Questions: Consider the following hypothetical mechanism: A → B+C k₁ B+D → E k₂ E+D → P+H If step 1 is the slowest step, then the overall rate law would be: a. v=k[B][D b. v=k[P][H] c. v=k[B][C] d. v=k[A

Consider the following hypothetical mechanism:
A → B+C k₁
B+D → E k₂
E+D → P+H

If step 1 is the slowest step, then the overall rate law would be:
a. v=k[B][D
b. v=k[P][H]
c. v=k[B][C]
d. v=k[A

Transcript text: Consider the following hypothetical mechanism: \[ \begin{aligned} A \rightarrow B+C & k_{1} \\ B+D \rightarrow E & k_{2} \\ E+D \rightarrow P+H & \end{aligned} \] If step 1 is the slowest step, then the overall rate law would be: a. $v=k[B][D$ b. $\quad v=k[P][H]$ c. $\quad v=k[B][C]$ d. $v=k[A$

Solution

Solution Steps

Step 1: Identify the Rate-Determining Step

In a reaction mechanism, the slowest step is the rate-determining step, which controls the overall reaction rate. According to the problem, the first step $ A \rightarrow B + C $ is the slowest step.

Step 2: Determine the Rate Law for the Rate-Determining Step

The rate law for the rate-determining step is based on the reactants involved in that step. For the step $ A \rightarrow B + C $, the rate law is: \[ v = k_1[A] \] where $ k_1 $ is the rate constant for the first step.

Step 3: Relate the Rate Law to the Overall Reaction

Since the first step is the slowest and rate-determining, the overall rate law for the reaction will be the same as the rate law for this step. Therefore, the overall rate law is: \[ v = k[A] \] where $ k $ is the effective rate constant for the overall reaction.