Equimolar Counter-Diffusion

In equimolar counter-diffusion, the molar fluxes or A and B are equal, but opposite in direction, and the total pressure is constant throughout. Hence we can write:

N = NA + NB = 0

[ Remember: pressure is caused by the collisions of molecules with the container wall. If the pressure is constant at any point in the container, then it must be implied that the number of molecules acting on the wall at any point is also constant. In other words, if certain amount of A has diffuse away, then they are replaced by the same amount of B ]

Under equimolar counter-diffusion, the diffusivity of A in B is the same as the diffusivity of B in A, i.e. DAB = DBA

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Fick's Law for Steady-State Equimolar Counter-Diffusion of Ideal Gas Mixture:

Consider 2-component gas mixture (A and B)

Ideal Gas Law: Pv = nRT

where P is the total pressure, and n is the total moles of gas

For component-A: pAv = nART

where pA is the partial pressure of A and nA is the moles of A

Concentration of A: Intermediate derivation 1

Differentiating with respect to distance z, we obtain:

Intermediate derivation 2

Replacing into the original Fick's Law, we have an alternative equation for ideal gas using partial pressure:

Under constant total pressure and temperature conditions, the above equation for can be integrated over a diffusional path from z2 to z1 to as follows:

Integration - part 1

Integrate from pA1 to PA2, where pA1 is the partial pressure of A at point 1 and pA2 is the partial pressure of A at point 2:

Integration - part 2

We have, for steady-state equimolar counter-diffusion of ideal gas mixture:

Similarly, the molar flux for component-B can be written as:

Integration - part 3

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