An enzyme acts as a catalyst in the fermentation of A to form product R. An aque

Question

An enzyme acts as a catalyst in the fermentation of A to form product R. An aqueous feed stream containing the enzyme and compound A flows into a CSTR at 25 L/min, and the initial concentration of A is 2 mol*L^-1. Determine the volume of the CSTR (in Liters, expressed to the nearest integer) needed to achieve 98% conversion of reactant A. You may assume that the enzyme concentration and volumetric flowrates are constant and the reaction follows Michaelis Menten kinetics. The maximum rate of destruction of the substrate is 0.4 mol/(L min). When the substrate concentration is 0.5 mol/L, the rate of destruction of the substrate is 0.2 mol/(L min), i.e. half of the maximum rate.

Explanation / Answer

For a CSTR, The characteristic equation

T= space time = CAOXA/(-rA)= CAOXA/(Vmax*CA/(KM+CA)}

XA= conversion =0.98 CAO= 2 mol/L, T= V/Vo, V= Volume of reactor and Vo= flow rate = 25 L/min

KM= 0.2 mol/L.min, Vmax= 0.4 mol/L.min, CA= CAO*(1-XA)= 2*(1-0.98)= 0.04 mol/L

T= CAOXA*(KM+CA)/ Vmax.CA= 2*0.98*(0.2+0.04)/(0.4*0.04)=29.4

V= 29.4*25 =735 L

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