The experimental rate law for the reaction \(\mathrm{A}+\mathrm{A} \rightarrow \mathrm{A}_{2}\) is Rate \(=k[\mathrm{~A}][\mathrm{BC}]\) Two mechanisms have been proposed for the reaction: Step 1: \(\mathrm{A}+\mathrm{B} \rightarrow \mathrm{AB}\) (slow) Step \(2: \mathrm{AB}+\mathrm{A} \rightarrow \mathrm{A}_{2}+\mathrm{B}\) (fast) and Step \(1: \mathrm{A}+\mathrm{BC} \rightarrow \mathrm{AB}+\mathrm{C}\) (slow) Step \(2: \mathrm{A}+\mathrm{AB} \rightarrow \mathrm{B}+\mathrm{A}_{2}\) (fast) Step \(3: \mathrm{B}+\mathrm{C} \rightarrow \mathrm{BC}\) (fast) (a) Show that each mechanism results in the correct overall reaction. (b) Which mechanism is consistent with the rate law? (c) Why does \(\mathrm{BC}\) appear in the rate law but not in the overall reaction?

In chemical kinetics, the term rate-determining step refers to the slowest step in a reaction mechanism that determines the speed at which the entire reaction proceeds. It's analogous to the narrowest section of a funnel that controls the flow rate of a fluid passing through it.

Consider a series of events, each with its own pace; the slowest one dictates the overall pace, just as in a relay race, the slowest runner sets the limit for the team's total time. In the case of our exercise, the reaction mechanism encompasses several steps, and identifying the rate-determining step is crucial for understanding the reaction kinetics.

Why is the rate-determining step so central to understanding reaction rates?

• It provides insight into the kinetics of the reaction.
• It assists in predicting the reaction's rate law based on the reactants involved in that slow step.
• It helps in designing reactions for optimal speed by possibly altering conditions to speed up the slowest step.

The experimental rate law of a reaction is an empirical relationship that defines the rate of the reaction in terms of the concentration of reactants, derived from experimental data. It is not necessarily intuitive and must be determined through laboratory studies rather than theoretical predictions.

The form of the rate law provides valuable information regarding the reaction mechanism, though it does not always reflect the stoichiometry of the overall reaction. Instead, it highlights the stoichiometry of the rate-determining step. In our textbook exercise, the experimental rate law is Rate = k[A][BC], which implies that the reaction rate is directly proportional to the concentration of A and BC, but not necessarily A alone, which would be inferred from the overall reaction.

Here's why the experimental rate law is key:

• It specifies which reactant concentrations are involved in controlling the reaction rate.
• It aids in verifying proposed reaction mechanisms by comparing predicted and experimental rate laws.
• It provides details that can be used for the optimization and scale-up of chemical processes.

The concept of reaction intermediates is indispensable in understanding complex reaction mechanisms. These are species that are formed during the reaction but are not present in the final equation. They are typically formed in an early step and consumed in a subsequent step of a reaction mechanism.

In our exercise, we encounter intermediates such as AB, which appears momentarily in the mechanism's steps but is neither a reactant nor a product of the overall reaction. These short-lived species can often provide clues about the mechanism and are essential for the construction of the correct rate law.

The role of reaction intermediates includes:

• Facilitating multi-step reaction processes.
• Being part of the rate-determining step, affecting the overall reaction rate.
• Allowing chemists to infer the pathway from reactants to products.

This is why, despite not appearing in the final chemical equation, intermediates are instrumental in the study of reaction mechanisms.