Reaction Rate Calculator: Integrated Rate Laws, Half-Life and the Arrhenius Equation
Rate laws, half-lives and the effect of temperature on reaction rate.
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How this calculator works
Choose concentration, Arrhenius, or activation energy.
For concentration pick the order, then enter the rate constant, the starting concentration and the time.
For the Arrhenius cases enter the activation energy and the two temperatures, or the two rate constants.
Formulas used
- [A] = [A]_0e^{-kt}\ (\text{first order})
- t_{1/2} = \frac{\ln2}{k}
- \ln\frac{k_2}{k_1} = \frac{E_a}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)
Worked example
With the default numbers in the calculator above:
- Concentration left (first order: exponential decay): 0.37 mol/L
- Half-life (it does not depend on the starting concentration): 13.86 s
- Straight line plot: ln[A] against time has slope -k: -1.00
- Fraction remaining: 36.79 %
Change the numbers in the calculator to see the full working, every step, for your own case.
A second worked example
A different case, with these numbers: Order of the reaction (concentration case) Second order; Rate constant (at the first temperature for the Arrhenius cases). Units depend on the order 0.2.
- Concentration left (second order): 0.20 mol/L
- Half-life (it gets longer as the concentration falls): 5.00 s
- Fraction remaining: 20.00 %
Common questions
How do I tell the order of a reaction?
Plot concentration, its log, and its reciprocal against time. The one that is a straight line gives the order: zero, first or second.
Does the half-life depend on concentration?
Only for zero and second order. For a first order reaction the half-life is constant.
What is the activation energy?
The energy barrier the molecules must climb for the reaction to go. A higher barrier means the rate rises faster with temperature.
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any first-year chemistry text (chemical kinetics and the Arrhenius equation).
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