Everything from the 4 lessons of this topic on a few pages: the key idea of each lesson, the diagram to remember, the points to learn and the traps examiners set. Read it, cover it, test yourself.
A rate equation has the form rate = k[A]m[B]n. The powers m and n are the orders with respect to each reactant (0, 1 or 2 at this level) and their sum is the overall order. Orders are found by experiment, never from the stoichiometric equation. In an initial-rates table, doubling a concentration while the others stay fixed multiplies the rate by 1 (zero order), 2 (first order) or 4 (second order). A first-order reaction has a constant half-life, and k = 0.693 / t½. The rate constant k changes only with temperature (or a catalyst), and its units depend on the overall order.
Orders come from experimental data, not from the coefficients in the balanced equation. Doubling a concentration and seeing the rate quadruple means second order, not fourth. A constant half-life proves first order only; do not use t½ = 0.693/k for other orders. Always give units for k, worked out from the overall order, and remember k does not change with concentration.
The rate-determining step is the slowest step in a mechanism. Only species that take part in the rate-determining step, or in fast steps before it, appear in the rate equation, and the order of each matches the number of its particles involved. A species with zero order joins the reaction after the slow step. An intermediate is made in one step and used up in a later one, so it never appears in the overall equation; a catalyst is used in one step and regenerated later, so it can appear in the rate equation but not in the overall equation. A mechanism is consistent with the data if its steps add up to the overall equation and its slow step matches the rate equation.
The rate equation tells you about the slow step, not the overall equation, so do not copy coefficients from the overall equation. A reactant that is zero order is still needed: it reacts in a fast step after the rate-determining step. An intermediate is formed then used up; a catalyst is used then regenerated. Do not call the transition state an intermediate: a transition state is a peak on the energy profile, an intermediate sits in a dip.
The rate constant k increases with temperature because a larger fraction of collisions have energy ≥ Ea. The Arrhenius equation is k = Ae−Ea/RT, where A is the pre-exponential factor (linked to collision frequency and orientation), T is in kelvin and R = 8.31 J K−1 mol−1. Taking logs gives ln k = ln A − Ea/RT, a straight line when ln k is plotted against 1/T: the gradient = −Ea/R and the intercept is ln A. A larger Ea means a steeper line, so the rate is more sensitive to temperature.
Always use T in kelvin and R in J K−1 mol−1, so Ea comes out in J mol−1: divide by 1000 for kJ. The gradient is negative; Ea = −gradient × R is positive. Plot ln k, not k, and 1/T, not T. Increasing concentration does not change k; only temperature and catalysts do.
A catalyst increases the rate by providing an alternative route with a lower activation energy, and is regenerated at the end. A homogeneous catalyst is in the same phase as the reactants and works by forming an intermediate, so its energy profile has two humps with a dip between them. Transition-metal ions are good homogeneous catalysts because they change oxidation state easily: Fe2+ or Fe3+ catalyses S2O82− + 2I−, and NO2 catalyses the oxidation of SO2 in the air. A heterogeneous catalyst is in a different phase, usually a solid with gaseous reactants, and works by adsorption, reaction on the surface and desorption. Adsorption must be neither too strong nor too weak. Enzymes are protein catalysts with highly specific active sites.
A catalyst lowers Ea by providing a different mechanism; it does not give molecules more energy and does not change ΔH or the position of equilibrium. Homogeneous means the same phase, not the same substance. In heterogeneous catalysis, stronger adsorption is not always better: products must be able to desorb. The catalysed profile has two humps with an intermediate in the dip.