Reaction Rate
Arrhenius rate constant k = A·exp(−Ea / RT) and rate-vs-temperature plots.
How to use this tool
See how temperature changes a reaction's speed. Use Find Eₐ from two rates to get the activation energy from two measured rate constants, or Predict k at T to estimate the rate constant at a new temperature.
Find Eₐ, what to enter
- Rate constant k₁ / k₂: how fast the reaction ran in two experiments (same units for both).
- Temperature T₁ / T₂: the temperature of each experiment, in kelvin (K = °C + 273.15). The two must differ.
Predict k, what to enter
- Pre-exponential A: the Arrhenius frequency factor (how often molecules collide with the right orientation).
- Activation energy Eₐ: the energy barrier, in kJ/mol.
- Temperature T: in kelvin.
Reading the result
In the first mode the headline is the activation energy Eₐ in kJ/mol (with the pre-exponential factor A below it); in the second it is the predicted rate constant k. A higher Eₐ means the rate is more sensitive to temperature.
Worked example
A reaction with k = 0.001 at 298.15 K (25 °C) speeding up to k = 0.005 at 318.15 K (45 °C) has Eₐ ≈ 63 kJ/mol.
Result
In two-rate mode the headline is the activation energy Eₐ (the barrier height) with the frequency factor A beneath it; a larger Eₐ means the rate is more temperature-sensitive. In predict mode you get k at your chosen temperature, in the same units as A. Keep every temperature in kelvin, a stray °C throws the exponent off completely.
Methodology
The Arrhenius equation k = A·e^(−Eₐ/RT) links rate constant to temperature. From two measurements, Eₐ = R·ln(k₂/k₁) / (1/T₁ − 1/T₂) and the pre-exponential factor follows from A = k₁·e^(Eₐ/RT₁). Temperatures are in kelvin; R = 8.314 J·mol⁻¹·K⁻¹.
Rule of thumb
- Near room temperature many reactions roughly double in rate per +10 °C (Eₐ ≈ 50 kJ/mol).