Problem $1(30/100)$: The following reaction

$AB+3C$

is to be carried out isothermally in a membrane reactor with no pressure drop. The membrane is

permeable to product $C$ and impermeable to all other species.

Derive a set of differential equations describing the change of molar flow rates of $A,B,$

and $C$ as a function of the reactor volume. Reaction and permeation rates should be written

explicitly as a function of molar flow rates.