Consider a reaction that occurs by the following mechanism:
A + BC → AC + B
AC + D → A + CD
The potential energy profile for this reaction is as follows:
(c) Which of the two steps in the mechanism is the rate-determining step? Write the rate law for the overall reaction.

Verified step by step guidance

1. <insert step 1> Identify the rate-determining step by analyzing the potential energy profile. The rate-determining step is the slowest step in the reaction mechanism, typically associated with the highest energy barrier or transition state.
2. <insert step 2> Compare the energy barriers of the two steps: A + BC → AC + B and AC + D → A + CD. The step with the higher energy barrier is the rate-determining step.
3. <insert step 3> Once the rate-determining step is identified, write the rate law based on this step. The rate law is determined by the reactants involved in the rate-determining step.
4. <insert step 4> For the rate-determining step, use the stoichiometry of the reactants to express the rate law. If the step is A + BC → AC + B, the rate law would be rate = k[A][BC].
5. <insert step 5> Combine the information from the rate-determining step to express the overall rate law for the reaction, ensuring it reflects the slowest step's reactants.

Key Concepts

Rate-Determining Step

The rate-determining step (RDS) is the slowest step in a reaction mechanism that dictates the overall reaction rate. It acts as a bottleneck, meaning that the speed of the entire reaction cannot exceed the speed of this step. Identifying the RDS is crucial for understanding how changes in conditions affect the reaction rate.

Reaction Mechanism

A reaction mechanism is a detailed description of the individual steps that occur during a chemical reaction. Each step involves the breaking and forming of bonds, and the sequence of these steps can influence the overall rate and products of the reaction. Understanding the mechanism helps in predicting the rate law and the effect of catalysts.

Rate Law

The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. It is typically formulated as rate = k[A]^m[B]^n, where k is the rate constant, and m and n are the orders of the reaction with respect to reactants A and B. The rate law can be derived from the rate-determining step and provides insight into how changes in concentration affect the reaction rate.