Equimolecular Counterdiffusion
If no bulk flow occurs in an element of length dx, the rates of diffusion of two gases A and B must be equal and opposite, that is .
The partial pressure of A changes by dPA over the distance dx. Similarly, the partial pressure of B changes dPB. As there is no difference in total pressure across the element (no bulk flow), dPA/dx must equal . For an ideal gas the partial pressure is related to the molar concentration by the relation
where nA is the number of moles of gas A in a volume V. As the molar concentration CA is equal to nA/ V therefore
Consequently, for gas A,
where DAB is the diffusivity of A in B. Similarly,
It therefore allows that DAB=DBA=D. If the partial pressure of A at x1 is PA1 and x2 is PA2, integration of above equation,
A similar equation may be derived for the counterdiffusion of gas B.
Read more about this topic: Molecular Diffusion