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The enzyme urease is immobilized in Ca-alginate beads 2 mm in diameter. Find Vma

ID: 89148 • Letter: T

Question

The enzyme urease is immobilized in Ca-alginate beads 2 mm in diameter. Find Vmax, thielle modulus, and effectiveness factor. I only need part a done, as I can figure out part B on my own if I know how its done. I'm currently stuck because the posted solution by chegg is incorrect, supposedly the answer to a is Vmax = 14.9 mmol/h, phi=3.7, and n=.94. Please do not answer if you cannot get these values. I'm not sure how my question is unclear. This is a textbook problem.

3.15. The enzyme. urease, is immobilized in Ca-alginate beads 2 mm in diameter. When the urea concentration in the bulk liquid is 0.5 mM the rate of urea hydrolysis is v 10 mmoles-l-h. Diffusivity of urea in Ca-alginate beads is D 1.5x10 5 cm2/sec, and the Michaelis constant for the enzyme is K 0.2 mM. By ncglccting thc liquid film resistance on the beads (i.e [Sol z ISJ) determine the following: a. Maximum rate of hydrolysis Vnt, Thiele modulus (D), and effectiveness factor (m). b. What would be the Vm, D, and n values for a particle size of Dp 4 mm? Hint: Assume m 3/ for large values of (O 2).

Explanation / Answer

(a) V= 10 mmoles/l.h , S= 0.5 mmoles , Km = 0.2 mmoles

V = Vmax . (S) / Km + (S)

   Vmax = V . (Km + S) / (S)

= 10 mmoles/l.h x (0.2+0.5) mmoles / 0.5 mmoles

= 14 mmoles/l.h

maximum rate of hydrolysis is 14 mmoles/l.h

effectiveness factor =

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