14 Reactor design A species spontaneously decays by a first-order process with a rate constant k. Untreated water contains the species at a concentration Cin.. It is desired to reduce the concentration to Cout=(1)Cin, where is the conversion efficiency. (So, for example, if 90 percent control were desired, would be 0.9 and the outlet concentration would be Cout=0.1Cin ) (a) Given k,, and Cin, derive an equation for the required mean fluid residence time, , for the case of an ideal plug-flow reactor (PFR). (b) Given k,, and Cin, derive an equation for the required mean fluid residence time, , for the case of an ideal completely mixed flow reactor (CMFR). (c) Instead of a single reactor, the proposed treatment system is to consist of n identical CMFRs in series. The mean residence time of fluid in each reactor is , so that the total mean residence time in the system is . Given k,,Cin, and n, derive an