Activation Energy Calculator
Calculate activation energy using the Arrhenius equation with temperature, rate coefficient, and frequency factor
Calculate Activation Energy
Temperature in Kelvin: 0.00 K
Reaction rate coefficient (units: per second)
Pre-exponential factor (temperature-independent)
Arrhenius Equation
Activation Energy: Ea = -R × T × ln(k/A)
Rate Coefficient: k = A × e^(-Ea/RT)
Frequency Factor: A = k × e^(Ea/RT)
Where: R = 8.314 J/(mol·K), T = temperature (K), k = rate coefficient (s⁻¹), A = frequency factor (s⁻¹)
Example Calculation
H₂ + I₂ → 2HI Reaction
Given: Temperature = 326°C (599.2 K)
Rate coefficient: k = 5.4×10⁻⁴ s⁻¹
Frequency factor: A = 4.73×10¹⁰ s⁻¹
Step-by-Step Solution
1. Convert temperature: 326°C + 273.15 = 599.2 K
2. Apply Arrhenius equation: Ea = -R × T × ln(k/A)
3. Calculate: Ea = -8.314 × 599.2 × ln(5.4×10⁻⁴ / 4.73×10¹⁰)
4. Ea = -8.314 × 599.2 × ln(1.14×10⁻¹⁴)
5. Ea = -8.314 × 599.2 × (-32.32) = 160,000 J/mol
Result: 160 kJ/mol activation energy
Common Reaction Examples
H₂ + I₂ → 2HI (Gas phase)
Ea ≈ 160 kJ/mol
T: 599.2 K, k: 5.4e-4 s⁻¹
2ClNO → 2Cl + 2NO
Ea ≈ 100 kJ/mol
T: 298 K, k: 2.8e-8 s⁻¹
Enzyme catalyzed reaction
Ea ≈ 50 kJ/mol
T: 310 K, k: 1.2e-3 s⁻¹
Combustion of methane
Ea ≈ 200 kJ/mol
T: 773 K, k: 2.5e-2 s⁻¹
Protein denaturation
Ea ≈ 75 kJ/mol
T: 343 K, k: 4.8e-6 s⁻¹
Atmospheric ozone formation
Ea ≈ 85 kJ/mol
T: 288 K, k: 1.1e-9 s⁻¹
Quick Reference
Gas Constant (R)
8.314 J/(mol·K)
Temperature
Always use Kelvin for calculations
Energy Units
1 kJ/mol = 1000 J/mol
Rate Units
Usually s⁻¹ (per second)
Calculation Tips
Higher Ea = slower reaction rate
Temperature must be in Kelvin
k and A must have same units
Enzymes lower activation energy
Negative Ea is rare but possible
Understanding Activation Energy
What is Activation Energy?
Activation energy (Ea) is the minimum amount of energy required for a chemical reaction to occur. It represents the energy barrier that reactant molecules must overcome to form products.
Key Concepts
- •Energy Barrier: Higher barrier = slower reaction
- •Temperature Effect: Higher T = faster reaction
- •Catalysts: Lower Ea without changing products
- •Enzymes: Biological catalysts that lower Ea
Arrhenius Parameters
Rate Coefficient (k)
Measures how fast the reaction proceeds at a given temperature
Frequency Factor (A)
Pre-exponential factor related to collision frequency
Temperature (T)
Must be in absolute temperature (Kelvin) for calculations
Remember: The Arrhenius equation shows exponential dependence of reaction rate on temperature.
Applications of Activation Energy
Industrial Processes
Optimize reaction conditions, design catalysts, and control reaction rates in manufacturing.
Biochemistry
Understand enzyme kinetics, metabolic pathways, and drug interactions in biological systems.
Environmental Science
Study atmospheric reactions, pollution degradation, and climate-related chemical processes.