Integrated Rate Law Calculator
Zero, first and second order, with half-life and the linear plot.
Work out Integrated Rate Law. Zero, first and second order, with half-life and the linear plot. Written for the problem set you are stuck on.
Units depend on the order: M/s for zero, 1/s for first, 1/(M·s) for second.
Concentration remaining
0.36788 M
First order · half-life 6.9315 s
Half-life is the fastest way to identify an order from data. First order is the only one where it stays constant no matter how much you started with — that is why radioactive decay, which is first order, has a single quotable half-life. Zero order half-life shrinks as the reaction proceeds; second order grows. The plot that comes out straight is the other test: [A] against t for zero order, ln[A] for first, 1/[A] for second.
How the Integrated Rate Law Calculator works
Pick a reaction order and this gives the concentration remaining after any elapsed time, the half-life at that starting concentration, and which plot comes out as a straight line. The half-life behaviour is the fastest way to identify an order from experimental data.
Also known as: first order reaction calculator · second order half life calculator · reaction order calculator · rate law calculator
Frequently asked questions
What are the integrated rate laws?
Zero order: [A] = [A]₀ − kt. First order: ln[A] = ln[A]₀ − kt. Second order: 1/[A] = 1/[A]₀ + kt. Each one is the rate law integrated over time.
How do I find the reaction order from data?
Plot all three forms and see which is straight. [A] against t means zero order, ln[A] against t means first, 1/[A] against t means second. The slope then gives k.
Why is only first-order half-life constant?
Because the first-order half-life, ln2/k, has no concentration term in it. Zero order half-life is [A]₀/2k and grows with concentration; second order is 1/(k[A]₀) and shrinks. A constant half-life is strong evidence for first order.
What are the units of k?
They depend on the order, which is a useful check: M/s for zero order, s⁻¹ for first order, M⁻¹s⁻¹ for second. If a quoted k has units that do not match the claimed order, something is wrong.
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