Name: reaction mechanisms and rate-determining steps
Uploaded: 2023-04-30T18:28:32.000Z
Duration: 2 min 31 s
Channel: JoVE

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Chemistry

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Multi-Step Reactions

A chemical reaction is often represented by an overall balanced chemical equation indicating the reactants and products.
However, the actual reaction is often more complex and transpires in multiple steps. For instance, this reaction of nitric oxide with hydrogen forming nitrogen gas and water takes place in three distinct, successive steps. These steps are called the reaction mechanism.
Each step in the reaction mechanism is called an elementary reaction and represents the interaction, such as bond breakage or formation, between the reacting species.
Specific molecules, like dinitrogen dioxide and nitrous oxide, are formed during one elementary step and consumed during another. Such species are called reaction intermediates.
Reaction intermediates are not the same as transition states, which exist only during the transformation of reactants to products.
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&#8212;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.
This text is adapted from <a href="https://openstax.org/books/chemistry-2e/pages/12-6-reaction-mechanisms">Openstax, Chemistry 2e, 12.6: Reaction Mechanisms</a>.

multi-step reactions

Chemical reactions often occur in a stepwise fashion involving two or more distinct reactions taking place in a sequence. A balanced equation indicates the reacting species and the product species, but it reveals no details about how the reaction occurs at the molecular level. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs. Each of the steps in a reaction mechanism is called an elementary reaction. These elementary reactions occur in sequence, as represented in the step equations, and they sum to yield the balanced chemical equation describing the overall reaction. In a multistep reaction mechanism, one of the elementary steps progresses slower than the others &#8212; sometimes significantly slower. This slowest step is called the rate-limiting step (or rate-determining step). A reaction cannot proceed faster than its slowest step, and hence, the rate-determining step limits the overall reaction rate.
Unlike balanced equations representing an overall reaction, the equations for elementary reactions are explicit representations of the chemical change. An elementary reaction equation depicts the actual reactant(s) undergoing bond-breaking/making and the product(s) formed. Rate laws may be derived directly from the balanced chemical equations for elementary reactions. However, this is not the case for most chemical reactions, where balanced equations often represent the overall change in the chemical system resulting from multistep reaction mechanisms. Therefore, the rate law must be determined from experimental data, and the reaction mechanism must be subsequently deduced from the rate law.
For instance, consider the reaction of NO2 and CO:
<img alt="Chemical equilibrium equation: NO&#8322;(g) + CO(g) &#8594; CO&#8322;(g) + NO(g), atmospheric reaction diagram." src="/files/ftp_upload/11699/11699_Equation1.svg" style="text-align: center; height: 22px;" data-altupdatedat="1761830439000" data-alt="Figure1" />
The experimental rate law for this reaction at temperatures above 225 &#176;C is:
<img alt="Chemical reaction rate equation, Rate=k[NO2][CO], kinetic study, formula image." src="/files/ftp_upload/11699/11699_Equation2.svg" style="text-align: center; height: 19px;" data-altupdatedat="1761830439000" data-alt="Figure2" />
According to the rate law, the reaction is first-order with respect to NO2 and first-order with respect to CO. However, at temperatures below 225 &#176;C, the reaction is described by a different rate law that is second-order with respect to NO2:
<img alt="Chemical kinetics equation, Rate = k[NO&#8322;]&#178;, formula for reaction rate analysis." src="/files/ftp_upload/11699/11699_Equation3.svg" style="text-align: center; height: 21px;" data-altupdatedat="1761830439000" data-alt="Figure3" />
This rate law is not consistent with the single-step mechanism, but it is consistent with the following two-step mechanism:
<img alt="Chemical reaction kinetics; NO2 + NO2 &#8594; NO3 + NO (slow); reaction equation; gas-phase dynamics." src="/files/ftp_upload/11699/11699_Equation4.svg" style="text-align: center; height: 21px;" data-altupdatedat="1761830439000" data-alt="Figure4" />
<img alt="Chemical reaction equation, NO&#8323;(g) + CO(g) &#8594; NO&#8322;(g) + CO&#8322;(g), showing gas phase kinetics." src="/files/ftp_upload/11699/11699_Equation5.svg" style="text-align: center; height: 21px;" data-altupdatedat="1761830439000" data-alt="Figure5" />
The rate-determining (slower) step gives a rate law showing second-order dependence on the NO2 concentration, and the sum of the two elementary equations gives the net overall reaction.
In general, when the rate-determining (slower) step is the first step in the reaction mechanism, the rate law for the overall reaction is the same as the rate law for this step. However, when the rate-determining step is preceded by an elementary step involving a rapidly reversible reaction, the rate law for the overall reaction may be more difficult to derive, often due to the presence of reaction intermediates.
In such instances, the concept that a reversible reaction is at equilibrium when the rates of the forward and reverse processes are equal can be utilized.

Chemical reactions often occur in a stepwise fashion involving two or more distinct reactions taking place in a sequence. A balanced equation indicates ...

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KEY TERMS AND CONCEPTS

reaction mechanisms and rate-determining steps

Chemical reactions can happen in a sequence of steps. A balanced chemical equation shows the reactants and products, but it does not show how the reaction occurs at the molecular level. The reaction mechanism, or reaction path, gives that step-by-step detail.

Each step in a mechanism is an elementary reaction. These elementary reactions happen in order, and together they add up to the balanced equation for the overall reaction. In a multistep mechanism, one step is often much slower than the others. This slowest step is the rate-limiting step, also called the rate-determining step.

The rate-determining step controls how fast the whole reaction can go. A reaction cannot move faster than its slowest step. Unlike an overall balanced equation, an elementary reaction shows the actual reactants that break and form bonds.

For elementary reactions, the rate law can be written directly from the chemical equation. For most reactions, that is not possible because the balanced equation represents the overall change, not each step. In those cases, the rate law must be found from experiments, and the mechanism is then deduced from that rate law.

The reaction between NO2 and CO shows how this works. At temperatures above 225 °C, the experimental rate law is first-order in NO2 and first-order in CO. At temperatures below 225 °C, the rate law is different and is second-order in NO2. That lower-temperature rate law does not fit a single-step mechanism, but it does fit a two-step mechanism.

In that two-step mechanism, the slower step produces the rate law with second-order dependence on NO2. The two elementary equations then combine to give the net overall reaction. In general, when the rate-determining step is the first step, the overall rate law matches that step.

The rate law can be harder to work out when a fast reversible step comes before the slow step. This can happen because intermediates form during the reaction. In those cases, the idea of equilibrium is useful, where the forward and reverse rates are equal.

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Chemical reactions can happen in a sequence of steps. A balanced chemical equation shows the reactants and products, but it does not show how the reaction occurs at the molecular level. The reaction mechanism, or reaction path, gives that step-by-step detail. Each step in a mechanism is an elementary reaction. These elementary reactions happen in order, and together they add up to the balanced equation for the overall reaction. In a multistep mechanism, one step is often much slower than the...

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HS-PS1-4

Effect of Temperature Change on Reaction Rate

The Arrhenius equation,

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Reaction Mechanisms and Rate-Determining Steps

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