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
