Reaction Mechanisms
A chemical reaction written as a single equation — such as the conversion of hydrogen and iodine gas into hydrogen iodide — rarely tells us how the molecules actually collide and rearrange at the atomic level. A reaction mechanism is the sequence of elementary steps that together describe the complete transformation of reactants into products. Each elementary step represents a single molecular event: a collision, a bond breaking, or a bond forming. Understanding mechanisms allows chemists to explain why a reaction has a particular rate law, predict intermediates, and design better catalysts. Not all steps in a mechanism proceed at the same speed. One step is invariably much slower than the others and acts as a 'bottleneck', controlling the overall rate at which products form. This bottleneck is called the rate-determining step (RDS). Just as the slowest worker on an assembly line sets the production pace, the RDS sets the reaction rate. The rate law predicted by the mechanism must match the experimentally determined rate law — this is the key test of whether a proposed mechanism is valid. Advanced treatments introduce the steady-state approximation (SSA), which assumes that the concentration of any reactive intermediate remains essentially constant throughout the reaction because it is consumed as quickly as it is formed. This approximation allows chemists to derive rate laws for complex multi-step mechanisms without having to measure the concentrations of unstable intermediates directly, and it underpins much of modern mechanistic analysis in physical organic chemistry and biochemistry.
- Elementary Steps and Molecularity
- Intermediates vs. Transition States
- Identifying the Rate-Determining Step
- Worked Mechanism Example: NO₂ + CO → NO + CO₂
- Steady-State Approximation (Advanced)
Elementary Steps and Molecularity
An elementary step is a reaction that occurs in a single molecular event with no intermediate stages. The molecularity describes how many reactant particles are involved: unimolecular (one particle dissociates or rearranges), bimolecular (two particles collide), or termolecular (three particles collide simultaneously — rare). For an elementary step only, the rate law can be written directly from the stoichiometric coefficients. For example, the bimolecular elementary step A + B → products has rate = k[A][B]. This direct relationship does NOT apply to overall balanced equations, only to elementary steps.
Intermediates vs. Transition States
A reaction intermediate is a species that is produced in one elementary step and consumed in a later step; it appears in the mechanism but not in the overall equation. It exists in a local energy minimum on the reaction profile. A transition state, by contrast, is the highest-energy arrangement of atoms at the peak of an energy barrier — it cannot be isolated. For example, in the reaction of NO₂ with CO, the intermediate NO₃ is formed and then reacts away, while the transition states are the fleeting collision complexes at each energy peak.
Identifying the Rate-Determining Step
The rate-determining step is the slowest elementary step in the mechanism. The overall reaction can proceed no faster than this step allows. The rate law for the overall reaction is therefore equal to the rate law for the RDS. If the RDS involves species that are intermediates (not original reactants), the expression must be rewritten in terms of measurable reactant concentrations using equilibrium expressions for the fast steps preceding the RDS. The predicted overall rate law must then be compared with the experimentally determined rate law to validate the mechanism.
Worked Mechanism Example: NO₂ + CO → NO + CO₂
The experimentally determined rate law is rate = k[NO₂]². This is second order in NO₂ and zero order in CO. A two-step mechanism accounts for this: Step 1 (slow, RDS): NO₂ + NO₂ → NO₃ + NO. Step 2 (fast): NO₃ + CO → NO₂ + CO₂. Overall: NO₂ + CO → NO + CO₂. Because Step 1 is the RDS and involves two NO₂ molecules colliding, the predicted rate law is rate = k₁[NO₂]², which matches experiment. CO does not appear in the rate law because it is involved only in the fast step after the bottleneck.
Steady-State Approximation (Advanced)
When an intermediate I is reactive and present in very low concentrations, the SSA sets d[I]/dt ≈ 0. This means the rate of formation of I equals its rate of consumption. Consider a mechanism: A ⇌ I (k₁ forward, k₋₁ reverse, fast equilibrium) then I → P (k₂, slow). SSA on [I]: k₁[A] = k₋₁[I] + k₂[I], so [I] = k₁[A]/(k₋₁ + k₂). The rate of product formation is rate = k₂[I] = k₁k₂[A]/(k₋₁ + k₂). If k₋₁ >> k₂ (fast pre-equilibrium), this simplifies to rate = (k₁k₂/k₋₁)[A] = k_obs[A], first-order overall. The SSA is fundamental in enzyme kinetics (Michaelis-Menten) and atmospheric chemistry.
The Key Equation
- k_1 — Forward rate constant for Step 1 (s⁻¹ or mol⁻¹ dm³ s⁻¹): Governs how quickly the intermediate I is formed from reactant A
- k_{-1} — Reverse rate constant for Step 1 (s⁻¹ or mol⁻¹ dm³ s⁻¹): Governs how quickly intermediate I reverts back to reactant A
- k_2 — Rate constant for Step 2 (RDS) (s⁻¹): Rate constant for the slow step converting intermediate I into product P
- [\text{I}] — Steady-state concentration of intermediate (mol dm⁻³): Concentration of I held approximately constant under SSA conditions
- [\text{A}] — Concentration of reactant A (mol dm⁻³): Measurable concentration of the original reactant driving the reaction
Worked Example
Problem. A reaction between ozone and nitrogen monoxide is proposed to proceed via the following mechanism: Step 1 (fast equilibrium): O₃ ⇌ O₂ + O (K_eq = k₁/k₋₁) Step 2 (slow, RDS): O + NO → NO₂ (rate constant k₂) Overall: O₃ + NO → NO₂ + O₂ (a) Identify the intermediate. (b) Write the rate law predicted by the RDS. (c) Express the rate law entirely in terms of measurable reactant concentrations.
Answer. rate = k_obs [O₃][NO][O₂]⁻¹, where k_obs = k₂K_eq = k₁k₂/k₋₁
Origins · 1 minHenry Eyring and how this was discovered
Henry Eyring developed transition state theory (also called activated complex theory) in 1935, providing a quantitative framework for calculating reaction rates from molecular properties. His Eyring equation relates the rate constant to the activation enthalpy and entropy of the transition state, giving a molecular-level explanation for why reactions speed up with temperature and why mechanisms pass through high-energy transition states. His work is foundational to understanding why the rate-determining step — the step with the highest-energy transition state — controls overall reaction rates. Eyring was a devout member of the Church of Jesus Christ of Latter-day Saints and famously said he saw no conflict between his deep religious faith and his rigorous scientific work — he wrote several books exploring the relationship between science and religion throughout his career.
Related Concepts
- Rate Law and Rate Constant — The rate law predicted by a mechanism must match the experimentally determined rate law; understanding how rate laws are written and measured is essential before analysing mechanisms.
- Activation Energy and the Arrhenius Equation — Each elementary step has its own activation energy; the RDS has the highest activation energy barrier, which is quantified by the Arrhenius equation and transition state theory.
- Catalysis — Catalysts work by providing an alternative mechanism with a lower-energy rate-determining step; understanding mechanisms explains how and why catalysts increase reaction rates.
- Dynamic Equilibrium — Fast pre-equilibrium steps in a mechanism are analysed using equilibrium constants to eliminate intermediate concentrations from the rate law.
- Collision Theory — Collision theory explains why bimolecular elementary steps require two particles to collide with sufficient energy and correct orientation, underpinning the molecular basis of elementary step rate laws.