What it does
How fast a reactant disappears depends on its concentration through the rate law, rate = k[A]ⁿ. Integrating it gives a different curve for each order: a straight fall for zero order, an exponential decay for first order and a 1/t shape for second order. This tool fits all three to your data and tells you which one the data prefer.
- Each law is fitted directly to [A] against time by non-linear least squares. This is better than fitting the straight-line plots, which stretch the errors of small concentrations.
- Support is the Akaike weight: the chance that each law is the best of the three, given your data.
- k with its standard error, [A]₀ and the half-life come with every fit.
- A free-order fit lets n take any value, to check that the winning order is really a whole number.
- The classic straight-line plots ([A], ln [A] and 1/[A] against time) are one tap away, as in a textbook.
- Arrhenius analysis turns rate constants at several temperatures into the activation energy Ea, with a 95 % range, and the pre-exponential factor A. The Eyring equation gives ΔH‡, ΔS‡ and ΔG‡, and you can predict k at any temperature.
How to use it
- Paste time and concentration as two columns, or press Load an example. Use the reactant that is consumed. Absorbance works if it is proportional to concentration.
- Set the time and concentration units so k gets the right unit.
- Read the best order and k. Check the plot: the points should scatter evenly around the solid curve, with no pattern.
- For the activation energy, paste temperature and k pairs below, in °C or K.
Worked example
The example is a simulated run of dinitrogen pentoxide decomposing at 45 °C, 2 N₂O₅ → 4 NO₂ + O₂, with 1 % noise. The tool finds first order with k = (6.17 ± 0.03) × 10⁻⁴ s⁻¹ and a half-life of about 1,120 s (ln 2 ÷ k). The first-order support is 100 %, and the free-order fit gives n close to 1. The ln [A] plot is a straight line, while [A] and 1/[A] curve.
The Arrhenius example uses the textbook data for methyl isonitrile isomerising to acetonitrile: k = 2.52 × 10⁻⁵ s⁻¹ at 189.7 °C up to 3.16 × 10⁻³ s⁻¹ at 251.2 °C. The slope of ln k against 1/T is −Ea/R, which gives Ea ≈ 158 kJ/mol (textbooks quote 160 kJ/mol to two figures) and A ≈ 1.8 × 10¹³ s⁻¹.
Questions
Why fit [A] directly and not the straight-line plots? Taking logs or reciprocals gives the smallest, least certain concentrations the most weight. A direct fit treats every point evenly, the way the measurement errors really are. The straight-line plots are still shown because they make the order easy to see.
How many points do I need? At least three, but use more than five spread over two or three half-lives. Over a short time all three laws look alike.
What about reactions with two reactants? Use a large excess of one (pseudo-first-order conditions): its concentration barely changes, so the other behaves as first order with k′ = k[B].
Is my data sent anywhere? No, every fit runs in your browser.
Last updated 2026-11-08.