Introduction
Where thermodynamics asks whether a reaction can happen, kinetics asks how fast it happens and by what step-by-step pathway — a reaction can be thermodynamically favourable (ΔG < 0) yet proceed so slowly it appears not to happen at all (diamond converting to graphite is a classic example).
1. Rate of reaction and the rate law
Reaction rate is the change in concentration of a reactant or product per unit time. The rate law, rate = k[A]m[B]n, is an experimentally determined relationship (not derivable from the balanced equation alone) between rate and reactant concentrations, where k is the rate constant.
2. Order and molecularity
Order is the experimentally observed exponent of each concentration term in the rate law (can be zero, fractional, or negative). Molecularity is the number of molecules that must collide in a single elementary step of a mechanism, and is always a small whole number. Order and molecularity coincide only for a genuinely single-step (elementary) reaction; for multi-step reactions, order reflects the slowest (“rate-determining”) step’s stoichiometry.
3. Integrated rate equations and half-life
Integrating the rate law over time gives concentration as an explicit function of time, letting you predict concentration at any future moment rather than only the instantaneous rate. Each reaction order has a characteristic half-life behaviour: for first-order reactions, half-life is constant (independent of starting concentration) — the same mathematical signature as radioactive decay (Physics Chapter IV) — while for zero- and second-order reactions, half-life depends on the initial concentration.
4. Temperature dependence and activation energy
The Arrhenius equation, k = Ae^(−Ea/RT), describes how the rate constant increases sharply with temperature. Activation energy (Ea) is the minimum energy colliding molecules must possess to react — it represents an energy barrier between reactants and products (visualised in a reaction-coordinate diagram) that must be overcome regardless of the reaction’s overall thermodynamic favourability.
5. Reaction mechanisms and elementary steps
A mechanism is the sequence of elementary steps by which an overall reaction actually proceeds at the molecular level. Intermediates are species produced in one step and consumed in a later one (never appearing in the overall balanced equation). The overall rate law is determined by the slowest step (rate-determining step) — this is why the empirical rate law often does not match the coefficients of the overall balanced equation.
6. Basic theories of reaction rates
Collision theory treats a reaction as requiring molecules to collide with sufficient energy and correct orientation; only a fraction of collisions meet both conditions, which is why reaction rates are far lower than naive collision-frequency estimates. Transition state theory refines this by proposing that colliding molecules pass through a high-energy, unstable “activated complex” at the peak of the energy barrier before forming products, providing a more detailed picture of why activation energy exists and how catalysts (Chapter 5) work by lowering it.
Key Takeaways
- The rate law is determined experimentally, not from stoichiometry; order (from the rate law) and molecularity (from an elementary step) coincide only for single-step reactions.
- Integrated rate laws give concentration versus time; first-order half-life is uniquely concentration-independent, mirroring radioactive decay.
- The Arrhenius equation quantifies how strongly rate depends on temperature via the activation energy barrier.
- Multi-step mechanisms proceed through intermediates, with the slowest step controlling the overall observed rate law; collision theory and transition state theory both explain why an energy barrier must be overcome.