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Chapter 13: Problem 107

The rate law for the following reaction $$ \mathrm{CO}(g)+\mathrm{NO}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{NO}(g) $$ is rate \(=k\left[\mathrm{NO}_{2}\right]^{2}\). Suggest a plausible mechanism for the reaction, given that the unstable species \(\mathrm{NO}_{3}\) is an intermediate.

Short Answer

Expert verified
The plausible mechanism for the reaction, based on given rate law and the intermediate, is a two-step process: Step 1, \(NO_2 + NO_2 \longrightarrow NO_3 + NO\); Step 2, \(NO_3+CO \longrightarrow NO_2+CO_2\).

Step by step solution

01

Identify reactants and products

The given reaction is \( \mathrm{CO}(g)+\mathrm{NO}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{NO}(g) \). Reactants are CO and \(NO_2\). Products are \(CO_2\) and NO.
02

Propose first elementary step

The rate law suggests that the rate-determining step involves two \(NO_2\) molecules. Additionally, \(NO_3\), an unstable species, is an intermediate. Therefore, the first elementary step could be \(NO_2 + NO_2 \longrightarrow NO_3 + NO\).
03

Propose second elementary step

The intermediate \(NO_3\) and remaining reactant \(CO\) must react to form the other product \(CO_2\). So, the second step could be \(NO_3+CO \longrightarrow NO_2+CO_2\).
04

Add up the steps and compare to initial reaction

If we add up the two elementary steps, we get \(NO_2 + NO_2 + CO \longrightarrow NO_3 + NO + NO_3 + CO_2\), which simplifies to \(CO+NO_2 \longrightarrow CO_2+NO\). This is identical to the initial reaction, confirming that the proposed mechanism is consistent with the reaction.

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