Mass Diffusivity (gas)

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

Diffusivity Equation

• Mass Diffusivity of a Liquid
• Mass Diffusivity of a Solid
• Mass Diffusivity of a Gas