Chapter 15, Problem 70E

The following mechanism has been proposed to account for the rate law of the decomposition of ozone to ${\text{O}}_2\left(g\right):$

$\begin{array}{l}{\text{O}}_3+\text{M}\underset{k_{-1}}{\overset{k_1}{\rightleftharpoons }}{\text{O}}_2+\text{O}+\text{M}\\ \text{O}+{\text{O}}_3\stackrel{k_2}{\to }2{\text{O}}_2\end{array}$

Apply the steady-state hypothesis to the concentration of atomic oxygen, and derive the rate law for the decomposition of ozone. (M stands for an atom or molecule that can exchange kinetic energy with the particles undergoing the chemical reaction.)