Chapman Enskog Equation For Gas Phase Diffusivity Calculator

Chapman Enskog Equation:

\[ D_{AB} = \frac{1.858 \times 10^{-7} \times T^{3/2} \times \sqrt{\left(\frac{1}{M_A} + \frac{1}{M_B}\right)}}{P_T \times \sigma_{AB}^2 \times \Omega_D} \]

Temperature of Gas:

Molecular Weight A:

kg/mol

Molecular Weight B:

kg/mol

Total Pressure of Gas:

Characteristic Length Parameter:

Collision Integral:

Diffusion Coefficient (D_AB):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Chapman Enskog Equation?

The Chapman Enskog equation is a theoretical model that predicts the diffusion coefficient for binary gas mixtures. It provides a more accurate assessment of gas phase diffusivity based on kinetic theory of gases and molecular interactions.

2. How Does the Calculator Work?

The calculator uses the Chapman Enskog equation:

\[ D_{AB} = \frac{1.858 \times 10^{-7} \times T^{3/2} \times \sqrt{\left(\frac{1}{M_A} + \frac{1}{M_B}\right)}}{P_T \times \sigma_{AB}^2 \times \Omega_D} \]

Where:

\( D_{AB} \) — Diffusion coefficient (m²/s)
\( T \) — Temperature of gas (K)
\( M_A \) — Molecular weight of component A (kg/mol)
\( M_B \) — Molecular weight of component B (kg/mol)
\( P_T \) — Total pressure of gas (at)
\( \sigma_{AB} \) — Characteristic length parameter (m)
\( \Omega_D \) — Collision integral (dimensionless)

Explanation: The equation accounts for molecular interactions and temperature effects on gas diffusion, providing a fundamental theoretical basis for predicting diffusivity in binary gas mixtures.

3. Importance of Diffusion Coefficient Calculation

Details: Accurate diffusion coefficient calculation is crucial for designing separation processes, predicting mass transfer rates, modeling chemical reactions, and understanding transport phenomena in gas phase systems.

4. Using the Calculator

Tips: Enter temperature in Kelvin, molecular weights in kg/mol, total pressure in technical atmosphere, characteristic length in meters, and collision integral (dimensionless). All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: Why use Chapman Enskog equation instead of empirical correlations?
A: Chapman Enskog provides a theoretical foundation based on kinetic theory, offering better accuracy across wider temperature and pressure ranges for binary gas systems.

Q2: What are typical diffusion coefficient values for gases?
A: Gas phase diffusion coefficients typically range from 10⁻⁶ to 10⁻⁵ m²/s at atmospheric pressure and room temperature.

Q3: How does temperature affect diffusion coefficients?
A: Diffusion coefficients increase with temperature (approximately T³/² dependence) as molecular motion becomes more vigorous.

Q4: What are the limitations of this equation?
A: The equation assumes ideal gas behavior and may be less accurate for polar molecules, high-pressure systems, or near critical conditions.

Q5: How is the collision integral determined?
A: The collision integral is typically obtained from tabulated values based on the reduced temperature and the Lennard-Jones potential parameters for the gas pair.