Final answer:
The overall balanced equation for the given mechanism is B₂ + A → D + C₂. The rate-determining step is Step 1 with a rate law of rate = k[B₂][B2]. E3 is identified as the intermediate, and the overall rate law expression is rate = k₁[B₂][B2].
Step-by-step explanation:
To determine the overall balanced equation for a reaction given the proposed mechanism, we must sum up all the elementary steps and cancel out any intermediates (species that are produced and then consumed in the mechanism) to get the net balanced equation. In this case, the steps are:
- Step 1: B₂ + B2 → E3 + D (slow)
- Step 2: E3 + A → B₂ + C₂ (fast)
By adding these steps together and canceling E3, which appears to be an intermediate, the overall reaction is:
B₂ + A → D + C₂
The rate-determining step is the slow step, which is Step 1.
Therefore, the rate law for this reaction is based on this step: rate = k[B₂][B2]. In this scenario, [E3] is not included in the overall rate law because it is an intermediate and its concentration is determined by other steps in the mechanism.
Identifying Intermediates and Writing Rate Laws
(b) The intermediate in this reaction is E3.
(c) The rate law for Step 1, which is the slow and therefore rate-determining step, is rate = k₁[B₂][B2]. As Step 2 is fast, its rate law would normally be rate = k₂[E3][A], but since it is not the rate-determining step, it does not dictate the overall rate law.
(d) The overall rate law, assuming Step 1 is the slow step, is rate = k₁[B₂][B2].