Final answer:
The rate law for the overall reaction based on its mechanism and the rate-determining first step is rate = k[AB]^2[C]. The rate law reflects the rate dependence on the concentration of reactants involved in the slow initial step. Experimental verification is necessary to confirm the rate law.
Step-by-step explanation:
Determining the Rate Law
To determine the rate law for the overall reaction, we must consider the given reaction mechanism and identify the rate-determining step. The rate-determining step in a reaction mechanism is typically the slowest step and controls the overall rate of the reaction. According to the information provided, the mechanism consists of two steps:
- Step 1: 2AB + C (slow)
- Step 2: B + C → E (fast)
The first step is the rate-determining step since it is labeled as slow. Therefore, the rate law for the overall reaction is determined by the rate law of this slow first step. Since step 1 involves the reactants 2AB and C, the rate law would be expressed as:
rate = k[AB]^2[C]
It's important to note that the rate law cannot be deduced directly from the overall balanced equation of the reaction; it must be derived from the mechanism and experimentally confirmed.
Now, to address the overall rate constant k, it should be clear that this constant is specific for step 1, which is our slow, rate-determining step. While the letter used to represent the rate constant in the general form (k) is the same as in the question (k), this k value is specific to the rate-determining step and can be different from the k values for other steps in the mechanism.