⏳ Reaction Half-Life (First-Order Kinetics)

Written and maintained by the PhDino author · Last reviewed 21 September 2026 · Checked against 1 independent reference calculation · how PhDino checks its numbers

How long it takes a first-order reaction to use up half its remaining reactant, and how much is left after any elapsed time.

A first-order reaction is one whose rate depends directly on the concentration of a single reactant — the more of it there is, the faster it's consumed, which produces the same characteristic exponential decay curve seen in radioactive decay (itself a first-order process). One consequence of that shape is a genuinely constant half-life: the time it takes to go from any concentration to half that concentration is the same number, no matter what concentration you started from.

That's a distinguishing feature of first-order kinetics specifically — a reaction whose rate instead depends on the square of a reactant's concentration (second-order) has a half-life that changes as the reaction proceeds, unlike the fixed half-life here.

Key formula

t½ = ln(2) / k
[A] = [A]₀ × e^(−kt)

Variables

k

the reaction's rate constant, with units of inverse time for a first-order reaction

[A]₀

initial concentration of the reactant

t

elapsed time

Notes & limitations

• The rate constant k is specific to a particular reaction at a particular temperature — it typically increases substantially with temperature, which is why the same reaction run warmer proceeds noticeably faster (and has a correspondingly shorter half-life).
• This assumes the reaction is genuinely first-order in the first place — confirming that (rather than assuming it) is usually done experimentally, by checking whether a plot of ln[concentration] against time comes out as a straight line.