Rate-determining Step

The path that reactants follow to form the products in a chemical reaction is known as the mechanism of the reaction. It is the slowest step of a reaction mechanism that determines the overall rate of reaction and is termed the rate-determining step.

The total number of molecules of the reacting species that take part in the rate-determining step appears in the rate equation of the reaction.

The rate equation for any given reaction is essential as it provides information about details like the mechanism of the reaction. A reaction can occur in a single step, or in multiple steps. 

In case the reaction proceeds in multiple steps, one of those steps is the slowest. It is the rate of this step that determines the overall rate of reaction. The reason is that this step places a limit on how fast the reaction can proceed.

This implies that no other step in the reaction mechanism can proceed slower than this rate-determining step. Comparatively, all other steps in the mechanism are generally fast.

It is also to be noted that the rate-determining step has the highest energy of activation, Ea, among all the steps of the mechanism. This is shown by the tallest peak in the potential energy diagram of the reaction.

For the general reaction A → B, there can be the following steps involved in the mechanism:

  1. A → X (Fast)
  2. X → Y (Slow)
  3. Y → B (Fast)

As indicated, the second step being the slowest, will be the rate-determining step for this reaction. It is this step that will actually decide how quickly the reaction is completed.

The reactants involved in the this step can be found in the rate law or rate expression. This information can then be utilized to propose a mechanism for a given reaction.

Example of Rate-Determining Step

An example is the rate law 

Rate = k [NO2]2

For the reaction

NO2(g) + CO(g) → NO(g) + CO2(g)

It can be determined from the rate equation/law that the rate of reaction is independent of the concentration of carbon monoxide.

The rate law also shows that the mechanism of this reaction involves more than one step. This is made obvious by the fact that CO is one of the reactants in the balanced chemical equation, but it is not included in the rate-determining step. So there must be at least one more step that contains CO as a reactant.

Furthermore, it is made clear that the rate-determining step involves 2 molecules of NO2.

A mechanism can be proposed from the information provided.

Since the rate law shows that there is a step containing two molecules of NO2, which is the rate-determining step, we can start with 2 reactant molecules of NO2. This will be the slow, rate-determining step:

Step I: NO2(g) + NO2(g) → NO3(g) + NO(g) (Rate-determining step)

We also know from the balanced chemical equation that a NO molecule is one of the products of the reaction, so it must be shown as such.

NO3, on the other hand, is the reaction intermediate*. It is produced by the reaction between two NO2 molecules. Since NO3 is not a part of the balanced equation, it must be utilized as one of the reactants in another step. 

Another reactant is the CO molecule, which appears in the balanced equation but has not been involved as a reactant in the first step.

Step II: NO3(g) + CO(g) → NO2(g) + CO2(g)

Adding the two steps together and removing the reaction intermediate (as it appears on the reactants’ as well as the products’ side) and other duplicate species, we get the balanced chemical equation.

NO2(g) + NO2(g) + NO3(g) + CO(g) NO3(g) + NO(g) + NO2(g) + CO2(g)

NO2(g) + CO(g) → NO(g) + CO2(g)

NO2 + CO Potential Energy Diagram - Rate Determining Step

The given mechanism is an example of the fact that a balanced chemical equation alone may not give any information about the way a reaction actually takes place.

*(A new species that does not appear in the overall balanced equation but is produced and later used in any of the steps of the mechanism is known as the reaction intermediate. 

The reaction intermediate is relatively unstable than the reactants or products and hence has a temporary existence. However, it is a species with normal bonds and can be isolated under special conditions).

Concepts Berg

Why is the slow step the rate determining step?

It is because the slow step limits the rate at how fast a reaction can proceed. This is why it is called the rate-determining step. The rest of the steps are generally faster.

What is RDS in organic chemistry?

The Rate-determining step is the slowest step in the mechanism of a reaction. This step has the greatest activation energy which can be shown in a potential energy diagram. Therefore, it is this step that determines the overall rate of reaction.

Is the rate-determining step the highest peak?

In a potential energy diagram, the rate-determining step has the greatest energy of activation, Ea, which is represented by the highest peak in a potential energy diagram. Kinetically, the rate-determining step proceeds the most slowly of all the steps in the mechanism of a reaction.

How do you know which step is the slow step?

The step that occurs the slowest is also called the rate-determining step in the mechanism of a reaction. The slow step can be identified from the molar concentration of reactants given in the rate law/equation along with the rate constant. In case there is none, it implies that the reaction follows zero-order kinetics.

The method of initial rates can be used to determine the rate law. The techniques involved in determining the rate of a reaction include spectrometry, conductivity, potentiometry, titrimetry, and manometry.

Moreover, the rate-determining step has the greatest activation energy of all the steps. So it can be determined with the help of a potential energy diagram as well, if it is provided.

Furthermore, the steps involving electrostatic forces occur faster whereas those involving redistribution of the electronic cloud are relatively slower in general.

What is the rate-determining step in E1cB?

The removal of the leaving group is the rate-determining step in elimination unimolecular conjugate base. This occurs after a conjugate base has been formed of the substrate in the first step. So the rate-determining step happens to be the second one.

What is the rate-determining step in acid-catalyzed dehydration of ethanol?

The removal of water molecule with the corresponding formation of carbocation is the slow, rate-determining step in the acid-catalyzed dehydration of ethanol. This happens to be the second step after the protonation of ethanol.

Does the rate-determining step have the highest activation energy?

Yes, the rate-determining step is the one with the highest activation energy. This is shown by the highest peak in the potential energy diagram of a reaction.

References

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