2.9:
Multi-Step Reactions
A chemical reaction is often represented by an overall balanced chemical equation indicating the reactants and products.
However, the actual reaction is often more complex and transpires in multiple steps. For instance, this reaction of nitric oxide with hydrogen forming nitrogen gas and water takes place in three distinct, successive steps. These steps are called the reaction mechanism.
Each step in the reaction mechanism is called an elementary reaction and represents the interaction, such as bond breakage or formation, between the reacting species.
Specific molecules, like dinitrogen dioxide and nitrous oxide, are formed during one elementary step and consumed during another. Such species are called reaction intermediates.
Reaction intermediates are not the same as transition states, which exist only during the transformation of reactants to products.
Reaction mechanisms are hypothesized based on their balanced chemical equations, and experimentally determined rate laws of each elementary step.
Each step has a specific reaction rate, rate constant, and activation energy. The slowest step is called the rate-determining step and influences the net reaction rate. It can be used to verify the rate law for the overall reaction and to validate a proposed reaction mechanism.
Consider the decomposition of nitrous oxide to nitrogen and oxygen. The experimentally determined rate law does not correspond to the rate expression of a single-step reaction, which is corroborated by the observed presence of oxygen atoms—a reaction intermediate.
Hence, a reaction mechanism is proposed where all steps cumulate to give the overall reaction.
First, the rate constants indicate that the first step is the rate-limiting step. It is the slowest, and thus influences the overall reaction rate. A rate law proposed from this step can be set equal to the overall rate law.
This proposed rate law, directly derived from the molecular concentration of the elementary reactant, matches the experimental rate law and verifies the predicted reaction mechanism.
This text is adapted from Openstax, Chemistry 2e, 12.6: Reaction Mechanisms.
2.9:
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.