NO2(g) + CO(g) → NO(g) + CO2(g) The reaction between NO2(g) and CO(g) is represented above. The elem — Kinetics Chemistry Question

STEPS:

1. Understand the concept of the Rate^-Determining Step (RDS): In a multi-step reaction mechanism, the overall rate of the reaction is limited by the slowest elementary step, often called the rate-determining step. This step acts as a "bottleneck"; the reaction cannot proceed any faster than this step allows.
2. Identify the rate-determining step in the proposed mechanism:
* Step 1: $2\ \text{NO}_2(g) \rightarrow \text{NO}(g) + \text{NO}_3(g)$ is labeled as (slow).
* Step 2: $\text{NO}_3(g) + \text{CO}(g) \rightarrow \text{NO}_2(g) + \text{CO}_2(g)$ is labeled as (fast).
* Therefore, Step 1 is the rate-determining step, and the rate of the overall reaction is determined solely by the rate of Step 1.
3. Write the rate law for the rate-determining step:
* Unlike overall chemical reactions (where reaction orders must be determined experimentally), the rate law of an elementary step is derived directly from its stoichiometric coefficients.
* In Step 1, the reactant is $\text{NO}_2$, and its stoichiometric coefficient is $2$ (signified by $2\ \text{NO}_2$).
* This means two molecules of $\text{NO}_2$ must collide in this elementary step, making it a second-order process with respect to $\text{NO}_2$:
$$\text{Rate} = k_1[\text{NO}_2]^2$$
4. Determine the overall rate law:
* Since Step 1 is the slowest step and its reactants ($\text{NO}_2$) are stable starting materials rather than temporary intermediates, the overall rate law for the reaction is simply the rate law of Step 1.
* This gives an overall rate law of:
$$\text{Rate} = k[\text{NO}_2]^2$$
5. Conclude: The derived rate law matches Option B perfectly.

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WHY_OTHERS_WRONG:

• Option A is incorrect: This is the rate law that would be predicted if the overall reaction occurred in a single, elementary step ($\text{NO}_2 + \text{CO} \rightarrow \text{NO} + \text{CO}_2$). However, the proposed mechanism shows that carbon monoxide ($\text{CO}$) only participates in Step 2, which is fast. Because $\text{CO}$ is involved after the rate-determining step, changing its concentration has no effect on the overall rate of the reaction, so its order must be zero.
• Option C is incorrect: This represents the rate law for Step 2 ($\text{Rate} = k_2[\text{NO}_3][\text{CO}]$). Because Step 2 is fast, it does not determine the rate of the overall reaction. Furthermore, overall rate laws must only contain stable reactants; they cannot include reaction intermediates like $\text{NO}_3$ (which is produced in Step 1 and consumed in Step 2).
• Option D is incorrect: This rate law has no physical or thermodynamic basis. It incorrectly attempts to multiply reactants from both the slow and fast steps while also including the intermediate species $\text{NO}_3$.