Rate-Determining Steps

Most chemical reactions proceed in a multistep reaction mechanism. But how is a reaction mechanism determined?

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.

However, many reactions start with a fast initial step followed by a rate-determining step. How can reaction mechanisms be proposed in such cases?

Consider the formation of nitrosyl bromide. The experimental rate law is second-order for nitric oxide and first-order for molecular bromine.

The first step is a fast equilibrium step with equal forward and reverse reaction rates, followed by the second rate-determining step, which contains a reaction intermediate. Consequently, the proposed rate law will hold the intermediate.

Therefore, a straightforward comparison between the proposed rate law, containing the reaction intermediate with an unknown concentration, and the experimental rate law, accommodating the starting reactants, is difficult.

However, assuming that the first step is in equilibrium, the intermediate concentration can be set equal to the reactants' concentrations. Substituting this relationship into the proposed rate law, and combining the rate constants into an overall rate constant, generates an expression consistent with the experimental rate law.

Combining the elementary steps gives the overall balanced equation satisfying the second requirement for a reaction mechanism. Thus, the proposed two-step reaction mechanism of nitrosyl bromide formation is valid.