Integrated Rate Law Calculator
Zero, first and second order, with half-life and the linear plot.
Zero, first and second order, with half-life and the linear plot.
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
Where to go next
The Integrated Rate Law question rarely arrives on its own. These are the ones that usually come with it:
- Half-Life Calculator — Exponential decay, and why it never reaches zero.
- Arrhenius Equation Calculator — Rate constants, and where the 'doubles per 10 degrees' rule comes from.
- Equilibrium Constant Calculator — Kp from Kc, with Δn counting gases only.
- Speed Distance Time Calculator — Any one of the three from the other two, in four units.
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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Related calculators
Half-Life Calculator
Exponential decay, and why it never reaches zero.
OpenArrhenius Equation Calculator
Rate constants, and where the 'doubles per 10 degrees' rule comes from.
OpenEquilibrium Constant Calculator
Kp from Kc, with Δn counting gases only.
OpenSpeed Distance Time Calculator
Any one of the three from the other two, in four units.
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