Consider the formation of p-nitrophenol from p-nitrophenyl trimethyl acetate. The process is known as enzymatic hydrolysis and it occurs in the presence of the enzyme elastase. Along with the formation of p-nitrophenol, trimethyl acetic acid is also formed which is an undesired byproduct. p-nitrophenol is an important intermediate in the manufacture of several pharmaceuticals. Your role as a Chemical Engineer is to maximize the production of p-nitrophenol. The reactions can be denoted as: E+S → P+ES R1
ES+PE+A R2
where E denotes the enzyme elastase, S denotes the substrate p-nitrophenyl trimethyl acetate, ES denotes enzyme-substrate intermediate and A denotes the trimethyl acetic acid. The rate of the reactions 1 and 2 are given by:
r1 = k1Cs/KM + C
r2 = k2Cp
where Cs and Cp denote the concentrations of the substrate and the product, k1 and k2 are the rate constants given by 0.015 s-1 and 0.0026 s-1. KM is the Michaelis - Menten constant and is given by 5.53 mol/m3. All the reactants and products are in the liquid phase. The initial concentrations of S and E are 0.5 mol/m3 and 0.001 mol/m. Consider the above reaction to occur in a batch reactor for 15 minutes.
A. Plot the concentration profiles of S, P and A as a function of time in a single figure.
B. Plot the selectivity of P with respect to 5 as a function of time b.