Mass Diffusivity (gas)

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The Mass Diffusivity of a Gas calculator computes the diffusivity based on two molar masses, an empirical coefficient, the absolute temperature, pressure, average collision diameter and a temperature dependent collision integral.
INSTRUCTIONS: Choose units and enter the following:

(T) Temperature of the gas mixture
(p) Pressure of the combined gases
(σ₁) Collision diameter of substance 1
(σ₂) Collision diameter of substance 2
(M₁) Molar mass of substance 1
(M₂) Molar mass of substance 2
(Ω) Collision integral for the combining gases

Mass Diffusivity of a Gas(D): The diffusivity is returned in stokes (cm²/s).

The Math / Science

The Mass Diffusivity of a Gas equation computes the mass diffusivity or diffusion coefficient for a pair of real gases , each with a specified temperature. The formula used in this mass diffusivity of a gas calculator is:

$D = (1.858*10^-3 * T ^(3/2) * sqrt( 1/M_1 + 1/M_2))/(p * (1/2*(sigma_1 + sigma_2))^2 * Omega)$

where:

D is the diffusivity of an ideal gas.
T - the temperature of the gas mixture
p - pressure of the combined gases
$sigma_1$ - the collision diameter of substance 1
$sigma_2$ - the collision diameter of substance 2
$M_1$ - the molar mass of substance 1
$M_2$ - the molar mass of substance 2
$Omega$ - the collision integral for the combining gases

The diffusivity or diffusion coefficient characterizes the relationship between the molar flux due to molecular diffusion and the gradient force of a c concentration of the material's molecules that drives diffusion.

Diffusivity is specified for one substance relative to another. In this case there are two substances labeled substance 1 and substance 2.

For a common pair of gases, air and water vapor, we have the gas characteristics:

air collision diameter ( $sigma_"air"$ ) - 3.72 Angstroms
water collision diameter ( $sigma_(H_2O)$ ) - 2.641 Angstroms
air's molar mass ( $M_"air"$ ) - 28.97 g/mol
water's molar mass ( $M_(H_2O$ ) - 18.01528 g/mol

This example's environment is characterized by a pressure (p) of 1 atm and a temperature (T) of $25^o C$ and the collision integral is 1.005.

This example will result in a diffusion coefficient (D) for air and water in gaseous combination of 0.282 $cm^2$ /s

The Math / Science

Diffusivity Equation