The immobilized enzyme layer shown in the figure below is designed to convert substrate A to product B according to the simplified reaction A → B with simplified rate equation R_A = –kc_A. In this process, the steady-state concentrations of substrate A in the bulk liquid and the interface between the enzyme layer and its inert support surface were measured, with c_A∞ = 1.0 mmol/m³ at z = 0, and c_AL = 0.25 mmol/m³ at z = L. The effective diffusion coefficient of substrate A within the enzyme layer is D_Ae = 2.0 X 10^–5 cm²/s, and the thickness of the immobilized enzyme layer is L 0.2 cm. The surrounding fluid is well mixed, and the concentration of substrate A at the surface of the enzyme layer can be taken as the bulk concentration of substrate A in the surrounding liquid.
a. What are valid boundary conditions for this process?
b. Based on the measured values for c_A∞ and c_AL, what is the first-order rate constant k?
c. If the total exposed surface area of the enzyme layer is S = 2.0 m², what is the production rate of product B?
d. Based on your calculation of the Thiele modulus, is the process reaction controlled, diffusion controlled, or neither?

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Well-mixed liquid phase CA. 1.0 mmol/m³ = Enzyme layer Z=0 Nonporous support Z=L= z = L = 0.2 cm CAL = 0.25 mmol/m³