Three Fundamental Patterns
Every simple reaction falls into one of three kinetic orders, each with a distinct concentration-time profile. Zero-order reactions consume reactant at a constant rate — the concentration drops linearly until it hits zero. First-order reactions show exponential decay with a constant half-life. Second-order reactions slow down dramatically as reactant is consumed, with concentration following a 1/(1 + kt[A]₀) curve.
Integrated Rate Laws
The integrated rate laws transform differential rate equations into algebraic expressions relating concentration to time. For first order, [A] = [A]₀ exp(−kt) — the same exponential decay seen in radioactive decay and pharmacokinetics. For second order, 1/[A] = 1/[A]₀ + kt gives a hyperbolic concentration profile that approaches zero asymptotically but never quite reaches it.
Half-Life Diagnostics
The dependence of half-life on initial concentration is a powerful diagnostic. If halving [A]₀ does not change t½, the reaction is first-order. If t½ halves when [A]₀ doubles, it is zero-order. If t½ doubles when [A]₀ halves, it is second-order. This simulation lets you verify these relationships interactively.
Visual Comparison
The canvas plots all three integrated rate laws simultaneously, highlighting the selected order. The characteristic diagnostic plot (the one that gives a straight line for the chosen order) is shown alongside the concentration vs time curve. You can immediately see why plotting ln[A] vs t is the test for first-order kinetics — it linearizes the exponential decay.