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Assignment 2: Mass balances in chemical reactors (5 marks) Background. A chemical constituent flows between three reactors as depicted in Fig. 1. Steady-state mass balances can be written for a substance that reacts with first-order kinetics. For example, the mass balance for reactor 1 is - - - (1) where Q1,1n = the volumetric inflow to reactor 150 (L/min), C1,1n= the inflow concentration to reactor 10 (g/L), Qu = the flow from reactor ito Cs = the concentration of reactor i(g/L), k = a first-order decay rate (/min), and V1= the volume of reactor i (mp). 02,in = 12 = C2,in = 220 V2 = 50 Q2,1 = 22 03.2 = 5 01.2 = 5 V1 = 100 V3 = 150 = 150 Q1.3 = 117 Q3,out = 112 C1,in = 10 Figure 1: Flow diagram for 3 chemical reactors. Assignment a) If k = 0.2/min, write the mass balances for all three reactors as a system of linear algebraic equations. b) Compute the LU decomposition for this system. c) Use the LU decomposition to compute the matrix inverse. d) Use the matrix inverse to answer the following questions: (i) What are the steady-state concentrations for the thrce reactors? (ii) What fractions of this concentration come from reactor 1 and reactor 27 (iii) If the inflow concentration to the second reactor is set to zero, what is the resulting reduction in concentration of reactor 17 (iv) If the in- flow concentration to reactor 1 is doubled, and the inflow concentration to reactor 2 is halved, what is the concentration of reactor 3?

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