Pharmaceutical Engineering : Mass Transfer - Equimolecular Counter Diffusion

**EQUIMOLECULAR COUNTERDIFFUSION**

If
no bulk flow occurs in the element of length d*x*, shown in Figure 4.1, the rates of diffusion of the two gases, A
and B, must be equal and opposite, that is,

N_{A}= - N_{B}

The
partial pressure of A changes by *d*P_{A}
over the distance *dx*. Similarly, the
partial pressure of B changes by *d*P_{B}.
Since there is no difference in total pressure across the element (no bulk
flow), *d*P_{A}/d*x* must equal -*dP*_{B}/d*x*. For an
ideal gas, the partial pressure is related to the molar concentration by the
relation

P_{A}V
= *n*_{A}RT

where
n_{A} is the number of moles of gas *A*
in a volume *V*. Since the molar
concentration, C_{A}, is equal to n_{A}/V,

P_{A}
= C_{A}RT

Therefore,
for gas A, equation (4.1) can be written as

where
D_{AB} is the diffusivity of A in B. Similarly,

It
therefore follows that D_{AB} = D_{BA} = D. If the partial pressure of A at *x*_{1} is P_{A1} and that
at x_{2} is P_{A2}, integration of equation (4.2) gives

A
similar equation may be derived for the counterdiffusion of gas B.

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