Activation Energy Calculator

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Chemistry

The activation energy is the minimum energy a reaction needs to proceed. This calculator uses the two-temperature form of the Arrhenius equation: give it the rate constants at two temperatures and it solves for the activation energy (Ea). Enter k₁ at T₁ and k₂ at T₂ (temperatures in Kelvin) and it returns Ea in both kJ/mol and J/mol.

Formula

ln(k₂/k₁) = (Ea/R) × (1/T1 - 1/T2) → Ea = R × ln(k₂/k₁) × T₁ × T₂ / (T₂ - T₁)
  • Two-temperature Arrhenius form: ln(k₂/k₁) = (Ea/R) × (1/T₁ − 1/T₂).
  • Rearranged for activation energy: Ea = R × ln(k₂/k₁) × T₁ × T₂ ÷ (T₂ − T₁).
  • R is the gas constant, 8.314 J/(mol·K); temperatures must be in Kelvin.
  • A larger activation energy means the reaction rate is more sensitive to temperature.
  • The result divided by 1000 converts J/mol to kJ/mol, the more common reporting unit.

Example Calculation

Inputs
  • Rate constant at T1 (k₁): 0.001
  • Temperature 1 (T1): 300 K
  • Rate constant at T2 (k₂): 0.01
  • Temperature 2 (T2): 310 K

If the rate constant rises tenfold (0.001 to 0.01) as temperature goes from 300 K to 310 K, then Ea = 8.314 × ln(10) × 300 × 310 ÷ 10 ≈ 178,000 J/mol, or about 178 kJ/mol.

Frequently asked questions

What is activation energy?
It is the minimum energy that reacting molecules must have for a reaction to occur. Higher activation energy means a slower reaction at a given temperature.
What inputs do I need?
The rate constants at two temperatures (k₁ and k₂) and those two temperatures in Kelvin (T₁ and T₂).
Why must temperatures be in Kelvin?
The Arrhenius equation is based on absolute temperature. Using Celsius or Fahrenheit would give wrong results, so convert to Kelvin first.
What does a high activation energy imply?
A high Ea means the reaction rate changes sharply with temperature — a small temperature rise speeds it up a lot.
Can I find Ea from a graph instead?
Yes. Plotting ln(k) against 1/T gives a straight line whose slope is −Ea/R. This calculator does the equivalent from two points.