Complex Reaction Mechanisms
A reaction mechanism describes the sequence of elementary steps through which reactants transform into products. Understanding the mechanism is essential: the overall rate law can only be derived from the microscopic kinetics of each elementary step.
Elementary Steps and Intermediates
An elementary step is a reaction whose molecularity is its actual microscopic stoichiometry — it occurs in a single collision event. Types include:
- Unimolecular (molecularity 1): A → products; rate = k[A]
- Bimolecular (molecularity 2): A + B → products; rate = k[A][B]
- Termolecular (molecularity 3): rare; encountered in radical recombination
A reaction intermediate is a species produced in one step and consumed in a later one. It does not appear in the overall stoichiometry, and it must be algebraically eliminated to give the observable rate law.
Energy Profile
The energy profile plots potential energy along the reaction coordinate. Each elementary step shows:
- a transition state (‡) at the activation-energy maximum Ea,i;
- a local minimum if a stable intermediate exists.
For a two-step sequence:
| Step | Ea (kJ·mol⁻¹) | Δ‡H (kJ·mol⁻¹) |
|---|---|---|
| 1 (slow) | 120 | +80 |
| 2 (fast) | 30 | −110 |
The overall barrier is controlled by the highest point on the profile.
Rate-Determining Step
The rate-determining step (RDS) is the kinetically slowest step — the one with the highest activation barrier. Two standard cases:
- Direct RDS: the first step is slow; its rate law equals the overall rate law.
- Pre-equilibrium: a fast equilibrium precedes the RDS. Express the intermediate concentration via the equilibrium constant K, then substitute.
Example: for the mechanism
A ⇌ I (fast, K₁ = k₁/k₋₁) I + B → P (slow, k₂)
v = k₂[I][B] = k₂K₁[A][B] → second-order overall rate law.
Rate Law Derivation and Experimental Check
Formal procedure:
1. Write all elementary steps with their individual rate expressions. 2. Identify the intermediate and the RDS. 3. Express v in terms of initial species concentrations only. 4. Compare predicted orders against experimental data (initial-rates method, isolation method).
A mechanism is consistent if its derived rate law matches observations; it is never uniquely proven — multiple mechanisms can produce the same rate law.