Activation Energy from Two Rate Constants
Calculate activation energy Ea using two rate constants at two temperatures.
Uses the Arrhenius equation in linear form.
Classify reaction barrier.
Activation energy (Ea) is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to form products.
The Arrhenius equation:
k = A × e^(-Ea/RT)
Taking the ratio at two temperatures:
ln(k₂/k₁) = (Ea/R) × (1/T₁ - 1/T₂)
Solving for Ea:
Ea = R × ln(k₂/k₁) / (1/T₁ - 1/T₂)
Where:
- k₁, k₂ = rate constants at T₁ and T₂
- R = 8.314 J/mol·K
- T₁, T₂ = temperatures in Kelvin
Note on units: The units of k cancel in the ratio k₂/k₁, so any consistent units work (L/mol·s, s⁻¹, etc.).
Classification of activation energies:
- Ea < 40 kJ/mol: Low barrier — fast reaction, often diffusion-limited
- Ea 40–100 kJ/mol: Moderate — typical for most organic reactions
- Ea > 100 kJ/mol: High barrier — slow reaction, often requires catalyst or heat
Rule of thumb: For many reactions near room temperature, reaction rate doubles for every 10°C increase. This corresponds to Ea ≈ 50–60 kJ/mol.
Catalysts lower Ea by providing an alternative reaction pathway. Enzymes are biological catalysts that dramatically lower Ea — often by 50–100 kJ/mol.
Pre-exponential factor A: The factor A (frequency factor) represents the collision frequency and orientation factor. It can be determined from a single rate constant once Ea is known: A = k / e^(-Ea/RT).