To determine the overall reaction from the given reaction mechanism, we analyze the provided steps of the reaction and combine them, carefully canceling out intermediate species that appear on both sides of the individual reactions.
The given steps are:
1. [tex]\(2 A \rightarrow B + 2 C\)[/tex] (slow)
2. [tex]\(B + C \rightarrow D + E\)[/tex] (fast)
3. [tex]\(C + D \rightarrow E + F\)[/tex] (fast)
Step-by-Step Process:
1. Write down each reaction step:
[tex]\(2 A \rightarrow B + 2 C\)[/tex]
[tex]\(B + C \rightarrow D + E\)[/tex]
[tex]\(C + D \rightarrow E + F\)[/tex]
2. Sum all the reactants and products:
- Reactants: [tex]\(2 A + B + C + C + D\)[/tex]
- Products: [tex]\(B + 2 C + D + E + C + E + F\)[/tex]
3. Combine like terms:
- Reactants: [tex]\(2 A + B + 2 C + D\)[/tex]
- Products: [tex]\(B + 2 C + D + 2 E + F\)[/tex]
4. Cancel out intermediates that appear on both sides of the equation:
- Cancel [tex]\(B\)[/tex] on both sides.
- Cancel [tex]\(2 C\)[/tex] on both sides.
- Cancel [tex]\(D\)[/tex] on both sides.
After canceling, we get:
- Reactants: [tex]\(2 A\)[/tex]
- Products: [tex]\(2 E + F\)[/tex]
Hence, the overall reaction is:
[tex]\[2 A + 2 C \rightarrow 2 E + F\][/tex]
This matches the reactions listed in the provided options and is reflected in the correct simplified form:
[tex]\[2 A + 2 C \rightarrow 2 E + F\][/tex]
Thus, the correct answer is:
[tex]\[2 A + 2 C \rightarrow 2 E + F\][/tex]
