Multi-Step Reactions

Chemical reactions often occur in a stepwise fashion involving two or more distinct reactions taking place in a sequence. A balanced equation indicates the reacting species and the product species, but it reveals no details about how the reaction occurs at the molecular level. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs. Each of the steps in a reaction mechanism is called an elementary reaction. These elementary reactions occur in sequence, as represented in the step equations, and they sum to yield the balanced chemical equation describing the overall reaction. In a multistep reaction mechanism, one of the elementary steps progresses slower than the others — sometimes significantly slower. This slowest step is called the rate-limiting step (or rate-determining step). A reaction cannot proceed faster than its slowest step, and hence, the rate-determining step limits the overall reaction rate.

Unlike balanced equations representing an overall reaction, the equations for elementary reactions are explicit representations of the chemical change. An elementary reaction equation depicts the actual reactant(s) undergoing bond-breaking/making and the product(s) formed. Rate laws may be derived directly from the balanced chemical equations for elementary reactions. However, this is not the case for most chemical reactions, where balanced equations often represent the overall change in the chemical system resulting from multistep reaction mechanisms. Therefore, the rate law must be determined from experimental data, and the reaction mechanism must be subsequently deduced from the rate law.

For instance, consider the reaction of NO₂ and CO:

The experimental rate law for this reaction at temperatures above 225 °C is:

According to the rate law, the reaction is first-order with respect to NO₂ and first-order with respect to CO. However, at temperatures below 225 °C, the reaction is described by a different rate law that is second-order with respect to NO₂:

This rate law is not consistent with the single-step mechanism, but it is consistent with the following two-step mechanism:

The rate-determining (slower) step gives a rate law showing second-order dependence on the NO₂ concentration, and the sum of the two elementary equations gives the net overall reaction.

In general, when the rate-determining (slower) step is the first step in the reaction mechanism, the rate law for the overall reaction is the same as the rate law for this step. However, when the rate-determining step is preceded by an elementary step involving a rapidly reversible reaction, the rate law for the overall reaction may be more difficult to derive, often due to the presence of reaction intermediates.

In such instances, the concept that a reversible reaction is at equilibrium when the rates of the forward and reverse processes are equal can be utilized.