Collision theory and the Maxwell–Boltzmann distribution — plus, at Higher Level, rate equations, reaction mechanisms and the Arrhenius equation.
This HL lesson has the SL essentials — collision theory and the Maxwell–Boltzmann distribution — and then the Additional Higher Level material: the rate equation and order of reaction, reaction mechanisms and the rate-determining step, and the Arrhenius equation. AHL sections are marked in purple.
The rate of reaction is the change in concentration of a reactant or product per unit time (mol dm⁻³ s⁻¹) — the gradient of a concentration–time graph, steepest at the start. For particles to react they must collide with energy ≥ the activation energy (Eₐ) and with the correct orientation. Rate rises with concentration/pressure (more frequent collisions), surface area (more exposed particles), temperature (many more particles exceed Eₐ) and a catalyst (lower Eₐ).
Particles have a spread of kinetic energies. The shaded area beyond Eₐ is the fraction able to react. Raising the temperature spreads the curve to the right (much larger shaded area); a catalyst lowers Eₐ without changing the curve:
The rate equation links rate to reactant concentrations:
rate = k [A]m [B]n
k is the rate constant (temperature-dependent); m and n are the orders with respect to A and B, and m + n is the overall order. Crucially, the orders are found experimentally, not from the stoichiometric coefficients — they depend on the mechanism. The units of k change with the overall order (so that rate always comes out in mol dm⁻³ s⁻¹):
| Overall order | rate = | units of k |
|---|---|---|
| 0 | k | mol dm⁻³ s⁻¹ |
| 1 | k[A] | s⁻¹ |
| 2 | k[A]² or k[A][B] | mol⁻¹ dm³ s⁻¹ |
| 3 | k[A]²[B] … | mol⁻² dm⁶ s⁻¹ |
To find the order in a reactant, see how the rate responds when you change its concentration (keeping others constant). Select an order to see the rate–concentration shape and the "double the concentration" test:
Most reactions happen as a series of elementary steps — the mechanism. A species made in one step and used up later is an intermediate. The slowest step is the rate-determining step (RDS): it is the bottleneck, so the rate equation contains only the species involved up to and including the RDS. Toggle which step is slower and watch the predicted rate equation change:
The rate constant depends on temperature through the Arrhenius equation:
k = A e−Eₐ/RT ⇒ ln k = ln A − (Eₐ/R)(1/T)
where A is the Arrhenius (frequency) factor and R = 8.31 J K⁻¹ mol⁻¹. The second form is a straight line: plotting ln k against 1/T gives a gradient of −Eₐ/R and an intercept of ln A. So you can find the activation energy from the slope. Drag the activation energy:
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