Chemistry - Chemical Kinetics Question with Solution | TestHub

Let $\mathrm{k}$ be the rate constant of given reaction

$2{\mathrm{O}}_3\stackrel{\mathrm{k}}{⟶}3{\mathrm{O}}_2$

From the slowest step $\mathrm{r}={\mathrm{k}}^{\text{'}}\left[\mathrm{O}\right]\left[{\mathrm{O}}_3\right]$ ... $\left(\mathrm{i}\right)$

To eliminate $\left[\mathrm{O}\right]$, (From fast step)

${\mathrm{k}}_{\mathrm{eq}}=\frac{\left[{\mathrm{O}}_2\right]\left[\mathrm{O}\right]}{\left[{\mathrm{O}}_3\right]}$

$\left[\mathrm{O}\right]=\frac{{\mathrm{k}}_{\mathrm{eq}.}\left[{\mathrm{O}}_3\right]}{\left[{\mathrm{O}}_2\right]}$

Now, substituting value of $\left[\mathrm{O}\right]$ in $\mathrm{Eq}$ $\left(\mathrm{i}\right)$

$\mathrm{r}=\frac{{\mathrm{k}}^{\text{'}}{\mathrm{k}}_{\mathrm{eq}}\left[{\mathrm{O}}_3\right]\left[{\mathrm{O}}_3\right]}{\left[{\mathrm{O}}_2\right]}$

Let ${\mathrm{k}}^{\text{'}}{\mathrm{k}}_{\mathrm{eq}}=\mathrm{k}$

Thus, $\mathrm{r}=\mathrm{k}{\left[{\mathrm{O}}_3\right]}^2{\left[{\mathrm{O}}_2\right]}^{-1}$