Chemical Kinetics�Lecture 6

CML101

August 07, 2024

Rate Determining Step (RDS)

In these diagrams of reaction schemes, heavy arrows represent steps with large rate constants and light arrows represent steps with small rate constants. (a) The first step is rate-determining; (b) the second step is rate-determining; (c) although one step has a small rate constant, it is not rate-determining because there is a route with a large rate constant that circumvents it.

In general, the rate-determining step (RDS) is the step in a mechanism that controls the overall rate of the reaction. The rate-determining step must be a crucial gateway for the formation of products, and not just a reaction with a small rate constant. If another reaction with a larger rate constant can also lead to products, then the step with the small rate constant

is irrelevant because it can be sidestepped (adjacent figure).

Rate Determining Step (RDS)

The reaction profile for a mechanism in which the first step (RDS) is rate-determining

The rate law of a reaction that has a rate-determining step can often—but certainly not always—be written down almost by inspection. If the first step in a mechanism is rate-determining, then the rate of the overall reaction is equal to the rate of that step because the rate constants of the subsequent steps are such that the intermediates immediately flow through these steps to give products. Moreover, because the rate-determining step is the one with the smallest rate constant, then it follows that the rate-determining step is the one with the highest activation energy. Once over the initial barrier, the intermediates cascade into products

Example of Reaction Mechanism

A number of gas-phase reactions follow first-order kinetics, as in the isomerization of cyclopropane to propene:

The problem with the interpretation of first-order rate laws is that presumably a molecule acquires enough energy to react as a result of collisions with other molecules. However, collisions are simple bimolecular events, so how can they result in a first-order rate law? First-order gas-phase reactions are widely called ‘unimolecular reactions’ because they also involve an elementary unimolecular step in which the reactant molecule changes into the product.

A representation of the Lindemann–Hinshelwood mechanism of unimolecular reactions. The species A is excited by collision with A, and the energized A molecule (A*) may either be deactivated by a collision with A or go on to decay by a unimolecular process to form products