Activation Energy Graph Calculator

Calculate and visualize activation energy from an Arrhenius plot. Find Ea from slope, determine A from intercept, and predict rate constants at new temperatures.

🌡️ Kinetics📐 ln k = ln A - Ea/RT (linear form)🧪 Chemistry
k1 at T1 (K)
T1 (K)
k2 at T2 (K)
T2 (K)
Predict k at T3 (K, optional)
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Activation Energy Graph Calculator—ln k = ln A - Ea/RT (linear form)kJ/mol

Step-by-Step Examples

Example 1
From Two Rate Constants

k(300K)=0.0100, k(320K)=0.0400. Find Ea.

  • Ea = -R*ln(k2/k1)/(1/T2-1/T1)
  • = -8.314*ln(0.0400/0.0100)/(1/320-1/300)
  • = -8.314*1.386/(-2.083x10^-4) = 55.4 kJ/mol
  • A = 0.0100*exp(55400/(8.314*300)) = 1.98x10^9
✓ Ea = 55.4 kJ/mol, A = 1.98x10^9
Example 2
Predict at New Temperature

Same system: Ea=55.4 kJ/mol, A=1.98x10^9. Predict k at 400 K.

  • k = 1.98x10^9 * exp(-55400/(8.314*400))
  • = 1.98x10^9 * exp(-16.65) = 1.98x10^9 * 5.87x10^-8
  • = 0.116 s^-1
✓ k(400 K) = 0.116 (predicted)
Example 3
Arrhenius Plot Slope

From Arrhenius plot: slope = -Ea/R = -6665 K^-1.

  • Ea = -slope * R = -(-6665) * 8.314 = 55,400 J/mol = 55.4 kJ/mol
✓ Ea = 55.4 kJ/mol from plot slope

Real-World Applications

🧪
Kinetics Research
Arrhenius plot is the primary tool for determining activation energy from experimental rate data.
🌡️
Drug Stability
Accelerated stability testing: measure degradation rate at 3+ temperatures, extrapolate to room T.
🏭
Process Optimization
Ea determines optimal operating temperature for maximizing rate while minimizing side reactions.
🌍
Climate Science
Arrhenius activation energies for soil organic matter decomposition determine CO2 release sensitivity to warming.

Common Mistakes to Avoid

⚠️
Ea must be positive

If you get negative Ea: check which temperature is T1 vs T2, or check k values. Rate constant always increases with T, so k2/k1 > 0 if T2 > T1.

⚠️
Use at least 3 temperature points for reliability

Two points give exact Ea but no error estimate. Three or more points allow a linear regression for more reliable Ea.

⚠️
R in J/molK, Ea in J before converting

R = 8.314 J/molK. Result from calculation is Ea in J/mol. Divide by 1000 for kJ/mol.

Frequently Asked Questions

What is an Arrhenius plot? ▾
Graph of ln(k) vs 1/T. Should be a straight line: slope = -Ea/R, y-intercept = ln(A). Linearity confirms Arrhenius behavior.
What causes deviation from Arrhenius behavior? ▾
Non-constant Ea (curved Arrhenius plot) indicates: multiple mechanisms, tunneling (curved at low T), or complex reaction with competing steps.
What is the compensation effect? ▾
For a series of reactions, larger Ea often correlates with larger ln(A). Entropy-enthalpy compensation. Common in heterogeneous catalysis.
What is tunneling in kinetics? ▾
At low temperatures, light particles (H atoms, protons) can tunnel through activation barrier. Rate higher than Arrhenius predicts. Important for enzyme-catalyzed H transfer.
How do I get Ea from a linear regression? ▾
Plot ln(k) vs 1/T. Fit best-fit line: slope = -Ea/R. Ea = -slope * R. Error in Ea from standard error of slope.

Related Chemistry Calculators

🌡️ Arrhenius Equation🌡️ Activation Energy⏱️ Rate Constant⏱️ Reaction Rate⏱️ Half-Life

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 from Two Temperatures →Arrhenius Equation Calculator →Stokes-Einstein Diffusion Calculator →Chemistry Formula Explorer →