One of your friends, a chemist who does extracurricular research in his garage, has stumbled upon a new homogeneous catalyst that greatly increases the rate of the liquid-phase reaction: A + B R (in presence of a catalyst). MW: A = 95, B = 134, R = 229 The reaction is essentially irreversible at the experimental conditions, and the catalyst is completely soluble in the reaction mixture. As a chemical engineer, you know that R is a valuable product. With the idea of forming a company to manufacture it, you consult with your friend John, a marketing specialist. John estimates that 10,000,000 pounds per year of R (100% basis) could be sold without disturbing the current selling price. According to economic analyses performed by a third friend, Ben, a financier, this would be a highly profitable operation. Thus, the Embryonic Chemical Company is born. Ben manages to negotiate a lease on the property of a defunct chemical company. The building contains only a single 100-gallon CSTR, but Ben is certain this reactor will be sufficient because it " . . . looked pretty . . . big." Meanwhile, back in the garage, your chemist friend has been studying the reaction in greater detail. He has found that the reaction is "clean," i.e., there are no side reactions, as long as the catalyst concentration, Cc, does not exceed 1.0 x 10-4 lb.mol/gal. You therefore choose this concentration for use in the plant. A stoichiometric mixture of A and B at reaction temperature contains 0.035 lb.mol/gal of each component and has a density of 8.00 lb/gal. In doing the research, attention has been confined to stoichiometric mixtures of A and B because John has determined that the product can be sold directly as it comes from the reactor (without a final purification) if the feed is stoichiometric and the final conversion is 93% or more. This is a big advantage because your building contains no separation equipment. In analyzing the kinetic data, you find that a sufficient rate equation is

-rA (lb*mol/h*gal) = kCcCaCb / (1+KCb)

k=1.51*10^6 gal^2/(lb*mol)^2*h

K=85.0gal/lb*mol

The feed will be a stoichiometric mixture of A and B, and the conversion must be at least 93%. Allow for 10% downtime, i.e., 7890 operating hours per year. A plug flow reactor needs to be added before the CSTR to reach 10,000,000 lbs of product in a year. What is the volume of this plug flow reactor? ALTERNATIVELY, if a plug flow reactor was added after the CSTR, what would its volume have to be to reach 10,000,000lbs of product in a year?