Problem 3 Consider a simple enzymatic reaction running in a perfectly mixed batch bioreactor in the presence of soluble biocatalyst undergoing inactivation. SubstrateerymeProduct Reaction kinetios is described by Michaelis-Menten equation while a kinetic model of an accompanying deactivation process of a biocatalyst is independent of the substrate concentration. With such assumptions the kinetic equations for the mathematical model of the process together with the initial and final conditions are as follows: dtdCS=kR(KM+CS)CECSdtdCE=kDCECS(t=0)=CS0,CS(t=tf)=CStCE(t=0)=CBD,CE(t=tf)=CBt The effect of temperature on the reaction kR and deactivation kD rate constants are described by the Arrhenius equations. 1. Find the temperature of the reaction occurring under isothermal condition and determine its batch operation time. 2. Show the time distribution of substrate and enzyme concentrations for temperature evaluated above. 3. Find the volume of the reactor required for the proces. Process is characterized by the following kinetic parameters: The lower Tmin=293K and upper Ttax=343K temperature constraints must be taken into account