(5) A stream of pure gas A enters a reactor at a constant inlet flow rate n1=3mol/min. Initially, the reactor and both the inlet and outlet streams contain pure A. At time t=0, the reaction AB starts to take place in a reactor with the reaction rate rA=knA,sys where k=0.7min1 is a reaction rate constant. According to the stoichiometry of the reaction, rA=rB because B is generated at the same rate A is consumed. The reactor is well mixed so that the composition in the reactor is the same as the composition of the outlet stream. The volume of the reactor is V=4L. The reactor and inlet and outlet streams are all at a pressure and temperature of P=100atm and T=300K. Assume ideal gas behavior. (a) Draw and label a diagram of the system. Use the notation of the mole balances given below. (b) Derive an expression for nA,sys as a function of time. Use the residence time = V/V1 to make the time dimensionless where V1 is the volume flow rate of the inlet stream. Do not plug values into your expression. HINT: The arguments of logarithms and exponentials should be dimensionless. (c) What is the steady state value of xA in the reactor? That is, after the reactor has run for a very long time, what constant value does xA finally reach? Give a numerical answer. (d) Differential Mole Balances (Binary System of A and B) Species A: dtdnA,sys=nA1nA2+rA Species B: dtdnB,sys=nB1nB2+rB Total: dtdnsys=n1n2+rA+rB where nsys=nA,sys+nB,sys and n1=nA1+nB1 and n2=nA2+nB2