first-order reaction
Think of a crowd leaving a stadium where each person decides independently, at any moment, whether to head for the exit. When the stands are full, lots of people stream out at once; as the crowd thins, the outflow slows in proportion. A first-order reaction behaves just like that: its speed is directly proportional to how much reactant is currently present.
Formally, a first-order reaction has the rate law rate = k[A], so the rate is proportional to the first power of one reactant's concentration. Integrating gives an exponential decay of concentration with time, which shows up as a straight line when you plot ln[A] against time. Its defining feature is a constant half-life: the same time elapses to drop from full to half as from half to a quarter, regardless of how much you started with.
First-order reactions matter because they are everywhere and especially simple to handle: radioactive decay, many drug eliminations from the body, and numerous gas-phase decompositions all follow first-order kinetics. The caveat is that 'first order' is an experimental finding about the rate's dependence on concentration; a reaction can appear first order under special conditions (pseudo-first-order) even when its true mechanism is more complicated.
Dinitrogen pentoxide decomposes in the gas phase following rate = k[N₂O₅]. Whatever pressure you start at, its concentration always halves over the same fixed interval — the exponential, constant-half-life pattern that marks a first-order reaction.
Exponential decay with a fixed half-life — the signature of first order.
Pseudo-first-order is a useful trick: flood one reactant in large excess so its concentration barely changes, and a more complex reaction simplifies to apparent first order in the other reactant.