If no bulk flow occurs in an element of length dx, the rates of diffusion of two ideal gases (of similar molar volume) A and B must be equal and opposite, that is .
The partial pressure of A changes by dP over the distance dx. Similarly, the partial pressure of B changes dP. As there is no difference in total pressure across the element (no bulk flow), we have
For an ideal gas the partial pressure is related to the molar concentration by the relation
where n is the number of moles of gas A in a volume V. As the molar concentration C is equal to n/ V therefore
Consequently, for gas A,
where D is the diffusivity of A in B. Similarly,
Considering that dP/dx=-dP/dx, it therefore proves that D=D=D. If the partial pressure of A at x is P is P</sub>, integration of above equation,
A similar equation may be derived for the counterdiffusion of gas B.