Last updated: 2026-06-16

A zero-order reaction runs at a constant rate that does not depend on the reactant concentration. The concentration falls in a straight line with time until the reactant is exhausted. This calculator applies the zero-order integrated rate law to find the concentration remaining after a given time and reports the half-life. Zero-order kinetics appear whenever something other than the reactant — a saturated catalyst surface, a fixed light intensity, or an enzyme working at full capacity — sets the pace.

The integrated rate law

When the rate is constant, $-\dfrac{d[A]}{dt} = k$, integration gives a simple linear decline:

$[A] = [A]_0 - kt$

A plot of concentration against time is a straight line with slope $-k$. Once the reactant is gone the concentration stays at zero rather than becoming negative, so the calculator holds the result at zero past that point. The rate constant has units of concentration per time, such as $\mathrm{M/s}$.

Half-life

Setting $[A] = [A]_0/2$ gives a half-life proportional to the starting concentration:

$t_{1/2} = \frac{[A]_0}{2k}$

Because it depends on $[A]_0$, the half-life shortens as the reaction proceeds and the remaining concentration falls — the reverse of the constant first-order half-life.

Worked example

With $[A]_0 = 1.0\ \mathrm{M}$ and $k = 0.01\ \mathrm{M/s}$, after 60 seconds:

The half-life is $t_{1/2} = 1.0/(2 \times 0.01) = 50\ \mathrm{s}$, so the reactant is fully consumed at 100 seconds.

Why the rate stays flat

A reaction is zero-order when a bottleneck unrelated to the reactant concentration limits it. On a fully covered catalyst surface, for instance, adding more reactant cannot speed things up because every active site is already occupied. The classic biological example is the liver metabolizing alcohol at a fixed maximum rate once its enzymes are saturated. Compare the First-Order Integrated Rate Law Calculator and the Second-Order Integrated Rate Law Calculator for the concentration-dependent cases, and use the Average Reaction Rate Calculator to obtain a rate from measured data.