5.3 Rate-determining steps and their identification

Chemical reactions often involve multiple steps, and understanding which step controls the overall speed is central to predicting reaction behavior. The rate-determining step (RDS) is the slowest elementary step in a mechanism. It acts as a bottleneck: the entire reaction can only proceed as fast as this one step allows.

Identifying the RDS lets you write the correct rate law, predict how concentration changes affect speed, and understand why catalysts work the way they do.

Rate-Determining Steps

Rate-determining step definition

The rate-determining step is the slowest step in a multi-step reaction mechanism. It has the highest activation energy barrier of all the elementary steps, which means it requires the most energy to proceed. Because of this, it limits the overall rate of the reaction.

• The rate of the overall reaction equals the rate of the RDS.
• Speeding up the RDS (for example, by adding a catalyst) speeds up the whole reaction.
• Speeding up a step that is not the RDS has no meaningful effect on the overall rate.

Significance in reaction rates

The RDS controls the flow of material through the entire mechanism, much like the narrowest section of a pipe controls water flow.

• Intermediates tend to accumulate before the RDS because earlier steps produce them faster than the RDS consumes them.
• Steps after the RDS proceed quickly once material gets through the bottleneck.
• The rate law for the overall reaction is determined by the RDS. The reaction order with respect to each reactant comes from how those reactants appear in the RDS (and any prior equilibrium steps that feed into it).

For example, if the RDS is bimolecular involving one molecule of A and one molecule of B, the rate law will be $\text{rate} = k[\text{A}][\text{B}]$, which is second order overall.

Identification in reaction mechanisms

To find the RDS in a proposed mechanism, use these approaches:

1. Compare rate constants. The step with the smallest rate constant $k$ is the slowest. If you're given numerical values, the step with the lowest $k$ is the RDS.
2. Compare activation energies. On an energy diagram, the step with the tallest activation energy barrier is the RDS. More energy is needed to reach that transition state, so the step proceeds more slowly.
3. Match the experimental rate law. Write the rate law implied by each step as if it were the RDS. The step whose implied rate law matches the experimentally observed rate law is the actual RDS. This is the most common method in practice.
4. Consider molecularity as a rough guide. Termolecular steps (three molecules colliding simultaneously) are extremely rare and slow. Bimolecular steps are generally slower than unimolecular steps, all else being equal. But molecularity alone isn't enough to identify the RDS; you need the rate constants or experimental data.

Effects of changing conditions

Temperature: Increasing temperature increases the overall reaction rate primarily because it helps molecules overcome the activation energy barrier of the RDS. All steps speed up, but the RDS still benefits the most in terms of its impact on the overall rate.

Concentration: Only the concentrations of species that appear in the RDS (or in equilibrium steps before it) affect the overall rate.

• Increasing the concentration of a reactant in the RDS increases the overall rate.
• Changing the concentration of a reactant that only appears in a fast step after the RDS has no effect on the overall rate.

Catalysts: A catalyst lowers the activation energy of a specific step.

• If the catalyst lowers the activation energy of the RDS, the overall reaction speeds up.
• If the catalyst lowers the energy barrier enough, a different step may become the new RDS. The bottleneck shifts, and the rate law may change as a result.

Reaction Mechanisms and Kinetics

Relationship between reaction mechanisms and rate laws

A reaction mechanism is a proposed sequence of elementary steps that shows how reactants are converted to products. Each elementary step has a rate law that can be written directly from its molecularity: a unimolecular step is first order, a bimolecular step is second order, and so on.

The overall rate law is governed by the RDS. Here's the key connection:

1. Propose a mechanism with elementary steps that sum to the overall balanced equation.
2. Write the rate law for the proposed RDS. This gives a predicted rate law.
3. Compare the predicted rate law to the experimental rate law. If they match, the mechanism is consistent with the data. If they don't, the proposed mechanism (or the choice of RDS) is wrong.

This comparison is one of the main ways chemists validate or rule out proposed mechanisms. A mechanism can never be proven correct by kinetics alone, but it can be shown to be inconsistent with the data, which eliminates it from consideration.