Arrhenius Equation Calculator
Calculate reaction rate constants, activation energy, and temperature dependence using the Arrhenius equation
Calculate Using Arrhenius Equation
Temperature in Kelvin: 0.00 K
Energy barrier that must be overcome for reaction to proceed
Frequency factor related to collision frequency and orientation
Arrhenius Equation Forms
Exponential: k = A × e^(-Ea/RT)
Logarithmic: ln(k) = -Ea/RT + ln(A)
Linear form: ln(k) = -(Ea/R) × (1/T) + ln(A)
Where: k = rate constant, A = pre-exponential factor, Ea = activation energy, R = gas constant, T = temperature (K)
Example Calculation
NO₂ Decomposition Reaction
Reaction: 2NO₂(g) → 2NO(g) + O₂(g)
Temperature: 320°C (593.15 K)
Rate constant: k = 0.5 M/s
Activation energy: Ea = 115 kJ/mol
Find: Pre-exponential factor (A)
Step-by-Step Solution
1. Convert units: Ea = 115 kJ/mol × 1000 = 115,000 J/mol
2. Rearrange Arrhenius equation: A = k / e^(-Ea/RT)
3. Calculate exponent: -Ea/RT = -115,000/(8.314 × 593.15) = -23.32
4. Calculate A: A = 0.5 / e^(-23.32) = 0.5 / (8.46×10⁻¹¹)
5. A = 6.71×10⁹ M/s
Result: Pre-exponential factor A = 6.71×10⁹ M/s
Common Reaction Examples
NO₂ decomposition
2NO₂(g) → 2NO(g) + O₂(g)
T: 593.15 K, Ea: 115 kJ/mol
k: 5.0e-1, A: 6.7e+9
H₂ + I₂ → 2HI
H₂(g) + I₂(g) → 2HI(g)
T: 599.2 K, Ea: 160 kJ/mol
k: 5.4e-4, A: 4.7e+10
Enzyme catalyzed
Substrate → Product (enzyme)
T: 310 K, Ea: 50 kJ/mol
k: 1.2e-3, A: 1.5e+8
Protein denaturation
Native protein → Denatured protein
T: 343 K, Ea: 75 kJ/mol
k: 4.8e-6, A: 8.2e+6
DNA melting
Double-strand DNA → Single-strand DNA
T: 368 K, Ea: 95 kJ/mol
k: 3.2e-5, A: 2.1e+7
Combustion reaction
CH₄ + 2O₂ → CO₂ + 2H₂O
T: 773 K, Ea: 200 kJ/mol
k: 2.5e-2, A: 2.1e+12
Quick Reference
Gas Constant (R)
8.314 J/(mol·K)
Boltzmann Constant (kB)
1.381×10⁻²³ J/K
Temperature
Always use Kelvin for calculations
Rate Constant Units
Depend on reaction order (M¹⁻ⁿ·s⁻¹)
Calculation Tips
Higher T = higher k (faster reaction)
Lower Ea = higher k (easier reaction)
ln(k) vs 1/T gives straight line
Slope = -Ea/R in linear plot
Units must be consistent throughout
Understanding the Arrhenius Equation
What is the Arrhenius Equation?
The Arrhenius equation describes how the rate constant of a chemical reaction depends on temperature. It shows the exponential relationship between temperature and reaction rate, explaining why reactions generally proceed faster at higher temperatures.
Key Parameters
- •k: Rate constant (depends on reaction order)
- •A: Pre-exponential factor (collision frequency)
- •Ea: Activation energy (energy barrier)
- •R/kB: Gas or Boltzmann constant
- •T: Absolute temperature (Kelvin)
Equation Forms
Exponential Form
k = A × e^(-Ea/RT)
Direct calculation of rate constant
Logarithmic Form
ln(k) = -Ea/RT + ln(A)
Linear relationship for plotting
Linear Plot Form
ln(k) = -(Ea/R) × (1/T) + ln(A)
y = mx + b format for graphing
Remember: The equation assumes constant activation energy and pre-exponential factor over the temperature range.
Applications of the Arrhenius Equation
Chemical Kinetics
Predict reaction rates at different temperatures, design optimal reaction conditions, and understand temperature dependence.
Catalysis Research
Compare catalyst effectiveness, determine activation energy reductions, and optimize catalytic processes.
Material Science
Study material degradation, polymer reactions, and temperature-dependent processes in materials.