The decomposition of ozone, , is proposed to proceed via the mechanism: (fast, forward rate constant — Chemical Kinetics Chemistry Question
Question
The decomposition of ozone, $2O_3 \rightarrow 3O_2$, is proposed to proceed via the mechanism: $O_3 \rightleftharpoons O_2 + O$ (fast, forward rate constant $k_1$, backward $k_{-1}$) and $O + O_3 \rightarrow 2O_2$ (slow, rate constant $k_2$). The correct rate law expression is:
Answer: A
💡 Solution & Explanation
Rate is determined by the slow step: $\text{Rate} = k_2[O][O_3]$. Apply equilibrium to the fast step to substitute the intermediate $O$: $K_{eq} = \frac{k_1}{k_{-1}} = \frac{[O_2][O]}{[O_3]} \Rightarrow [O] = \frac{k_1}{k_{-1}} \frac{[O_3]}{[O_2]}$. Substituting this gives $\text{Rate} = \frac{k_1 k_2}{k_{-1}} [O_3]^2 [O_2]^{-1}$.
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