Gas Diffusion Calculator

Diffusion results for labs, HVAC, and safety checks. Pick a model, enter values, and compute. Download a tidy report, plus CSV for spreadsheets easily.

Calculator inputs

Please choose a model.
Enter a valid D.
Enter C₁.
Enter C₂.
Enter L.
Enter A.
Leave blank if you only need flux and rate.
Reset

Plot

A quick visual based on the selected model and results.

Required fields are marked with an asterisk. Units are converted automatically where provided.

Example data table

Example inputs show how steady-state diffusion can be reported. Replace with your measured values.

Model D C₁ C₂ L A t
Fick’s First Law 1.8×10⁻⁵ m²/s 1.0 mol/m³ 0.2 mol/m³ 0.010 m 0.005 m² 600 s
Characteristic time 1.8×10⁻⁵ m²/s 0.010 m Factor = 2
Graham’s Law M₁ = 4 g/mol, M₂ = 28 g/mol Optional: r₂ = 1.0

Formulas used

1) Fick’s First Law (steady state)
J = −D · (dC/dx), where J is molar flux, D is the diffusion coefficient, and dC/dx is the concentration gradient. The molar transfer rate is dN/dt = J · A.
2) Characteristic diffusion time (simple estimate)
For a length scale L, a common order-of-magnitude estimate is t ≈ L² / (kD), using k = 2 for a 1D reference case.
3) Graham’s Law (relative rates)
For two gases at the same temperature and pressure, r₁/r₂ = √(M₂/M₁), where M is molar mass.

How to use this calculator

  1. Select a model: Fick’s flux, diffusion time, or Graham’s ratio.
  2. Enter values and choose units from the dropdowns.
  3. Press Calculate to show results above the form.
  4. Use Download CSV for spreadsheets and logs.
  5. Use Download PDF to save a printable report.

If you are unsure about D, report the source and temperature with your results.

Technical notes

Operational scope

Use this calculator for steady diffusion across a slab, quick time-scale estimates, and gas-to-gas rate comparisons. The Fick flux option suits membranes, porous plugs, and stagnant films where a linear concentration profile is reasonable. Graham’s ratio supports screening of leak rates when pressure and temperature are comparable. For engineered barriers, pair results with permeability tests and report the geometry used.

Input quality checks

For reliable outputs, keep units consistent and avoid zero thickness or negative areas. When concentrations come from measurements, note the sampling method and temperature. Small errors in thickness propagate linearly into the gradient and therefore into the flux. The form applies basic validation so obviously nonphysical inputs are flagged early.

Unit conversions and scaling

Diffusion coefficients are commonly reported in m²/s or cm²/s, while concentration is often given in mol/L in laboratory work. The calculator converts these to SI internally, then reports results in SI-based units. This avoids silent scaling mistakes, especially when mixing centimeter-length membranes with liter-based concentration data. Converting area to m² is equally important because rates scale directly with cross section.

Interpreting flux direction

The sign of J reflects the chosen order of C₁ and C₂. A negative J indicates flow toward decreasing x, not a “negative amount” of gas. Use the flux magnitude when you only need rate size, and keep the sign when mapping direction through a system diagram. The plot helps confirm the linear profile assumption. If your system has convection or reactions, steady Fick behavior may not hold.

Time-scale estimation guidance

Characteristic diffusion time uses t ≈ L²/(kD) to estimate how quickly gradients smooth out. With k = 2 you get a 1D reference estimate; with k = 6 you approximate a 3D mean-square displacement form. Use this model for planning experiments, sensor placement, and purge or ventilation timing. In practice, choose L as the longest relevant path length for the slowest mode.

Reporting and export workflow

For audits and lab notebooks, export the CSV to preserve both inputs and outputs in a single row set. Use the PDF to create a shareable snapshot for reviews, especially when documenting D values from literature. Include gas identity, pressure, and temperature because diffusion parameters can shift significantly with conditions.

FAQs

What does the diffusion coefficient represent?

It quantifies how rapidly molecules spread through a medium. Larger D means faster mixing for the same gradient and geometry, assuming diffusion-dominated transport.

Why is the concentration gradient important?

Flux is proportional to the gradient. Doubling the concentration difference or halving the thickness doubles the gradient and therefore doubles the predicted flux.

Can I use this for turbulent flow or strong convection?

No. These models assume diffusion is the dominant mechanism. If bulk flow matters, use a mass-transfer coefficient or a full transport model instead.

What does a negative flux mean in the results?

It indicates direction based on your x-axis choice and concentration order. Use the magnitude for size, and the sign to track direction through your setup.

How should I choose the length scale for time estimates?

Use the longest relevant diffusion path that controls the slowest response, such as membrane thickness or a characteristic pore length in a barrier.

What’s the difference between diffusion and effusion in Graham’s law?

Graham’s law is often used for both, but it strictly describes effusion through a tiny orifice. As a quick ratio, it can still help compare relative rates under similar conditions.

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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.