Calculator Inputs
Choose a method, enter your values, and submit to place the result above this form.
Formula Used
D = |J × Δx / ΔC|
Use this when you know diffusion flux, diffusion distance, and the concentration gradient across the medium.
D = kB × T / (6 × π × η × r)
Use this for molecules or particles moving through a fluid when viscosity, temperature, and particle radius are known.
D2 = D1 × exp[(-Ea / R) × (1/T2 - 1/T1)]
Use this to estimate how a known diffusion coefficient changes when temperature changes, assuming one activation energy dominates.
How to Use This Calculator
- Select the method that matches your available data.
- Enter all required values and choose the correct units.
- Press the calculate button to show the result above the form.
- Review converted units, output values, and method notes.
- Use CSV or PDF export for reports, records, or lab files.
Tip: Keep units consistent with your source experiment or literature value before interpreting the result.
Example Data Table
| Method | Sample Inputs | Estimated D | Comment |
|---|---|---|---|
| Fick first law | J = 0.002 mol/m²·s, Δx = 1 mm, ΔC = 500 mol/m³ | 4.000000e-09 m²/s | Useful for steady one-dimensional diffusion tests. |
| Stokes-Einstein | T = 298 K, η = 0.89 cP, r = 0.5 nm | 4.904993e-10 m²/s | Common for dilute solutes in liquids. |
| Arrhenius adjustment | D1 = 1.2e-9 m²/s, Ea = 18 kJ/mol, T1 = 298 K, T2 = 320 K | 1.977384e-09 m²/s | Shows diffusion increase at higher temperature. |
Why Diffusion Coefficient Matters
The diffusion coefficient describes how quickly molecules, ions, or particles spread through a medium. In chemistry, it supports reaction engineering, membrane design, separation studies, corrosion analysis, pharmaceutical delivery, electrochemistry, and material characterization. A larger coefficient means species move more rapidly through the system under comparable conditions.
Because diffusion changes with temperature, viscosity, particle size, and concentration gradients, a flexible calculator helps compare methods quickly. This page lets you estimate the coefficient from direct transport data, from particle motion in a liquid, or by adjusting a known value for temperature. The extra unit conversions and export tools simplify reporting and reuse.
FAQs
1. What is a diffusion coefficient?
It is a transport property that measures how fast a substance spreads through a medium because of random molecular motion or a concentration gradient.
2. Which unit is most common?
The SI unit is m²/s. In chemistry papers, cm²/s is also common, especially for liquids, membranes, and electrochemical transport studies.
3. When should I use Fick first law?
Use it when you know the steady diffusion flux, diffusion distance, and concentration difference across the region you are studying.
4. When does Stokes-Einstein work best?
It works best for small spherical particles in dilute liquids where viscosity is known and continuum assumptions remain reasonable.
5. Why does temperature usually increase diffusion?
Higher temperature raises molecular energy and often lowers effective resistance to motion, so particles spread faster through many liquids and solids.
6. Can the diffusion coefficient be negative?
No. The coefficient itself is treated as positive. Direction belongs to the flux sign or the concentration gradient sign.
7. What can make my result inaccurate?
Wrong units, nonsteady experiments, large concentration changes, nonspherical particles, slip effects, and phase changes can all reduce accuracy.
8. Can I use this for gases, liquids, and solids?
Yes, but choose the method carefully. Each model has assumptions, so confirm it matches your phase, geometry, and measurement conditions.