Reaction Mechanism & Rate Law (College Board AP® Chemistry)
Study Guide
Written by: Oluwapelumi Kolawole
Reviewed by: Stewart Hird
Reaction Mechanism & Rate Law
An important tool used to verify a proposed reaction mechanism is its rate law
A rate law is an equation that shows the relationship between the rate of a reaction and the concentration of the reactants
Typically, rate laws are only determined experimentally
However, rate laws may be predicted from the assumed elementary reaction(s) of the reaction mechanism
If this prediction does not agree with the experimental rate law, the assumed mechanism must be wrong
For example, the reaction between nitrogen dioxide and fluorine gas
The overall equation is:
2NO2 (g) + F2 (g) → 2NO2F2 (g)
The experimental rate law, which is a summary of the experimental data, is:
Rate = k[NO2][F2]
If this reaction occurred in a single step, a proposed mechanism with a single elementary reaction would be:
NO2 (g) + NO2 (g) + F2 (g) → NO2F2 (g) + NO2F2 (g)
Rate laws for elementary reactions can obtained from the stoichiometric coefficient of the reactants in a balanced chemical equation
Hence, for the elementary reaction above, the rate law is given as:
Rate = k[NO2]2[F2]
However, this does not agree with the experimental rate law and must be discarded
Therefore, we can conclude that the reaction occurs in more than one step
Rate-Limiting Step
Many reactions are characterized by a multistep mechanism consisting of two or more elementary reactions
For example, the reaction above is believed to occur in two steps:
NO2 (g) + F2 (g) → NO2F2 (g) + F (step 1)
NO2 (g) + F → NO2F2 (g) (step 2)
Each step of the mechanism has its own rate constant, activation energy and rate law
The rate law for each of the steps are:
NO2 (g) + F2(g) → NO2F2 (g) + F Rate = k1[NO2][F2]
NO2 (g) + F → NO2F2 (g) Rate = k2[NO2][F]
Often one step, called rate-limiting step, is much slower than the others
It is usually the step with the highest activation energy and lowest rate constant
The rate-limiting step determines the overall rate of the reaction and the rate equation
In the reaction between nitrogen dioxide and fluorine gas, the step involving the reaction between NO2 and F2 molecules (step 1) is the slowest elementary step
The overall rate law for the reaction between nitrogen dioxide and fluorine gas is determined by the rate equation for the elementary reaction in step 1
This means that the rate law is:
Rate = k[NO2][F2]
This matches the molecularity of the equation for step 1, with one molecule of NO2 and one molecule of F2
In general, the rate law for a reaction may be determined from a balanced chemical equation describing the slowest step of the elementary reactions involved in its reaction mechanism
But, the determined rate law must agree with the experimental rate law in order to accept the proposed mechanism
Worked Example
The equation of the reaction between ozone and nitrogen dioxide is given as:
2NO2 (g) + O3 (g) → N2O5 (g)+ O2 (g)
A proposed reaction mechanism for the reaction involves two elementary reactions:
NO2 (g) + O3 (g) → NO3 (g) + O2 (g) (step 1)
NO3 (g) + NO2 (g) → N2O5 (g) (step 2)
The experimental rate law is:
k[NO2][O3]
What can you say about the relative rates of the two steps of the mechanism?
Identify the intermediate in the reaction mechanism
Answer:
Answer a)
The experimental rate law corresponds to the rate law of the first step:
Rate = k[NO2][O3]
Therefore, step 1 is the rate-limiting step with the slower reaction rate, while step 2 has a faster rate of reaction
Answer b)
The intermediate is NO3 because it is produced in step 1 and consumed in step 2
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