Experimental analysis shows that the homogeneous decomposition of ozone proceeds with a rate

$$\mathrm {-r_{O_3}=k[ O_3]^2[O_2 ]^{-1}}$$

$$\mathrm {-r_{O_3}=kC^2_{O_3}/C_{O_2}}$$

1. Suggest a two-step mechanism to explain this rate.

2. What is the overall order of reaction?

Solution :

The homogeneous decomposition of ozone proceeds as

$$ 2 \mathrm{O}_{3} \rightarrow 2 \mathrm{O}_{2} $$

and follows the rate law

$$ -\mathrm{r}_{\mathrm O_{3}}=\mathrm k\left[\mathrm{O}_{3}\right]^{2}\left[\mathrm{O}_{2}\right]^{-1} $$

The two-step mechanism, consistent with the rate, suggested is

Step 1: (fast, at equilibrium)

$$\mathrm{O}_{3} \underset{\mathrm{k}_{2}}{\stackrel{\mathrm{k}_{1}}{\rightleftharpoons}} \mathrm{O}_{2}+\mathrm{O} \quad$$

Step 2: (slow)

$$\quad \mathrm{O}+\mathrm{O}_{3} \stackrel{\mathrm{k}_{3}}{\longrightarrow} …