A stage extraction process is depicted in Fig. P9.13. In such systems, a stream

QUESTION:

A stage extraction process is depicted in Fig. P9.13. In such systems, a stream containing a weight fraction yin of a chemical enters from the left at a mass flow rate of F1. Simultaneously, a solvent carrying a weight fraction xin of the same chemical enters from the right at a flow rate of F2. Thus, for stage i, a mass balance can be represented as F1 yi1 + F2xi+1 = F1 yi + F2xi (P9.13a) At each stage, an equilibrium is assumed to be established between yi and xi as in K = xi yi (P9.13b) where K is called a distribution coefficient. Equation (P9.13b) can be solved for xi and substituted into Eq. (P9.13a) to yield yi1 1 + F2 F1 K yi + F2 F1 K yi+1 = 0 (P9.13c) If F1 = 400 kg/h, yin = 0.1, F2 = 800 kg/h, xin = 0, and K = 5, determine the values of yout and xout if a five-stage reactor is used. Note that Eq. (P9.13c) must be modified to account for the inflow weight fractions when applied to the first and last stages.