Activation Energy Calculator

Calculate activation energy Ea from rate constants at two temperatures using the Arrhenius equation. Find Ea in kJ/mol or use it to predict k at a new temperature.

🌡️ Kinetics📐 Ea = -R·ln(k2/k1) / (1/T2 - 1/T1)🧪 Chemistry

k1 (rate constant at T1)

T1 (K)

k2 (rate constant at T2)

T2 (K)

Please enter valid values.

Formula & Reference

Variable	Symbol	Formula	Units
Activation Energy Calculator	See formula	Ea = -R·ln(k2/k1) / (1/T2 - 1/T1)	kJ/mol

Step-by-Step Examples

Example 1

Two-Temperature Ea

k(300 K)=0.0100 s^-1, k(350 K)=0.100 s^-1.

ln(k2/k1) = ln(10) = 2.303
1/T1-1/T2 = 1/300-1/350 = 4.76x10^-4 K^-1
Ea = -8.314 x 2.303/(-4.76x10^-4) = +40.2 kJ/mol

✓ Ea = 40.2 kJ/mol

Example 2

Temperature Close Together

k(298 K)=0.0250, k(308 K)=0.0500 (reaction doubles per 10 C).

ln(0.0500/0.0250) = ln(2) = 0.6931
1/298-1/308 = 1.088x10^-4
Ea = -8.314 x 0.6931/(-1.088x10^-4) = 52.9 kJ/mol

✓ Ea = 52.9 kJ/mol (typical for 10-degree doubling)

Example 3

Enzyme Catalysis

k(25 C = 298K) = 1.00x10^3, k(37 C = 310K) = 2.50x10^3.

ln(2.50x10^3/1.00x10^3) = ln(2.5) = 0.916
1/298-1/310 = 1.30x10^-4
Ea = -8.314 x 0.916/(-1.30x10^-4) = 58.6 kJ/mol

✓ Ea = 58.6 kJ/mol for enzyme-catalyzed reaction

Real-World Applications

💊

Drug Stability Testing

Accelerated testing at elevated T uses Arrhenius to predict shelf life at room temperature.

🧪

Catalysis Research

Measuring Ea with and without catalyst shows activation energy reduction.

🏭

Process Optimization

Ea determines optimal operating temperature for industrial reactions.

🌍

Climate Models

Activation energies of soil respiration reactions determine CO2 release sensitivity to warming.

Common Mistakes to Avoid

⚠️

Note: sign of 1/T terms

Ea = -R ln(k2/k1) / (1/T2 - 1/T1). If k increases with T, ln(k2/k1) > 0 and (1/T2 - 1/T1) < 0, giving Ea > 0 (correct).

⚠️

Ea is always positive

Activation energy must be positive (endothermic barrier). If you get negative Ea, check which temperature is T1 and T2.

⚠️

Use Kelvin throughout

T1 and T2 must be in Kelvin. 25 C = 298 K, 50 C = 323 K.

Frequently Asked Questions

What are typical activation energies? ▾

Simple bond rotation: ~10 kJ/mol. Solution reactions: 40-80 kJ/mol. Gas-phase reactions: 100-200 kJ/mol. Heterogeneous catalysis often: 50-150 kJ/mol.

What is the Arrhenius pre-exponential factor A? ▾

A represents collision frequency with correct geometry. Found from intercept of ln(k) vs 1/T plot: ln(A) = y-intercept.

How does a catalyst lower Ea? ▾

Catalyst provides alternative reaction pathway with lower Ea. Does not change reactants or products; changes only the energy barrier.

What is the difference between Ea and DeltaH? ▾

Ea is kinetic activation barrier (always positive). DeltaH is thermodynamic heat change (can be + or -). Related but different concepts.

What is transition state theory? ▾

Proposes a high-energy transition state (activated complex) at the top of the energy barrier. Ea = energy difference between reactants and transition state.

Related Chemistry Calculators

Formula Explorer connections

Interpretation: This formula connects concentration, time, temperature or transport to the speed of a chemical process. Assumption: The reaction order and mechanism must match the model. Temperature, catalyst, mixing and mass-transfer limitations can alter the observed rate.

Activation Energy Graph Calculator →Activation Energy from Two Temperatures →Arrhenius Equation Calculator →Chemistry Formula Explorer →