The rate law of a reaction tells you how the reaction rate depends on reactant concentration, and its order (0, 1 or 2) completely changes how the half-life behaves. Here, red spheres of reactant A turn into product spheres inside the vessel exactly on the schedule set by the integrated rate law for the order you pick, while the panel on the right traces out concentration versus time and pins a marker at every half-life.
[A] = [A]₀ − kt. The rate is constant, so [A] falls in a straight line and hits zero at a finite time. Each successive half-life is shorter than the last.[A] = [A]₀e^(−kt). The half-life t½ = ln2 / k never changes — it does not depend on how much A is left. This is the same equation that describes radioactive decay.[A] = [A]₀ / (1 + [A]₀kt). Each half-life is twice as long as the one before it, because the rate drops off with the square of a shrinking concentration.A first-order half-life is the reason radiocarbon dating works: carbon-14 decays with a constant 5,730-year half-life no matter how much is left in a sample, so the fraction remaining alone tells you the elapsed time — exactly the property this simulation lets you watch play out in the reaction vessel.
Reactant molecules in a 3D vessel convert to product exactly on the schedule set by a zero-, first-, or second-order rate law, while a live concentration-versus-time curve pins a marker at every half-life crossing.
Zero-order half-lives shrink as the reaction proceeds, first-order half-lives stay perfectly constant, and second-order half-lives double each time — the timeline rail beneath the vessel makes the gap between pins visibly shrink, hold steady, or stretch.
Pick a reaction order, set the rate constant k and starting concentration, then watch the molecules turn from reactant (red) to product as the curve traces out. Switch context to relabel the same first-order math as radioactive decay.
Radiocarbon dating works only because radioactive decay is strictly first order: carbon-14's half-life is the same 5,730 years no matter how much of the isotope remains in a sample.