Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Discover detailed solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Given a reaction mechanism that has an overall reaction of [tex]2 O_3 \longrightarrow 3 O_2[/tex] and a rate of [tex]k[O_3][O][/tex], which is the correct rate-determining step?

A. [tex]O_3 + 2 O \rightarrow 3 O_2[/tex]
B. [tex]O_2 + O \rightarrow O_3[/tex]
C. [tex]O_3 \Leftrightarrow O_2 + O[/tex]
D. [tex]O_3 + O \rightarrow 2 O_2[/tex]

Sagot :

GinnyAnswer
Certainly! Let's analyze the given reaction mechanism and the provided information step-by-step to identify the rate-determining step.

### Overall Reaction
The overall reaction is:
[tex]\[ 2 \, O_3 \longrightarrow 3 \, O_2 \][/tex]

### Given Rate Law
The rate law is given as:
[tex]\[ \text{Rate} = k [O_3][O] \][/tex]

This rate law indicates that the rate of the reaction depends on the concentration of both [tex]\(O_3\)[/tex] and [tex]\(O\)[/tex]. This implies that the rate-determining step (the slowest step in the mechanism) involves one molecule of [tex]\(O_3\)[/tex] and one molecule of [tex]\(O\)[/tex].

### Analyzing the Options
1. Option 1: [tex]\(O_3 + 2 \, O \rightarrow 3 \, O_2\)[/tex]

- This step involves one [tex]\(O_3\)[/tex] molecule and two [tex]\(O\)[/tex] atoms.
- The rate law derived from this step would not match [tex]\(k[O_3][O]\)[/tex] because it involves a second-order dependency on [tex]\(O\)[/tex].

2. Option 2: [tex]\(O_2 + O \rightarrow O_3\)[/tex]

- This step involves one [tex]\(O_2\)[/tex] molecule and one [tex]\(O\)[/tex] atom.
- This does not directly involve [tex]\(O_3\)[/tex] as a reactant, which contradicts the given rate law that depends on the concentration of [tex]\(O_3\)[/tex].

3. Option 3: [tex]\(O_3 \Leftrightarrow O_2 + O\)[/tex]

- This is a reversible step involving [tex]\(O_3\)[/tex] breaking down into [tex]\(O_2\)[/tex] and [tex]\(O\)[/tex].
- Although it involves [tex]\(O_3\)[/tex], it is a reversible step and does not fit the typical rate-determining step criteria where the rate law directly represents the slowest irreversible step.

4. Option 4: [tex]\(O_3 + O \rightarrow 2 \, O_2\)[/tex]

- This step involves one [tex]\(O_3\)[/tex] molecule and one [tex]\(O\)[/tex] atom.
- The rate law derived from this step would be [tex]\(k[O_3][O]\)[/tex], which matches the given rate law perfectly.

### Conclusion
Based on the analysis above, the correct rate-determining step that fits the given rate law of [tex]\(k[O_3][O]\)[/tex] is:

[tex]\[ O_3 + O \rightarrow 2 \, O_2 \][/tex]

Hence, the correct answer is:

[tex]\[ \boxed{4} \][/tex]
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.