-Determining Step

In multi-step reactions, one step is significantly slower than the others, effectively controlling the overall reaction rate. In the mechanism discussed, the second step is slow, meaning it is rate-limiting, and the kinetics of this step is what governs the overall reaction rate.

Reaction Order Derivation

The overall reaction order emerges from the combination of the elementary steps when using the pre-equilibrium approximation. Although one elementary reaction is first order, when its equilibrium concentration is substituted into the rate law of the slow, rate-determining step, it yields an overall rate law that is second order with respect to the initial reactant.

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