Case 1
- Pre-exponential factor A (1/s)
- 100000000000001/s
- Activation energy Ea (J/mol)
- 75000J/mol
- Temperature T (K)
- 298.15K
0.7253851/s
Open with these valuesArrhenius Equation Calculator
0.7253851/s
Result: 0.725385 1/sk = A × exp(−Ea / (R × T)). Give the activation energy in joules per mole and the temperature in kelvin, never Celsius — a kJ/mol figure has to be multiplied by 1000 first. R is 8.314462618 J/(mol·K), exact since 2019. A = 1e13 1/s with Ea = 75000 J/mol at 298.15 K gives k ≈ 0.725385 1/s.
Worked examples
Case 2
- Pre-exponential factor A (1/s)
- 50000000000001/s
- Activation energy Ea (J/mol)
- 50000J/mol
- Temperature T (K)
- 350K
172,593.4351651/s
Open with these valuesCase 3
- Pre-exponential factor A (1/s)
- 100000000001/s
- Activation energy Ea (J/mol)
- 100000J/mol
- Temperature T (K)
- 500K
0.3575001/s
Open with these valuesHow it's calculated
k = A × exp(−Ea / (R × T))
- StepEnter the pre-exponential factor A — k comes out in the same unit.
- StepEnter the activation energy in joules per mole; multiply a kJ/mol value by 1000.
- StepEnter the absolute temperature in kelvin: a Celsius reading plus 273.15.
- ResultRead k, with R = 8.314462618 J/(mol·K) held exact.
Reference table
| A (1/s), Ea (J/mol), T (K) | Situation | k (1/s) |
|---|---|---|
| 10000000000000, 75000, 273.15 | 0 °C, ice water | 0.045497 |
| 10000000000000, 75000, 288.15 | 15 °C, cool room | 0.253849 |
| 10000000000000, 75000, 298.15 | 25 °C, standard | 0.725385 |
| 10000000000000, 75000, 308.15 | 35 °C, ten degrees warmer | 1.936269 |
| 10000000000000, 75000, 323.15 | 50 °C | 7.534948 |
| 10000000000000, 50000, 298.15 | Lower barrier, 25 °C | 17393.179681 |
| 10000000000000, 100000, 298.15 | Higher barrier, 25 °C | 0.000030252 |
Questions
How do I use the Arrhenius equation?
Multiply the pre-exponential factor by the exponential of −Ea / (R · T): k = A × exp(−Ea / (R · T)). Use joules per mole for the activation energy, kelvin for the temperature, and R = 8.314462618 J/(mol·K). For example, A = 1e13 1/s and Ea = 75000 J/mol at 298.15 K give k ≈ 0.725385 1/s.
What is the Arrhenius equation?
It is the relationship k = A · exp(−Ea / (R · T)) that describes how a reaction's rate constant depends on temperature. The exponential term is the fraction of collisions with enough energy to clear the activation barrier, so the rate constant rises steeply as the temperature increases.
What is the activation energy Ea?
The activation energy is the minimum energy, in joules per mole, that colliding molecules need before they can react. A higher Ea means a more negative exponent and a slower reaction, and it also makes the rate constant more sensitive to temperature.
Why must the temperature be in kelvin?
Because the exponent −Ea / (R · T) divides by the absolute temperature, T must be an absolute scale that starts at zero. Celsius would give wrong (or negative) values. Convert by adding 273.15 to a Celsius reading: 25 °C becomes 298.15 K.
What are the units of the rate constant?
The rate constant takes the same units as the pre-exponential factor A. For a first-order reaction A and k are in 1/s, as in this calculator. The exponential term is dimensionless because R · T and Ea are both in joules per mole, so only A sets the unit.
Sources and last check
Information, not professional advice.