Certainly! Let's break down the problem step-by-step.
### Part a: Writing the overall balanced equation
We start by examining the two given steps of the reaction mechanism:
1. [tex]\( \text{O}_3 \rightarrow \text{O}_2 + \text{O} \)[/tex]
2. [tex]\( \text{O}_3 + \text{O} \rightarrow 2 \text{O}_2 \)[/tex] (this step is slow)
To find the overall balanced equation, we'll need to combine these two steps.
1. The first reaction:
[tex]\[ \text{O}_3 \rightarrow \text{O}_2 + \text{O} \][/tex]
2. The second reaction:
[tex]\[ \text{O}_3 + \text{O} \rightarrow 2 \text{O}_2 \][/tex]
Next, add the two reactions together:
[tex]\[ \text{O}_3 + \text{O}_3 + \text{O} \rightarrow \text{O}_2 + \text{O}_2 + \text{O} + \text{O}_2 \][/tex]
Simplify by canceling out the intermediates that appear on both sides of the equation. In this case, [tex]\(\text{O}\)[/tex] appears on both sides and cancels out:
[tex]\[ \text{O}_3 + \text{O}_3 \rightarrow 3 \text{O}_2 \][/tex]
Thus, the overall balanced equation is:
[tex]\[ 2 \text{O}_3 \rightarrow 3 \text{O}_2 \][/tex]
### Part b: Identifying intermediates
An intermediate is a species that is produced in one step of the reaction mechanism and consumed in another step.
In the mechanism:
1. [tex]\( \text{O}_3 \rightarrow \text{O}_2 + \text{O} \)[/tex] - here, [tex]\(\text{O}\)[/tex] is produced.
2. [tex]\( \text{O}_3 + \text{O} \rightarrow 2 \text{O}_2 \)[/tex] - here, [tex]\(\text{O}\)[/tex] is consumed.
Since [tex]\(\text{O}\)[/tex] is produced in the first step and consumed in the second step, [tex]\(\text{O}\)[/tex] is an intermediate in this mechanism.
### Summary:
- The overall balanced equation is:
[tex]\[
2 \text{O}_3 \rightarrow 3 \text{O}_2
\][/tex]
- The intermediate in the reaction mechanism is:
[tex]\[
\text{O}
\][/tex]
