Gas Diffusion Coefficient Calculator

Calculator Inputs

Calculation Method

Gas A Name

Gas B Name

Temperature, T (K)

Pressure, P (atm)

Molar Mass A (g/mol)

Molar Mass B (g/mol)

Fuller Diffusion Volume A, ΣV

Fuller Diffusion Volume B, ΣV

Collision Diameter A, σ (Å)

Collision Diameter B, σ (Å)

Energy Parameter A, ε/k (K)

Energy Parameter B, ε/k (K)

Concentration Difference, ΔC (mol/m³)

Diffusion Path Length, L (m)

Area for Transfer Rate, A (m²)

Reset

Use Fuller volumes for empirical estimates, or Chapman-Enskog inputs for kinetic-theory based estimates using Lennard-Jones parameters.

Example Data Table

Gas Pair	Method	T (K)	P (atm)	Key Inputs	Approx. D (cm²/s)
Nitrogen / Carbon Dioxide	Fuller	298.15	1.0	ΣVA=18.5, ΣVB=26.9	0.159
Hydrogen / Air	Fuller	298.15	1.0	ΣVA=7.07, ΣVB=20.1	0.611
Oxygen / Nitrogen	Chapman-Enskog	300.00	1.0	σA=3.467, σB=3.798, εA/k=106.7, εB/k=71.4	0.206

These example values are illustrative and may vary with source data and parameter selection.

Formula Used

1) Fuller-Schettler-Giddings correlation

D_AB (cm²/s) = 0.00143 × T^1.75 × √(1/M_A + 1/M_B) ÷ [P × (ΣV_A^1/3 + ΣV_B^1/3)²]

Use this when diffusion volumes are available. It is popular for low-pressure binary gas mixtures and quick engineering estimates.

2) Chapman-Enskog correlation

D_AB (cm²/s) = 0.001858 × T^1.5 × √(1/M_A + 1/M_B) ÷ [P × σ_AB² × Ω_D]

Here, σ_AB = (σ_A + σ_B) / 2, ε_AB/k = √[(ε_A/k)(ε_B/k)], T* = T / (ε_AB/k), and Ω_D is the diffusion collision integral.

3) Fick’s law add-on for flux

|J| = D × (ΔC / L)

The calculator also estimates transfer rate magnitude using |N| = |J| × A, which helps connect diffusivity with process throughput.

How to Use This Calculator

Select a method. Choose Fuller for diffusion volumes or Chapman-Enskog for Lennard-Jones data.
Enter gas names, temperature, pressure, and both molar masses.
Fill the method-specific fields shown after selecting the method.
Optionally add concentration difference, diffusion length, and area to estimate flux and molar transfer rate.
Press the calculate button. Results appear above the form, directly under the header.
Use the CSV or PDF buttons to save the results for reports or calculations.
Review the Plotly chart to see how diffusivity changes with temperature at constant pressure.

FAQs

1) What does the gas diffusion coefficient represent?

It measures how quickly one gas species spreads through another. Higher values mean faster molecular mixing under the same temperature, pressure, and composition conditions.

2) When should I use the Fuller method?

Use Fuller when you have reliable diffusion volumes and need a practical engineering estimate for dilute gas mixtures, especially near low to moderate pressures.

3) When is Chapman-Enskog better?

Chapman-Enskog is better when collision diameters and Lennard-Jones energy parameters are known. It ties more directly to kinetic theory and intermolecular behavior.

4) Why does diffusivity increase with temperature?

Higher temperature raises molecular speed and collision energy. That usually improves molecular mobility, so binary gas diffusivity rises as temperature increases.

5) Why does diffusivity decrease as pressure increases?

Higher pressure packs molecules closer together, increasing collision frequency and reducing the average free path. That lowers the diffusion coefficient in both correlations.

6) Are the results valid for non-ideal gases?

These equations are mainly intended for dilute, near-ideal gas systems. At high pressure or strong non-ideal behavior, more advanced transport models may be needed.

7) What units does this calculator return?

Diffusivity is reported in cm²/s and m²/s. Flux is shown in mol/m²·s, and transfer rate is shown in mol/s when area is entered.

8) Can I use this for membrane or packed-bed work?

Yes, as a starting point. But real membrane, porous, or packed systems often need effective diffusivity corrections for porosity, tortuosity, or Knudsen effects.