Question

By using an appropriate example and diagram, explain the steady state diffusion of component A through non-diffusing component B for molecular diffusion of gases.

Answer 1

Solution :

This is the other special case of diffusion. 2 examples are shown in the Figure below.

Case (a) shows the diffusion of benzene in air. Liquid benzene is stored in a long tube, with one end of the tube exposed to air. The air inside the tube is stagnant, and benzene is evaporating through this stagnant air. The diffusion path is from point 1 at the gas-liquid interface to point 2 at the edge of the tube, i.e. across the distance ( z2 - z1 ).

Case (b) shows an ammonia-air mixture exposed to liquid water. The ammonia diffuses through the gas mixture from point 1 in the bulk gas phase to point 2 at the gas-liquid interface and eventually is being absorbed into water. Air is assumed to be non-soluble in water, hence it does not diffuse, i.e. it is the non-diffusing component. Again, the diffusion path is the distance ( z2 - z1 ).

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The general equation is:

In this case, NB = 0, and the equation simplifies to

Again, using the Ideal Gas equation, we have:

where pA is the partial pressure of A, and P is the total pressure

Differentiating with respect to distance z,

and substituting

We obtain by re-arranging:

Integrating from point 1 to point 2: the partial pressure of A changes from pA1 to pA2 :

We have the equation for diffusion whereby only 1 component (say component A) is diffusing:

The other component (i.e. component B) is stagnant or non-diffusing.

Note: In the above equation the driving force for diffusion in the gas phase is expressed in terms of partial pressure. Other measure of concentration in the gas phase includes mole fraction, volume %, etc.

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