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# Question 3. Consider a porous catalyst with a cylindrical geometry having an inner radius ri, outer radius r2and an axial length L, embedded in an impermeable substrate. Gas A is maintained at a constant concentration CA in the open area at the center and diffuses from the interior of the cylinder toward the outer wall of the cylinder. While doing so, it reacts with the catalyst to produce gas B: A-B This reaction is zero-order in the concentration of A, and proceeds at a constant rate per unit volume: rA- k (mol A)(m3 s)1 The effective diffusion coefficient of A is Deff. The system is at steady-state. mpermeable Substrate Catalyst a) Use a shell balance to derive the differential equation that describes how the concentration b) c) d) of A changes in the radial direction. Clearly state all assumptions in your solution. What boundary conditions will you use to solve this diff. eq.? Solve the diff. eq. to find the concentration of A as a function of r. Derive the effectiveness factor for this system when the concentration of A is non-zero at all positions. (copying an equation from notes is worth zero points)

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