To complete this solution, solve all the parts in sequence. For making plots use MatLab, Polymath or Excel as per your convince. • • Avoid submitting solutions from Al Write each and every explanation in detail Presentable skills helps to improve ratings and feedback • Try to submit the solution in one pdf (Handwritten) • Separate software file needs to be uploaded 1. (10 pt) Consider the following biochemical reactions that occur in an aqueous solution: S+E ES ES 2 P+E k₁ k-1 where E is a free enzyme that catalyses substrate S to produce product P. (1) a. (2 pt) Write the material balances for species S. E, ES, and P in a well-stirred batch fermenter. b. (2 pt) Denoting the time-dependent species concentrations as cs, CE, CES and cp, show that the total enzyme concentration is conserved: CE(t)+CES(t)=CE(0) + CES (0) = Eo c. (4 pt) Assume that k₁ »k-1,k2 such that Eo remains small. Show that with this assumption, the overall reaction SP has an effective rate constant r defined by Rp=r= μες 1+ Kcs' Rs = -r μ where and K depend on k₁, k-1, k2 and Eo. For full credit, you must find the expressions for u, K in terms of ki, k-1, k2, Eo. d. (2 pt) Solve numerically the full (part a) and reduced (part c) models to find CE(t), CES(t), cs(t), cp(t) for the following parameters (units: mole, liter, hour): CE (0) = 1, CES(0) = 0, cs(0) = 50, cp(0) = 0 k₁ =5, k11, k₂ = 10 Submit plots comparing concentrations vs. time for the full and reduced models.