Arrhenius Equation Calculator
Rate constant k, activation energy Ea from two temperatures, or k at a new temperature.
k = A·e^(−Ea/RT). From two measurements, Ea = R·ln(k₂/k₁) ÷ (1/T₁ − 1/T₂). If a rate constant goes from 0.0012 at 25 °C to 0.0048 at 45 °C, Ea = 8.314 × ln 4 ÷ (1/298.15 − 1/318.15) = 54.7 kJ/mol.
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How to use it
- Choose what to solve for: k, activation energy, or k at a new temperature.
- Enter the values you know; temperatures can be in °C or K.
- Read the result and, for two temperatures, how many times faster the reaction runs.
What you enter
- A, Ea and T
- or k₁, T₁, k₂, T₂
- or k₁, T₁, Ea and T₂
What you get
- Rate constant k
- Activation energy (kJ/mol and kcal/mol)
- Pre-exponential factor A
- Rate change factor
Formula
k = A·e^(−Ea/RT) | ln(k₂/k₁) = (Ea/R)(1/T₁ − 1/T₂)
R = 8.314 J/(mol·K); T in kelvin (°C + 273.15); Ea in J/mol inside the exponent.
Worked example: activation energy
Input: k₁ = 0.0012 at 25 °C, k₂ = 0.0048 at 45 °C
Result: Ea = 54.7 kJ/mol
Typical of many enzyme-free solution reactions; a 20 °C rise quadruples the rate.
Questions
What does the Arrhenius equation tell you?
How a reaction's rate constant depends on temperature. A higher activation energy means the rate is more sensitive to temperature.
How do I find activation energy from two temperatures?
Use Ea = R × ln(k₂/k₁) ÷ (1/T₁ − 1/T₂) with temperatures in kelvin and R = 8.314 J/(mol·K). Divide by 1000 for kJ/mol.
Does a 10 °C rise really double the rate?
Only for activation energies of roughly 50 kJ/mol near room temperature. The rule of thumb is the Q10 idea; the Arrhenius equation gives the exact factor for your Ea.
What are the units of A?
The same as k, so they depend on the reaction order: s⁻¹ for first order, M⁻¹·s⁻¹ for second order.
Limitations
- Assumes Ea and A do not change with temperature.
- Enzyme reactions deviate once the enzyme denatures.
References
- Atkins P, de Paula J, Keeler J (2018) Atkins' Physical Chemistry, 11th ed. Oxford University Press, ch. 17.
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