You are to convert the 5 mM fumaric acid in a waste stream into malate using fumarase immobilized on nonporous spherical particles. The enzyme has a turnover number of 23/sec, and a Km of 1.55 mM. The immobilized enzyme particles are 1 mm in diameter, and they contain 99.4 x 10-4 mg enzyme/cm2 of support. The mass transfer coefficient is 2 x 10-4 cm/sec. The molecular weight of fumarase is 48,000.
a) What is the fumaric acid concentration on the surface of the particles?
b) What is the effectiveness factor for the immobilized enzyme?
c) What should the reaction rate be to treat 1 liters of the waste stream per day?
d) What surface area is required to yield the required reaction rate?
e) How many particles would be required?