Arrhenius Reaction Rate Calculator
Calculate chemical reaction rate constants using the Arrhenius equation.
Find how temperature affects reaction speed and determine activation energy from two rate measurements.
How It Works
The Arrhenius equation is one of the most important relationships in chemistry. Proposed by Swedish chemist Svante Arrhenius in 1889, it describes how the rate of a chemical reaction changes with temperature. Arrhenius received the Nobel Prize in Chemistry in 1903 for this and related contributions.
The Arrhenius equation:
k = A × e^(−Ea / RT)
Where:
- k = rate constant (units depend on reaction order)
- A = pre-exponential factor (also called the frequency factor or collision frequency)
- Ea = activation energy in Joules per mole (J/mol) — enter in kJ/mol, the calculator converts
- R = universal gas constant = 8.314 J/(mol·K)
- T = absolute temperature in Kelvin (K = °C + 273.15)
What is activation energy (Ea)? Activation energy is the minimum energy that reacting molecules must have for a collision to result in a chemical reaction. Think of it as the “energy hill” that reactants must climb before they can convert to products. High Ea = reaction is slow at room temperature, very sensitive to temperature changes. Low Ea = reaction proceeds readily even at low temperatures.
What is the pre-exponential factor (A)? A accounts for the frequency of collisions and the fraction of those collisions that have the correct orientation for reaction. It has the same units as k and can be estimated from experimental data or theoretical collision theory.
Finding activation energy from two rate measurements: When you have measured rate constants at two different temperatures, you can calculate Ea using:
Ea = R × ln(k₂/k₁) / (1/T₁ − 1/T₂)
The Rule of 10 (Van’t Hoff rule): As a rough rule of thumb for many biological and industrial reactions, the reaction rate approximately doubles for every 10°C (18°F) increase in temperature. This is often called the Q₁₀ rule in biochemistry. The Arrhenius equation explains why this happens — it is the mathematical consequence of the exponential relationship between temperature and reaction rate.
Real-world applications:
| Field | Application |
|---|---|
| Food industry | Predicting shelf life and spoilage rates at different storage temperatures |
| Pharmaceuticals | Drug stability testing — predicting expiration dates |
| Catalysis | Designing industrial catalysts to lower Ea and speed reactions |
| Biochemistry | Enzyme kinetics — understanding how body temperature affects metabolism |
| Materials science | Predicting corrosion rates, polymer degradation |
| Environmental chemistry | Atmospheric reaction rates, ozone depletion modeling |
Activation energy reference values:
| Reaction Type | Typical Ea |
|---|---|
| Enzyme-catalyzed biological reactions | 20–50 kJ/mol |
| Acid-base neutralization | 8–20 kJ/mol |
| Radical reactions | 0–40 kJ/mol |
| Thermal decomposition | 80–250 kJ/mol |
| Industrial catalytic reactions | 50–150 kJ/mol |
Example calculation: A reaction has A = 1×10¹³ s⁻¹ and Ea = 75 kJ/mol. At 25°C (298 K): k = 1×10¹³ × e^(−75000 / (8.314 × 298)) = 1×10¹³ × e^(−30.27) ≈ 7.9×10⁻¹ s⁻¹ At 35°C (308 K): k ≈ 1.7 s⁻¹ — more than double, consistent with the Rule of 10.