Pure butanol is to be fed into a semibatch reactor containing pure ethyl acetate to produce butyl acetate and ethanol. The reaction ([ethyl acetate] +[ butanol ] [butyl acetate] + [ethanol]) is elementary and reversible. The reaction is carried out isothermally at 300K. At this temperature, the equilibrium constant is 1.08 and the specific reaction rate is 9 105L/mols. Initially, there is 200L of ethyl acetate in the vat, and butanol is fed at a volumetric rate of 0.05L/s. The feed and initial concentrations of butanol and ethyl acetate are 10.93 and 7.72mol/L, respectively. a. Apply the isothermal reactor design algorithm to this system to derive a set of coupled differential equations to solve in terms of the molar flowrates of all species