Chemical Kinetics Calculator
Arrhenius rate constants and activation energy, plus rate and half-life from the rate law.
Arrhenius: k = A·exp(−Ea/(R·T)), T in kelvin, Ea in J/mol. Two-point: Ea = R·ln(k₂/k₁)/(1/T₁ − 1/T₂), A = k₁/exp(−Ea/(R·T₁)). Rate: v = k·[A]ⁿ; t½ = [A]₀/(2k) (n = 0), ln2/k (n = 1), 1/(k·[A]₀) (n = 2).
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What it does
Kinetics describes how fast a reaction proceeds, not how far it goes. The Arrhenius equation links the rate constant to temperature through the activation energy, so a small change in Ea or T can change a rate by orders of magnitude. Once k is known, the rate law gives the instantaneous rate for a given concentration, and the integrated forms give the half-life that is often the most useful single number for planning an experiment.
When to use it
Use the Arrhenius mode to predict how much faster a reaction runs at 37 °C than at 25 °C, to extract Ea from a two-temperature assay, or to estimate A when only k values are available. Use the rate mode to convert a measured rate constant into an expected rate at your working concentration, or to compare half-lives across reaction orders so you can choose a sampling interval that actually resolves the kinetics.
FAQ
- How do I get the activation energy from two rate constants?
- Rearrange the Arrhenius equation for two temperatures: Ea = R·ln(k₂/k₁)/(1/T₁ − 1/T₂), with temperatures in kelvin. The result is in J/mol and is shown in kJ/mol. The pre-exponential factor then follows from A = k₁/exp(−Ea/(R·T₁)). Note that this two-point form assumes Ea is constant over the interval, which is a good approximation for modest temperature ranges.
- What are the units of the rate constant?
- They depend on the overall reaction order: mol·L⁻¹·s⁻¹ for zero order, s⁻¹ for first order, and L·mol⁻¹·s⁻¹ for second order. Only a first-order rate constant is a true frequency, which is why the Arrhenius pre-exponential factor A has the same units as k.
- How does half-life depend on reaction order?
- For zero order, t½ = [A]₀/(2k) and the half-life shrinks as the concentration falls. For first order, t½ = ln2/k and is independent of concentration, which is why radioactive decay and many elimination reactions have a fixed half-life. For second order, t½ = 1/(k·[A]₀), so it doubles as the concentration halves.
- What is the pre-exponential factor A?
- A is the frequency factor, the rate constant extrapolated to infinite temperature. It bundles the collision frequency and the steric probability that a collision has the right orientation. It is often close to 10¹³ s⁻¹ for unimolecular gas-phase reactions and smaller when the reacting groups must align precisely.