Question

If a slow step precedes a fast step in a two-step mechanism, do the substances in the fast step appear in the overall rate law? Explain.

Short answer

Substances in the fast step do not appear in the overall rate law because the slow step determines the reaction rate.

Step-by-step solution

Understand the Reaction Mechanism

In a two-step reaction mechanism, there are typically two elementary steps: one slow step and one fast step. The overall rate of the reaction depends largely on the slow step, which is known as the rate-determining step.

Identify the Rate-Determining Step

The slow step is the rate-determining step. This means that the rate of the overall reaction is governed by the rate at which this slow step occurs. The substances involved in this step are what primarily influence the overall rate law.

Analyze the Influence of the Fast Step

Since the fast step follows the slow step, the substances formed or consumed in the fast step do not directly influence the overall rate law because the slow step's rate has already determined the reaction rate. Essentially, the substances in the fast step reach equilibrium quickly and do not appear in the rate law.

Construct the Overall Rate Law

The overall rate law is constructed based on the rate-determining step. Only the reactants (and sometimes intermediates if they appear in the slow step) of this slow step will appear in the rate law. Substances purely involved in the fast step do not contribute to the rate law.

Key concepts

reaction mechanism

In chemical reactions, a reaction mechanism is a detailed step-by-step description of how reactants transform into products. Most reactions occur through a series of intermediate steps, rather than a single event. These steps are called elementary steps. Understanding the mechanism helps chemists figure out which step is the slowest, and therefore, which one limits the overall rate of the reaction. This slowest step is called the rate-determining step. By knowing the detailed mechanism, we can better predict and control the reaction's behavior. In our example, we are dealing with a two-step mechanism where one step is slower (rate-determining) and one is faster.

elementary steps

Each elementary step in a reaction mechanism represents a single event at the molecular level. These steps can involve the breaking and making of chemical bonds. For a given mechanism, chemists can write out each elementary reaction, which together represent the full reaction. These steps are not usually observable directly but are inferred from experimental data and the reaction's overall behavior. Each elementary step has its own distinct rate law which only depends on the species involved in that step. In our example, the two elementary steps include a slow step and a fast step. The slow step controls the reaction rate, while the fast step quickly reaches equilibrium and does not directly affect the rate law.

overall rate law

The overall rate law of a reaction describes how the rate of the reaction depends on the concentration of reactants. It is derived from the rate-determining step of the reaction mechanism. Reactants and intermediates that are involved in this slow step appear in the rate law equation. For two-step mechanisms where the slow step precedes the fast step, only the concentrations of species in the slow step will appear in the overall rate law. The substances from the fast step do not directly influence the rate because the fast step quickly reaches equilibrium. Thus, for our example, the substances in the rate-determining (slow) step determine the overall rate law.

reaction kinetics

Reaction kinetics is the study of the rates at which chemical reactions occur. It involves understanding how different factors such as concentration, temperature, and the presence of catalysts affect the reaction rate. By examining the rate laws and mechanisms, chemists can predict the reaction rate under various conditions. Studying kinetics provides insights into the efficiency and speed of reactions, which is crucial for industries relying on chemical processes. In our two-step mechanism example, the reaction kinetics is primarily determined by the rate-determining step. Understanding this can help in optimizing the conditions to achieve the desired reaction rate efficiently.