(g) Calculate the average A1 and A2 (= VA1A2 = A) and calculate 3. Design of packed tower for extraction. An inlet water solution of 400kg/h containing 10 wt% acetone is extracted with the pure solvent trichloroethane in a countercurrent packed tower at 25 °C. Water and trichloroethane are essentially immiscible. The exit concentration in the water (raffinate) stream is set at 1.0 wt % (a) Plot the equilibrium data given in the table in example 12.7-4 and fit the data using a second order polynomial (b) Using the feed condition, calculate L' (the mass flow rate of the inert water). Calculate L1. (c) For V-300kg/h (the mass flow rate of the inert trichloroethane), calculate y2 (solute concentration in the extract phase at the exit). (Hint: make a mass balance on the solute over the entire tower.) (d) Calculate V2. (f) Calculate A1 = mtv. A,- and A =-AA2. (g) If the height of a transfer unit Ho 1m, using the equation (12.7-22), calculate the number of transfer units Nou and the tower height. (Note that Hou and Nou are different from HoG and NoG we derived during the class. The equation we derived was based on the extract phase. A similar equation can be derived based on the raffinate phase, which is the next problem. Either way you can estimate the tower height HoLNoL-Hog Noc) (h) Using the method introduced in the class, derive (12.7-22) nd (12.7-4) can be used to calculat the coordinates of , and VSs, ar, Equations (12.7-3) streams V; and Lx Usually, the nows and composias Streams desired exit composition raN is set. If we plot straight line must connect these three points. Then over, Lv and V, must also lie on the phase Ib, and mass fraction, kg eositions of Lo and V.are known and diagram, which ties together the two entealculate pot In terms of the V Lo VN. and M as in Fig LN.M. and V, must lie 21 LN. M, a as shown. These balances aiso hoid for mol and mol fractions, and so on. defined in Eq (10.6-28). The value of the overall number of transfer where -y*) Nou can also be determined using Eq. (10.6-53) as EXAMPLE 12.7.1. Material Balance for Coun Pure solvent isopropyl ether at the rate of V tract an aqueous solution of Lo -200 kg/h contairn countercurrent multistage extraction. The desi in the aqueous phase is 4%. Calculate the ether extract V, and the VN-600 kg/h is being used to 30 wt % acetic acid (A) by exit acetic acid concentration ions and amounts of the OL aqueous raffinate LN Use equilibrium data from EXAMPLE 12.7-4 Extraction of Acetone from Water with Trichloroethane Solution: The given values are V -600. yANEO,V Eac 0.30. rm" 0.70,Xco = 0. and ΧΑ,-0.04. In Fig. 12.7.3. V n inlet water solution of 800 kg/h containing 12.0 wt% acetone is extracted with the solvent trichloroethane containing 0.5 wt% acetone in a countercurrent tower at 25°C The solvents water and trichloroethane are essentially im- miscible in each other up to a concentration of acetone in water of 27 wt %. The exit concentration in the water (raffinate) stream is set at 10 wt % acetone. The equilibrium data are as follows (T3), where x is the weight fraction of acetone in plotted. Also. since Ly is on the phase boundary, it can be plotend L, ate For the mixture point M, substituting into Eqs. (12.7.3) and (127-4) Loaco + VNYCN200(0)+600(1.0 CM the water solution and y in the trichioroethane solution: 4x40 + miyAN#1 200(0 30) + 600(0) 0.075 (12.74 Using these coordinates, the point M is plotted in Fig, 12.7-3. We locate V,by rawing a line from Ly through M and extending it until it intersects the phase boundary. This gives yA is obtained. By substitut 0.0120 0.0196 0.02940.0476 0.04620.074 0.0571 0.0909 -0.08 and yci -0.90. For Lv a value of -0017 t kg/h and V 0.0833 0.1304 0.1081 0.1666 0.1316 0.2000 ng into Eqs. (12.7-1) and (12.7-2) and solving.L-1 664 kg/h. Sta ge-to-stage calculations for countercurrent extraction. has been made is to go stage by stage to determine The next step after an the concentrations at each stage I number of stages N needed to reach Lin Fig. 12.7-1 (a) Determine the minimum solvent