Chapter 20, Problem 20.79E

Many gas-phase reactions require some inert body, usually represented as $\text{M}$, to absorb or supply energy in a collision in order to proceed. In the spontaneous decomposition of ozone, ${\text{O}}_{\text{3}}$, we can suggest the mechanism

$\begin{array}{c}{\text{O}}_{\text{3}}+\text{M}\stackrel{}{\to }{\text{O}}_{\text{3}}{}^{*}+\text{M}\\ {\text{O}}_{\text{3}}{}^{*}\stackrel{\text{RDS}}{\to }{\text{O}}_2+\cdot \text{O}\cdot \\ \cdot \text{O}\cdot +{\text{O}}_{\text{3}}\stackrel{}{\to }2{\text{O}}_2\end{array}$

for the overall reaction

${\text{2O}}_{\text{3}}\stackrel{}{\to }{\text{3O}}_2$

In the mechanism, ${\text{O}}_{\text{3}}{}^{*}$ refers to an ozone molecule in some energetically excited state that can react spontaneously to form ${\text{O}}_2$ and $\text{O}$ atoms. Determine the rate law of the proposed mechanism in terms of ${\text{O}}_{\text{3}}$ and $\text{M}$, where the second step is the rate-determining step. Will adding an inert gas like $\text{Ar}$ to a sample of ozone increase or decrease the rate of the reaction?