Calculate diffusion coefficients, activation energy, temperature dependence, Arrhenius plot data, inverse values, comparison tables, and downloadable calculation reports.
Generate diffusion values across a temperature range using D₀ and Ea.
| Temperature (K) | 1/T (K⁻¹) | D | ln(D) |
|---|---|---|---|
| No range calculated yet. | |||
D = D₀e−Ea/(RT)
ln(D₂/D₁) = −(Ea/R)(1/T₂ − 1/T₁)
Here, D is diffusion coefficient, D₀ is the pre-exponential factor, Ea is activation energy, R is the gas constant, and T is absolute temperature.
Diffusion often becomes faster as temperature rises. The Arrhenius equation models that temperature sensitivity with an exponential relationship. It connects the diffusion coefficient to activation energy, temperature, and a pre-exponential factor. Activation energy represents the energetic barrier that particles must overcome. A larger activation energy usually creates stronger temperature dependence. The pre-exponential factor represents a theoretical scale for diffusion. It depends on the material, mechanism, and chosen model.
Arrhenius calculations require absolute temperature in kelvin. Celsius or Fahrenheit values must first be converted. Using them directly would make the exponent physically incorrect. This calculator performs those conversions automatically before evaluating the equation. It also converts energy units into joules per mole. That keeps activation energy consistent with the gas constant. Scientific notation is especially useful because diffusion values can be extremely small.
Sometimes a known diffusion coefficient is available at one temperature. The reference-temperature form can estimate another value without explicitly knowing D₀. This approach compares reciprocal temperatures and applies the activation energy. The result also provides a diffusion ratio and percentage change. These outputs help compare process temperatures and estimate sensitivity over a range.
An Arrhenius plot uses ln(D) against 1/T. Ideal Arrhenius behavior produces a straight line. Its slope equals minus activation energy divided by the gas constant. The intercept equals ln(D₀). Experimental curvature can indicate changing mechanisms or model limitations. Users should therefore treat extrapolated results carefully. Always verify coefficients against measurements when accuracy is important. The calculator helps organize values for that analysis.
Arrhenius diffusion models appear in materials science, chemistry, geology, semiconductors, polymers, and heat-treatment studies. They can describe atomic, ionic, or molecular transport when one dominant mechanism applies. Results outside the measured temperature range require extra caution. Phase changes, structural transitions, concentration effects, or multiple mechanisms can change the apparent activation energy. For reliable work, compare predictions with experimental measurements and document the units, temperature range, and fitted parameters.
| Temperature (K) | D₀ (m²/s) | Ea (kJ/mol) | Calculated D (m²/s) |
|---|---|---|---|
| 300 | 1.0 × 10⁻⁶ | 80 | 1.18 × 10⁻²⁰ |
| 500 | 1.0 × 10⁻⁶ | 80 | 4.39 × 10⁻¹⁵ |
| 700 | 1.0 × 10⁻⁶ | 80 | 1.07 × 10⁻¹² |
| 900 | 1.0 × 10⁻⁶ | 80 | 2.27 × 10⁻¹¹ |
Arrhenius equations depend on absolute temperature. Kelvin provides the required absolute scale.
D₀ is the pre-exponential factor. It sets the scale of the Arrhenius diffusion model.
Yes. The calculator converts kJ/mol, cal/mol, and kcal/mol into consistent internal units.
Use the activation-energy mode with D₁, D₂, T₁, and T₂.
It shows ln(D) against 1/T. Linear behavior supports an Arrhenius-type relationship.
Some apparent models may produce negative values. Check the physical mechanism and experimental data.
No. Arrhenius calculations are model-based estimates and should be validated against reliable data.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.