What this calculator does
Measuring a rate constant at two temperatures is enough to determine the activation energy. Rate constants of 0.0021 at 298 K and 0.031 at 328 K give 72.9 kJ/mol.
Only the ratio of the rate constants matters, not their absolute values, because the pre-exponential factor cancels when the two measurements are divided. That is what makes this method practical: you never need to know A, which is the hardest quantity in the Arrhenius equation to determine independently.
The formula
Taking the Arrhenius equation at two temperatures and dividing eliminates the pre-exponential factor, leaving the log of the rate constant ratio proportional to the activation energy and the difference of reciprocal temperatures. The result is in joules per mole and is also reported in kilojoules, which is how activation energies are normally quoted.
| Term | Meaning |
|---|---|
| Activation energy (Ea) | The energy barrier a reaction must clear. |
| Two-point Arrhenius | Using two measurements to find Ea without knowing the pre-exponential factor. |
| Arrhenius plot | The graphical version: ln k against 1/T gives a straight line of slope −Ea/R. |
| Gas constant R | 8.3145 J/(mol·K), which is why the raw answer is in joules. |
The inputs explained
| Field | What to enter |
|---|---|
| Rate constant k₁ | Rate constant at the first temperature. |
| Temperature T₁ (K) | First temperature in kelvin. |
| Rate constant k₂ | Rate constant at the second temperature. |
| Temperature T₂ (K) | Second temperature in kelvin. A wider gap between the two gives a more reliable result. |
When to use it
Characterising a reaction
Activation energy is a basic kinetic parameter, needed before any rate can be predicted at a new temperature.
Assessing a catalyst
Measuring the activation energy with and without a catalyst quantifies exactly what it is doing.
Shelf life modelling
Accelerated stability testing needs an activation energy to extrapolate from elevated temperatures back to storage conditions.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What activation energy does each rate increase imply?
A range of rate constants at the higher temperature.
| Rate constant at 328 K | Activation energy Ea | ln(k₂/k₁) | Gas constant R used |
|---|---|---|---|
| k₂ = 0.0021 | 0.0 kJ/mol | 0 | 8.3145 J/(mol·K) |
| k₂ = 0.01 | 42.3 kJ/mol | 1.561 | 8.3145 J/(mol·K) |
| k₂ = 0.031 | 72.9 kJ/mol | 2.692 | 8.3145 J/(mol·K) |
| k₂ = 0.1 | 104.7 kJ/mol | 3.863 | 8.3145 J/(mol·K) |
Questions
Why do I not need the pre-exponential factor?
Because it cancels. Writing the Arrhenius equation at both temperatures and dividing one by the other eliminates A entirely, leaving only the rate constant ratio and the temperatures. This is what makes the two-point method usable with ordinary measurements.
Do the temperatures need to be in kelvin?
Yes, absolutely. The equation uses reciprocal absolute temperature, and Celsius values give a meaningless answer. Add 273.15 to convert. This is the single most common error in the calculation.
How far apart should the temperatures be?
Far enough for the rate difference to exceed the measurement error, typically at least 20 to 30 K. Too close and small experimental errors in the rate constants translate into large errors in Ea. Too far and the activation energy may not be genuinely constant across the range.
Is an Arrhenius plot better than two points?
Yes, where you have the data. Measuring at several temperatures and fitting ln k against 1/T averages out measurement error and reveals whether the relationship is genuinely linear. A curved plot indicates the mechanism changes over the range, which two points would hide.
For predicting a rate at a new temperature, see the Arrhenius equation calculator. For finding rate constants from concentration data, see the integrated rate law calculator.