What is the rate-determining step in a multistep reaction?

The rate-determining step, also called the rate-limiting step, is the slowest elementary step in a multistep reaction mechanism. Because a reaction cannot proceed faster than its slowest step, this step controls the overall reaction rate. Like a traffic bottleneck on a freeway, the rate-determining step limits how quickly the entire reaction progresses, regardless of how fast the other steps occur.

How does the rate-determining step relate to the overall rate law?

When the rate-determining step is the first step in a reaction mechanism, the rate law for the overall reaction is identical to the rate law for that elementary step. This allows chemists to derive the overall rate law directly from the slowest step and verify whether a proposed mechanism is consistent with experimentally determined rate laws.

Why do reaction intermediates appear in rate laws for fast initial steps?

When a fast equilibrium step precedes the rate-determining step, reaction intermediates form and appear in the rate law derived from the slow step. Since intermediates have unknown concentrations, chemists use the equilibrium condition from the fast step to express intermediate concentration in terms of reactant concentrations, eliminating the intermediate from the final rate law.

How can you verify a proposed reaction mechanism?

A proposed reaction mechanism is valid if two conditions are met: the elementary steps sum to give the overall balanced equation, and the rate law derived from the rate-determining step matches the experimentally determined rate law. When these criteria are satisfied, the mechanism accurately represents the reaction pathway.

What role does equilibrium play in mechanisms with fast initial steps?

In mechanisms where a fast step precedes the rate-determining step, the fast step reaches equilibrium, meaning forward and reverse reaction rates are equal. This equilibrium condition allows chemists to express intermediate concentrations in terms of reactant concentrations, enabling comparison between the proposed rate law and experimental data.

Why must reaction mechanisms be determined experimentally rather than from balanced equations?

Balanced chemical equations represent only the overall change in a system, not the actual pathway. Most reactions proceed through multistep mechanisms with different rate laws than predicted from the overall equation. Experimental rate laws must be determined first, then used to deduce the correct reaction mechanism and identify the rate-determining step.

How do you handle reaction intermediates when deriving rate laws from mechanisms?

Reaction intermediates produced in early steps and consumed in later steps cannot appear in the final rate law. To eliminate them, use the equilibrium expression from the fast step to express intermediate concentration in terms of reactants, then substitute this relationship into the rate law from the rate-determining step.

13.10

Rate-Determining Steps

31.4K views03:08 min

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.