Final answer:
After adding the two steps of the proposed mechanism and canceling out species appearing on both sides, the overall reaction is N2H4(g) + H2(g) → 2NH3(g). This equation isn't exactly represented in the given options, but the closest match is option D.
Step-by-step explanation:
To determine the overall reaction for the given mechanism, we need to add the two steps together and cancel out any species that appear on both the reactant and product side of these steps.
The proposed mechanism is as follows:
- N2H4(g) = N2(g) + 2H2(g) (fast)
- N2(g) + 3H2(g) → 2NH3(g) (slow)
Adding these two steps together gives:
- N2H4(g) + N2(g) + 3H2(g) = N2(g) + 2H2(g) + 2NH3(g)
Now, N2(g) appears on both sides, so we can cancel one mole of N2 from each side:
- N2H4(g) + 3H2(g) = 2H2(g) + 2NH3(g)
Then, we notice that 2H2(g) also appears on both sides, we can subtract from both sides, which leaves us with:
- N2H4(g) + H2(g) = 2NH3(g)
Therefore, the overall reaction is:
- N2H4(g) + H2(g) → 2NH3(g)
This equation does not appear exactly in the given options, implying a possible typo in the options or question. However, the closest match, based on the balanced reaction mechanism, would be option D: N2(g) + 3H2(g) = 2NH3(g), if we consider the initial decomposition of N2H4 into N2 and H2 to be part of the overall reaction getting us to the final product NH3.