Problem 2 Consider the isothermal and well-mixed chemical reactor shown in the schematic below. The rate of reaction occurring in the reactor is: r = -k CA³. Initially, the system is at steady state conditions and the flow rate in and out from the reactor, F, is 0.2m³/min. Also, the initial inlet concentration of component A, CAOS, is 2 mole/m³ and the reactor volume, V, is 5 m³. The reaction constant, k, is 0.5 (mole/m³)-2* min'. If the density change due to the reaction is zero and the flow rates in and out from the reactor remain constant, then: a) Summarize your data b) State any assumptions you make. c) Derive the non-linear model for the dynamic response of the concentration of A in the reactor, CA(t). Show all your derivations/calculations. d) Use the Euler method to solve the non-linear model for a step change in the inlet concentration, Cao, of size +1 mole/m³. e) Plot the non-linear responses of the system, i.e. make a plot of CAO and CA .vs. time F С до LL F V A P₁₁ = -K.C₁³

Fig: 1