Additional Homework Problems

CDP8-BB

  The catalytic reaction

IMAGE 08eq5.gif

     
    is carried out isothermally on a solid platinum wire in which the flow of the reactant is normal to the wire. The rate law on the solid platinum surface is
     
    IMAGE 08eq6.gif
     
    where C A is the concentration at the wire surface in the gas phase. Use bifurcation analysis to answer the following:

(a) What is the lowest feed concentration, C A0 , one can have and still have the possibility of multiple steady states?
(b) Derive an equation relating the wire diameter D to the velocity U, which divides a plot of U vs. D into two regions, one in which a multiple steady state (MSS) is possible and one in which a MSS is not possible.

     
    Additional information:
    IMAGE 08eq7.gif
     
    (c) The smallest platinum wire available has a diameter of 0.025 cm. For this wire, what is the largest gas velocity one can have and still have a possibility of multiple steady states? For flow normal to a wire, Sh = 0.4 Re0.4 Sc 1/3 . (See Chapter 11.)

[2nd Ed. P8-26]