Reaction Mechanisms and Rate Laws
Quick Notes
- The rate-limiting step is the slowest step in a reaction mechanism. It controls the overall reaction rate.
- If the first step is the rate-limiting step and is irreversible, the rate law is based on that step alone.
- The rate law reflects the molecularity of the slow step:
- Unimolecular: rate ∝ [A]
- Bimolecular: rate ∝ [A][B]
- Only reactants in the slowest step appear in the rate law.
- Intermediates should not appear in the final rate law.
- In a reaction profile diagram, each step gives one transition state (a peak is a transition state and a valley is an intermediate).
Full Notes
Rate-Limiting Step and Its Importance
In a multi-step reaction, not all steps occur at the same rate. The rate-limiting step (also called the slow step or ‘rate determining step’) determines how fast the overall reaction proceeds – much like how a single road obstruction controls the flow of traffic.
Rate-Limiting Step (RLS)
The slowest elementary step in a mechanism limits the overall reaction rate and determines the rate equation.
A species must appear in the rate equation only if it is part of (or influences) the rate limiting step.
Intermediates vs. Transition States
Understanding the difference between intermediates and transition states is crucial for interpreting reaction mechanisms and energy profiles.
- Intermediates: Exist for a measurable amount of time. Do not appear in the overall equation.
- Transition states: High-energy, unstable configurations that don’t actually exist for any measurable amount of time (like a ball thrown up in the air when it reaches its maximum height). Represented as peaks on an energy profile.
Key distinction: Intermediates are real, though short-lived; transition states are theoretical high energy states.
Energy Profile with Multiple Steps
A multi-step reaction will have multiple peaks: each peak = transition state; each valley = intermediate.
- The highest peak corresponds to the Rate Limiting Step, as it has the largest activation energy barrier (Ea).
Matching Mechanisms to Data
A proposed mechanism must match the overall balanced equation (stoichiometry) and be consistent with the rate equation (derived from experimental kinetics).
Remember that mechanisms are proposed using experimental kinetic and stoichiometric data. They are only predictions — there may be more than one possible mechanism for a given reaction.
Rate-Limiting Step Beyond Step One
Note - this isn’t actually covered in 5.8 and comes up in a more complicated form in 5.9 (see Topic 5.9) however in my experience its a good opportunity to introduce it now!
In many mechanisms, the rate limiting step occurs after the first step, often involving an intermediate formed earlier.
Example Reaction of NO₂ and CO
Overall equation: NO₂ + CO → NO + CO₂
Proposed mechanism:
NO₂ + NO₂ → NO + NO₃ (fast)
NO₃ + CO → NO₂ + CO₂ (slow, rate-determining)
The second step is the RDS, even though it's not first. The intermediate NO₃ is formed in step 1 and consumed in step 2. Since step 2 is the slow step, the rate depends on the concentrations of the reactants involved in (or before) that step.
Example Nitration of Benzene (Electrophilic Substitution)
HNO₃ + H₂SO₄ → NO₂⁺ + HSO₄⁻ + H₂O (fast)
Benzene + NO₂⁺ → Arenium ion (slow, rate-determining)
Arenium ion → Nitrobenzene + H⁺ (fast)
The second step (attack of the benzene ring) is the rate-determining step, not the first. The rate depends on the concentration of benzene and [NO₂⁺], which is formed quickly in step 1.
If you're told the first step is slow and irreversible, write the rate law using just the reactants from that first step. No need to worry about intermediates or fast steps.
Molecularity of the Elementary Step
The rate law of an elementary step (a single collision event) can be written directly from the stoichiometry of that step:
- Unimolecular (one particle involved): rate = k[A]
- Bimolecular (two particles involved): rate = k[A][B] or k[A]2
- Termolecular steps (three particles) are rare
Note: The overall reaction may have a different stoichiometry than the slow step.
What About Intermediates?
If an intermediate (a species produced and consumed in the mechanism) appears in the slow step, it must be replaced using an expression derived from a fast equilibrium step. For Topic 5.8, you are only expected to handle cases where the slow step is first, so this is not required here.
(see Topic 5.9 - Pre-Equilibrium Approximation)
Summary
When the first step in a reaction mechanism is the rate-limiting step, the rate law is determined solely by that step. Use the reactants in the slow step to write the rate law, matching their stoichiometric coefficients to the order in the rate law. This approach is valid when all steps are irreversible or when the slow step comes first, simplifying the connection between mechanism and kinetics.