The rate law for the decomposition of ozone to molecular

Chapter 14, Problem 64QP

(choose chapter or problem)

The rate law for the decomposition of ozone to molecular oxygen \(2 \mathrm{O}_{3}(g) \longrightarrow 3 \mathrm{O}_{2}(g)\) is rate = \(\text { rate }=k \frac{\left[\mathrm{O}_{3}\right]^{2}}{\left[\mathrm{O}_{2}\right]}\)

The mechanism proposed for this process is

\(\begin{array}{l} \mathrm{O}_{3} \underset{k_{-1}}{\stackrel{k_{1}}{\rightleftarrows}} \mathrm{O}+\mathrm{O}_{2}\\ \mathrm{O}+\mathrm{O}_{3} \stackrel{k_{2}}{\longrightarrow} 2 \mathrm{O}_{2} \end{array} \)

Derive the rate law from these elementary steps. Clearly state the assumptions you use in the derivation. Explain why the rate decreases with increasing \(\mathrm O_2\) concentration.