Cl(g) + O3(g) → ClO(g) + O2(g) (slow step) ClO(g) + O3(g) → Cl(g) + 2 O2(g) (fast step) 2 O3(g) → 3 — Kinetics Chemistry Question

STEPS:

1. Understand the concept of the rate-determining step: In a multi-step chemical reaction mechanism, the overall rate of the reaction is determined by the slowest elementary step, which is known as the rate-determining step.
2. Identify the rate-determining step from the proposed mechanism: Looking at the two elementary steps provided:
* Step 1: $\text{Cl}(g) + \text{O}_3(g) \rightarrow \text{ClO}(g) + \text{O}_2(g)$ is explicitly labeled as the slow step.
* Step 2: $\text{ClO}(g) + \text{O}_3(g) \rightarrow \text{Cl}(g) + 2\ \text{O}_2(g)$ is labeled as the fast step.
Because Step 1 is the slow step, the overall reaction rate is dictated by the rate of Step 1.
3. Write the rate law for the rate-determining step: Since Step 1 is an elementary reaction, its rate law is determined directly by the stoichiometry of its reactants:
* The reactants in Step 1 are one chlorine atom ($\text{Cl}$) and one ozone molecule ($\text{O}_3$), each with a stoichiometric coefficient of 1.
* This yields the rate law:
$$\text{Rate} = k[\text{Cl}][\text{O}_3]$$
4. Conclude the overall rate law: Because Step 1 determines the speed of the entire process, the rate law for the overall reaction is $\text{Rate} = k[\text{Cl}][\text{O}_3]$. Note that while chlorine ($\text{Cl}$) is a catalyst (consumed in Step 1 and regenerated in Step 2), it is a reactant in the rate-determining step and thus correctly appears in the rate law. This matches Option B.

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WHY_OTHERS_WRONG:

• Option A is incorrect: This rate law ($\text{Rate} = k[\text{O}_3]^2$) would occur if the overall reaction proceeded via a single, simple collision between two ozone molecules. It completely fails to account for the catalytic action of the $\text{Cl}(g)$ atom in the rate-determining slow step.
• Option C is incorrect: This rate law ($\text{Rate} = k[\text{ClO}][\text{O}_3]$) represents the rate of Step 2 (the fast step). Because Step 2 is fast, it does not limit the rate of the overall reaction. Additionally, $\text{ClO}$ is an intermediate species (produced in Step 1 and consumed in Step 2) rather than a starting reactant or catalyst.
• Option D is incorrect: This rate law ($\text{Rate} = k[\text{O}_3]^2/[\text{O}_2]$) typically arises from a mechanism that begins with a fast, reversible pre-equilibrium step (such as the decomposition of $\text{O}_3$ into $\text{O}_2$ and $\text{O}$) followed by a slow step. Because the slow step in this proposed mechanism is the very first step, there is no pre-equilibrium, and division by $[\text{O}_2]$ is not mathematically justified.