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title: "A student proposes the following two-step mechanism for the reaction \\(\\text{NO}_2\\text{(g)} + \\text{CO(g)} \\rightarrow \\text{NO(g)} + \\text{CO}_2\\text{(g)}\\):  Step 1: \\(\\text{NO}_2\\text{(g)} + \\text{NO}_2\\text{(g)} \\rightarrow \\text{NO}_3\\text{(g)} + \\text{NO(g)}\\) (slow) Step 2: \\(\\text{NO}_3\\text{(g)} + \\text{CO(g)} \\rightarrow \\text{NO}_2\\text{(g)} + \\text{CO}_2\\text{(g)}\\) (fast)  Which of the following rate laws is consistent with the proposed mechanism, and why?"
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url: "https://nerd-notes.com/ubq/119267/"
date_modified: "2026-08-19T12:39:35+00:00"
---

# A student proposes the following two-step mechanism for the reaction \(\text{NO}_2\text{(g)} + \text{CO(g)} \rightarrow \text{NO(g)} + \text{CO}_2\text{(g)}\):

Step 1: \(\text{NO}_2\text{(g)} + \text{NO}_2\text{(g)} \rightarrow \text{NO}_3\text{(g)} + \text{NO(g)}\) (slow)
Step 2: \(\text{NO}_3\text{(g)} + \text{CO(g)} \rightarrow \text{NO}_2\text{(g)} + \text{CO}_2\text{(g)}\) (fast)

Which of the following rate laws is consistent with the proposed mechanism, and why?

A student proposes the following two-step mechanism for the reaction \(\text{NO}_2\text{(g)} + \text{CO(g)} \rightarrow \text{NO(g)} + \text{CO}_2\text{(g)}\):

Step 1: \(\text{NO}_2\text{(g)} + \text{NO}_2\text{(g)} \rightarrow \text{NO}_3\text{(g)} + \text{NO(g)}\) (slow)
Step 2: \(\text{NO}_3\text{(g)} + \text{CO(g)} \rightarrow \text{NO}_2\text{(g)} + \text{CO}_2\text{(g)}\) (fast)

Which of the following rate laws is consistent with the proposed mechanism, and why?

- **A.** \(\text{Rate} = k [\text{NO}_2][\text{CO}]\), because the reaction orders in the rate law must match the stoichiometric coefficients of the reactants in the overall balanced equation.
- **B.** \(\text{Rate} = k [\text{NO}_2][\text{CO}]\), because \(\text{CO}\) is a reactant in Step 2, which rapidly converts the intermediate \(\text{NO}_3\) into products.
- **C.** \(\text{Rate} = k [\text{NO}_2]^2\), because Step 1 is the slow rate-determining step and its rate depends on the bimolecular collision of two \(\text{NO}_2\) reactant molecules.
- **D.** \(\text{Rate} = k [\text{NO}_2]^2\), because \(\text{NO}_2\) acts as a catalyst that is consumed in Step 1 and regenerated in Step 2.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/119267/*