Chemistry

Chemistry

Problem

For the decomposition of ozone in the presence of chlorine atoms the experimental rate law is rate = k[O3][Cl]. A proposed mechanism is: Step 1 O3 + Cl → ClO + O2 (slow) Step 2 ClO + O → Cl + O2 (fast) Justify how this mechanism is consistent with the observed rate law.
Intuitive explanation

The key is to recognize that the rate-determining step (the slow one) controls the overall reaction rate, and only reactants present in that step—or intermediates formed before it—appear in the rate law. Here, Step 1 is slow and consumes O3\text{O}_3 and Cl\text{Cl} directly, giving rate = k[O3][Cl]k[\text{O}_3][\text{Cl}]. The fast Step 2 then consumes the intermediate ClO\text{ClO} and doesn't affect the rate law. Since the proposed mechanism's rate-determining step matches the experimental rate law exactly, the mechanism is consistent.

Intuitive explanation

The key is to recognize that the rate-determining step (the slow one) controls the overall reaction rate, and only reactants present in that step—or intermediates formed before it—appear in the rate law. Here, Step 1 is slow and consumes O3\text{O}_3 and Cl\text{Cl} directly, giving rate = k[O3][Cl]k[\text{O}_3][\text{Cl}]. The fast Step 2 then consumes the intermediate ClO\text{ClO} and doesn't affect the rate law. Since the proposed mechanism's rate-determining step matches the experimental rate law exactly, the mechanism is consistent.

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