Chapter 3 — Chemical Kinetics
How fast do reactions go, what controls their speed, and how long until a substance is half gone? Rates, rate laws, half-lives and the Arrhenius equation.
Some reactions are over before you can blink: an explosion, the flash of a camera, the precipitate that forms the instant silver nitrate meets salt water. Others take a lifetime or longer: iron rusting on a railway bridge, a statue weathering in acid rain, carbon-14 decaying in an ancient piece of wood. Most of the reactions that matter in daily life lie in between, and their speed is something we constantly try to control. We slow some down: food goes in the refrigerator, medicines carry a "store below $25\ ^{\circ}\mathrm{C}$" label, and paint protects steel. We speed others up: a pressure cooker cooks dal faster, enzymes in washing powder digest stains, and a platinum catalyst in a car's exhaust destroys pollutants in milliseconds.
The earlier chapters asked how much: how much dissolves, how much energy a cell can deliver. This chapter asks how fast. You will learn to measure the rate of a reaction and to describe it with a rate law, whose form must be found by experiment and which hints at the hidden steps, the mechanism, by which the reaction happens. Integrating the rate law tells you how much reactant is left after any time and gives the half-life, which is used everywhere from radiocarbon dating to drug doses. Finally, the Arrhenius equation and collision theory explain why a small rise in temperature, or a pinch of catalyst, can change a rate enormously.
| Question | Key relation | Section |
|---|---|---|
| How fast is the reaction now? | $\text{rate}=-\dfrac{d[\mathrm{R}]}{dt}$ | 3.1 |
| How does the rate depend on concentrations? | $\text{rate}=k[\mathrm{A}]^{x}[\mathrm{B}]^{y}$ | 3.1 |
| How much is left after time $t$? | $k=\dfrac{2.303}{t}\log\dfrac{[\mathrm{R}]_{0}}{[\mathrm{R}]}$ | 3.2 |
| How long until half is gone? | $t_{1/2}=\dfrac{0.693}{k}$ | 3.2 |
| How does temperature change $k$? | $k=A\,e^{-E_{a}/RT}$ | 3.3 |
- calculate average and instantaneous rates from data or a graph, and relate the rates of change of different species through the stoichiometric coefficients;
- write a rate law, give the order and the units of the rate constant, distinguish order from molecularity, and find a rate law by the method of initial rates;
- use a proposed mechanism to identify intermediates, catalysts and the rate-determining step;
- use the integrated rate equations for zero- and first-order reactions, calculate half-lives, decide the order from graphs, and handle gas-phase and pseudo-first-order reactions;
- use the Arrhenius equation to find activation energies and rate constants at new temperatures, and explain the effect of temperature and catalysts with the Maxwell–Boltzmann distribution and collision theory.
Sections in this chapter
Rate of a Reaction and Rate Laws
Average and instantaneous rates, factors affecting rate, rate laws, order and molecularity, mechanisms, and the method of initial rates.
Integrated Rate Equations and Half-life
Zero- and first-order reactions, half-lives, finding the order from graphs, gas-phase and pseudo-first-order reactions.
Temperature and Rate: the Arrhenius Equation and Collision Theory
Activation energy, the Arrhenius equation, the Maxwell–Boltzmann distribution, catalysts and collision theory.