Consider the mechanism. O, + NO, → NO, + O, slow NO, + NO, → N,O5 fast O, + 2 NO, → O, + N,O5 - Identify the rate law for the overall reaction based on the mechanism. O rate = k[O,][NO,] = k[NO,]² O rate = k[O,][NO,J² rate = k[O,] O rate = k[NO, ][NO,]

Chemistry: The Molecular Science
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Author:John W. Moore, Conrad L. Stanitski
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Chapter11: Chemical Kinetics: Rates Of Reactions
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### Understanding the Mechanism

Consider the given mechanism involving two elementary steps:

**Step 1:**
\[ \text{O}_3 + \text{NO}_2 \rightarrow \text{NO}_3 + \text{O}_2 \quad (\text{slow}) \]

**Step 2:**
\[ \text{NO}_2 + \text{NO}_3 \rightarrow \text{N}_2\text{O}_5 \quad (\text{fast}) \]

The overall reaction derived from these steps is:
\[ \text{O}_3 + 2\text{NO}_2 \rightarrow \text{O}_2 + \text{N}_2\text{O}_5 \]

### Determining the Rate Law

The rate law for the overall reaction depends on the slow (rate-determining) step. The rate of the reaction is governed by the reactants in this slow step.

In the given mechanism, the slow (rate-determining) step is:
\[ \text{O}_3 + \text{NO}_2 \rightarrow \text{NO}_3 + \text{O}_2 \]

Therefore, the rate law can be written based on this step:
\[ \text{rate} = k[\text{O}_3][\text{NO}_2] \]

From the given options, the correct rate law is:
- \(\bigcirc\) \(\text{rate} = k[\text{O}_3][\text{NO}_2]\)

### Answer Choices:

- \(\bigcirc\) \(\text{rate} = k[\text{O}_3][\text{NO}_2]\)
- \(\textstyle\bigcirc\) \(\text{rate} = k[\text{NO}_2]^2\)
- \(\text{rate} = k[\text{O}_3][\text{NO}_2]^2\)
- \(\text{rate} = k[\text{O}_3]\)
- \(\text{rate} = k[\text{NO}_2][\text{NO}_3]\)
Transcribed Image Text:### Understanding the Mechanism Consider the given mechanism involving two elementary steps: **Step 1:** \[ \text{O}_3 + \text{NO}_2 \rightarrow \text{NO}_3 + \text{O}_2 \quad (\text{slow}) \] **Step 2:** \[ \text{NO}_2 + \text{NO}_3 \rightarrow \text{N}_2\text{O}_5 \quad (\text{fast}) \] The overall reaction derived from these steps is: \[ \text{O}_3 + 2\text{NO}_2 \rightarrow \text{O}_2 + \text{N}_2\text{O}_5 \] ### Determining the Rate Law The rate law for the overall reaction depends on the slow (rate-determining) step. The rate of the reaction is governed by the reactants in this slow step. In the given mechanism, the slow (rate-determining) step is: \[ \text{O}_3 + \text{NO}_2 \rightarrow \text{NO}_3 + \text{O}_2 \] Therefore, the rate law can be written based on this step: \[ \text{rate} = k[\text{O}_3][\text{NO}_2] \] From the given options, the correct rate law is: - \(\bigcirc\) \(\text{rate} = k[\text{O}_3][\text{NO}_2]\) ### Answer Choices: - \(\bigcirc\) \(\text{rate} = k[\text{O}_3][\text{NO}_2]\) - \(\textstyle\bigcirc\) \(\text{rate} = k[\text{NO}_2]^2\) - \(\text{rate} = k[\text{O}_3][\text{NO}_2]^2\) - \(\text{rate} = k[\text{O}_3]\) - \(\text{rate} = k[\text{NO}_2][\text{NO}_3]\)
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