Activation Energy (Two Rates) Calculator
Find the activation energy from two rate constants measured at two temperatures using the two-point Arrhenius equation.
How it works
ln(k₂ ÷ k₁) = −(Eₐ ÷ R)(1/T₂ − 1/T₁) · Eₐ = R × ln(k₂ ÷ k₁) ÷ (1/T₁ − 1/T₂) · R = 8.314 J/(mol·K)
The Arrhenius equation links a rate constant to temperature through the activation energy, the barrier reactant molecules must clear. Measuring the rate constant at two temperatures lets you eliminate the pre-exponential factor: subtracting the two Arrhenius expressions leaves a single equation in Eₐ. Rearranging gives the activation energy as the gas constant times the log of the rate-constant ratio, divided by the difference of the reciprocal temperatures. Temperatures must be in kelvin for the reciprocals to make sense.
Worked example
If k rises from 0.001 to 0.005 s⁻¹ as temperature goes from 300 K to 310 K: ln(0.005 ÷ 0.001) = 1.609, and (1/300 − 1/310) = 1.075×10⁻⁴ K⁻¹. Eₐ = 8.314 × 1.609 ÷ 1.075×10⁻⁴ ≈ 124,400 J/mol = 124.4 kJ/mol.
Sources: Arrhenius equation — Wikipedia
Frequently asked questions
Do temperatures have to be in kelvin?
Yes. The equation uses 1/T, so temperatures must be absolute (kelvin). Using Celsius would give the wrong reciprocals and a meaningless activation energy — add 273.15 to convert.
What value of R should I use?
Use R = 8.314 J/(mol·K) to get the activation energy in joules per mole, then divide by 1000 for kJ/mol. This calculator does both.
Why does the rate constant rise with temperature?
Higher temperature means more molecules have enough energy to clear the activation barrier, so a larger fraction of collisions is successful and k increases — steeply for a large activation energy.
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This calculator is for educational purposes. Double-check important results before acting on them.