Starting with the catalyst differential PFR equation:

Knowing that:

We can rewrite the differential equation:

The differential equation for component B is similar to A except that it is positive because it is a product the rate law:

It must also be taken into account that B is diffusing through the membrane walls. This will change the equation:

The rate will be governed by the equation :

k_c prime is the transport coefficient with respect to catalyst weight. We are not given a value for k_c prime, but we are given the diffusivity and the boundary layer thickness. Searching through material it can be found that

To find k_c prime just divide k_c by the catalyst bulk density. Plugging this back into the differential equation for the flow rate of B:

C doesn't diffuse through the membrane so:

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