Reaction order & half-life
The formulas look similar on paper — but zero, first and second order reactions decay completely differently. So run the reaction and watch. Switch order, change k or [A]₀, and press play — the curve, the half-life and the live concentration all update by the correct integrated rate law.
What the curves are telling you
Zero order
Rate is constant, independent of concentration — [A] falls in a straight line and hits exactly zero at a finite time. Unusual for typical solution reactions, but common for reactions limited by a catalyst surface or by light intensity.
First order — half-life is a constant
t½ = 0.693/k depends only on k, never on the starting concentration — this is why radioactive decay (a first-order process) always quotes a single half-life value regardless of how much material you start with.
Second order — half-life keeps changing
t½ = 1/(k[A]0) means each successive half-life is longer than the last as [A] drops — concentration and time-to-halve stay linked, unlike first order.
Reading the shape of the curve
You can often tell a reaction's order just from the shape of its concentration-vs-time plot: a straight line means zero order, a smooth exponential decay means first order, and a curve that flattens out more slowly than an exponential suggests second order.
Part of the Chemical Kinetics chapter — read the notes, grab the formula sheet and take the quiz. One of Priodemy for School, free with every EduSuite school.
What the order of a reaction tells you
Order is measured, not deduced
The order of a reaction is the power to which concentration is raised in the rate law. The crucial point, and the one most often missed, is that order cannot be read off the balanced equation. It is determined experimentally, because it reflects the slowest step of the actual mechanism rather than the overall stoichiometry. A reaction written with a coefficient of 2 may well be first order.
Each order produces a distinctive concentration-time curve, which is why plotting is the standard way to identify it. Zero order gives a straight line falling at a constant rate — the reaction proceeds at the same speed regardless of how much reactant is left, usually because something else, such as a catalyst surface, is saturated. First order gives an exponential decay. Second order gives a curve that falls steeply then flattens into a long tail, slowing far more dramatically as reactant is consumed.
Half-life is the giveaway
The fastest way to distinguish the orders is to measure successive half-lives. For a first-order reaction the half-life is t½ = 0.693/k — independent of concentration, so every successive half-life is identical. Start with twice as much and it still takes the same time to halve. This is why radioactive decay, which is first order, has a single quoted half-life.
No other order behaves this way. For zero order the half-life shortens as the reaction proceeds, since the rate is fixed but there is less left to consume each time. For second order it lengthens, doubling with each successive halving. Watch the marked intervals in the simulator: equal spacing means first order, and that single observation identifies it without any curve fitting.
Why temperature matters so much
The rate constant k depends on temperature through the Arrhenius equation, k = Ae−Ea/RT. Because temperature sits in an exponent, its effect is dramatic — a rough working rule is that many reactions roughly double in rate for each 10 °C rise. A catalyst works by lowering the activation energy Ea, which raises k without changing the equilibrium position at all.
Mistakes that cost marks
Reading order from the balanced equation. The exponents in a rate law come from experiment. Only for an elementary single-step reaction do they match the coefficients.
Confusing rate with rate constant. The rate changes continuously as reactants are consumed; k is fixed at a given temperature. Only k belongs in an Arrhenius calculation.
Getting the units of k wrong. They depend on the order — mol L⁻¹s⁻¹ for zero order, s⁻¹ for first, L mol⁻¹s⁻¹ for second. Quoting the wrong units usually costs a mark, and it is also a quick way to check your own answer.