Mechanism of the reaction is:
`A_(2) underset(k')overset(k)hArr 2A`
`A + B_(2) overset(k_(2))rarr C + B`
`B + A_(2) overset(k_(2))rarr C + A`
What is`(-d[A_(2)])/(dt)`

Explanation

To find the expression for \(-\frac{d[A_2]}{dt}\) based on the given reaction mechanism, we need to analyze the contributions from each reaction step involving \(A_2\).

### Step-by-Step Solution:

1. **Identify the Reactions**:
The mechanism consists of three reactions:
- \(A_2 \underset{k'}{\overset{k}{\rightleftharpoons}} 2A\)
- \(A + B_2 \overset{k_2}{\rightarrow} C + B\)
...