Activation Energy (Arrhenius) Calculator Formula
Understand the math behind the activation energy (arrhenius) calculator. Each variable explained with a worked example.
Formulas Used
Activation Energy
ea_j = 8.314 * log(k2 / k1) / (1/t1 - 1/t2)Activation Energy
ea_kj = 8.314 * log(k2 / k1) / (1/t1 - 1/t2) / 1000Variables
| Variable | Description | Default |
|---|---|---|
k1 | Rate Constant at T1 (k1) | 0.001 |
t1 | Temperature T1(K) | 300 |
k2 | Rate Constant at T2 (k2) | 0.01 |
t2 | Temperature T2(K) | 350 |
How It Works
Arrhenius Equation and Activation Energy
The Arrhenius equation relates the rate constant to temperature through the activation energy barrier.
Two-Point Formula
ln(k2/k1) = (Ea/R) × (1/T1 - 1/T2)
Solving for Ea:
Ea = R × ln(k2/k1) / (1/T1 - 1/T2)
where R = 8.314 J/(mol·K). Higher activation energy means the reaction rate is more sensitive to temperature.
Worked Example
A reaction with k1 = 0.001 s⁻¹ at 300 K and k2 = 0.01 s⁻¹ at 350 K.
- 01ln(k2/k1) = ln(0.01/0.001) = ln(10) = 2.303
- 021/T1 - 1/T2 = 1/300 - 1/350 = 0.000476
- 03Ea = 8.314 × 2.303 / 0.000476 = 40,206 J/mol = 40.21 kJ/mol
Frequently Asked Questions
What is a typical activation energy?
Uncatalyzed reactions: 40-200 kJ/mol. Catalyzed reactions: 20-80 kJ/mol. Enzyme-catalyzed: 10-50 kJ/mol. Very low Ea means the reaction is fast even at low temperatures.
How does a catalyst affect activation energy?
A catalyst provides an alternative reaction pathway with a lower activation energy. This increases the rate constant at all temperatures but does not change the equilibrium constant or thermodynamics.
What is the pre-exponential factor A?
The Arrhenius equation is k = A × exp(-Ea/RT). The factor A (also called the frequency factor) relates to how often molecules collide in the correct orientation. It can be found from k and Ea at a known temperature.
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