The rate at which substrates by enzymes are converted into products in the solution is shown in the table.

This enzyme is fixed inside a porous spherical particle with a radius of 0.7 cm to proceed with the catalytic reaction. The maximum reaction rate of the enzyme catalyst reaction in the immobilization system, V'm, is 5 mg/L-h, the effective diffusion coefficient, and De is 2x10-4 cm^2/s. It is assumed that the Boundary layer effect is negligible.

The bulk concentration, [Sb] of the substrate is 200 mg/L, and if necessary, use the figure given below to ask the following questions:

(1) What is Thiele modulus, ?

(2) What is ?

(3) What is the effective factor, ?

(4) Find the reaction rate under these conditions.

(5) Evaluate the performance of this immobilization system.

5 10 20 50 100 200 [S], mg/L v, mg/L.s 1.0 1.7 2.5 3.6 4.2 4.6 0.8 0.67 0.01 0.1 EFFECTIVENESS FACTOR (7) 0.4+ B = 10 0.2F 0.1 2 L1 40 60 80 100 6 8 10 20 THIELE MODULUS, . 5 10 20 50 100 200 [S], mg/L v, mg/L.s 1.0 1.7 2.5 3.6 4.2 4.6 0.8 0.67 0.01 0.1 EFFECTIVENESS FACTOR (7) 0.4+ B = 10 0.2F 0.1 2 L1 40 60 80 100 6 8 10 20 THIELE MODULUS