Problem: A stage extraction process is depicted in Fig. P12.9. 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 F₁Yi-1+ F2X+1 = F₁Yi + F₂Xi (P12.9.1) At each stage, an equilibrium is assumed to be established between Y, and Xi as in K Yi (P12.9.2) where K is called a distribution coefficient. Equation (P12.9.2) can be solved for X, and the result substituted into Eq. (P12.9.1) to yield Yi-1 − (1 + ½² K) Y + (¾½²K) Yi+1 = 0 - (P12.9.3) If F₁ = 400 kg/h, Yin = 0.1, F2 = 800 kg/h, Xin = 0, and K = 0.2, determine the values of Yout and Xout using 1 to 15 stages and plot them vs the number of stages. Note that Eq. (P12.9.3) must be modified to account for the inflow weight fractions when applied to the first and last stages.

Fig: 1