Arrhenius Equation Calculator

Calculate temperature effects on reaction rates and activation energy

Arrhenius Equation Calculator

Arrhenius Equation: k = A·e-Ea/RT
Relates rate constant to temperature and activation energy

Same units as k

kJ/mol

Kelvin (K)

Notes:

  • • R = 8.314 J/(mol·K) - Universal gas constant
  • • Temperature must be in Kelvin: K = °C + 273.15
  • • Higher Ea means greater temperature sensitivity
  • • k increases exponentially with temperature
  • • A is the pre-exponential or frequency factor

Understanding the Arrhenius Equation

The Arrhenius equation describes how the rate constant of a chemical reaction depends on temperature and activation energy. It's one of the most important equations in chemical kinetics for understanding and predicting reaction rates.

The Equation

k = A·e-Ea/RT

k = rate constant (units vary with reaction order)

A = frequency factor or pre-exponential factor (same units as k)

Ea = activation energy (J/mol or kJ/mol)

R = universal gas constant (8.314 J/(mol·K))

T = absolute temperature (K)

Linearized Form

ln(k) = ln(A) - Ea/RT

Plotting ln(k) vs 1/T gives a straight line with slope = -Ea/R and y-intercept = ln(A)

Example: Temperature Effect on Rate Constant

Given:

  • A = 1.0 × 1013 s-1
  • Ea = 75 kJ/mol
  • T = 298 K (25°C)

Calculate k:

k = (1.0 × 1013) × e-(75,000)/(8.314×298)

k = (1.0 × 1013) × e-30.3

k = (1.0 × 1013) × 8.54 × 10-14

k = 0.854 s-1

Activation Energy Interpretation

Ea Range (kJ/mol)CharacteristicExamples
< 20Very fast reactionsIon combinations
20-50Fast reactionsMany organic reactions
50-100Moderate reactionsEsterification
100-200Slow reactionsCracking reactions
> 200Very slow reactionsBond breaking in stable molecules

Temperature Rule of Thumb

Common Approximation: For many reactions with Ea around 50-60 kJ/mol, the rate approximately doubles for every 10°C increase in temperature.

Applications

  • 🌡️
    Temperature Control: Predicting optimal reaction temperatures in industrial processes
  • 🔬
    Mechanism Studies: Determining activation energies to understand reaction pathways
  • 💊
    Shelf Life: Predicting drug stability and food spoilage at different storage temperatures
  • ⚡
    Catalysis: Evaluating catalyst effectiveness by measuring Ea reduction

📊Quick Reference

R constant:

8.314 J/(mol·K)

Temperature:

Must be in Kelvin

Higher Ea:

More temperature sensitive

🔗Related Calculators

📐Related Formulas

🎯Where It's Used

  • 🏭

    Industry

    Process optimization

  • 🔬

    Research

    Mechanism studies