Separation Process Principles- 2n - Seader & Henley - Solutions Manual

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Unformatted text preview: tinued) Analysis: (continued) To calculate y-x and T-x-y curves from vapor pressure data, using Raoult's and Dalton's laws, Eq. (2-44 ) applies, as well as the sum of the mole fractions in the phases in equilibrium. Thus, KA = s yA PA T = xA P yA + y B = 1 s yB PB T = xB P , KB = , xA + x B = 1 (1, 2) (3, 4) Exercise 4.8 (continued) Analysis: (continued) Equations (1) to (4) can be reduced to the following equations for the mole fractions of benzene (A) in terms of the K-values: xA = 1 − KB KA − KB , y A = KA x A (5, 6) If the given vapor pressure data in Exercise 4.6 for benzene, and this exercise for toluene are fitted to Antoine equations, we obtain: PAs = exp 15.5645 − 2602.34 T + 211.271 (7) 3896.3 (8) T + 255.67 Where vapor pressure is in torr and temperature is in oC. Solving, Eqs. (1) to (8), PBs = exp 17.2741 − T, oC Ps of A, torr Ps of B, torr 80.1 82.5 85.0 87.5 90.0 92.5 95.0 97.5 100.0 102.5 105.0 107.5 110.0 110.5 759.9 817.4 880.8 948.0 1019.1 1094.1 1173.4 1256.9 1345.0 1437.6 1535.0 1637.3 1744.7 1766.8 290.0 314.9 342.7 372.5 404.4 438.5 474.9 513.7 555.2 599.3 646.2 696.1 749.1 760.1 KA KB xA yA 0.9998 1.0755 1.1590 1.2474 1.3409 1.4396 1.5439 1.6539 1.7697 1.8916 2.0198 2.1544 2.2957 2.3248 0.3816 0.4144 0.4510 0.4901 0.5321 0.5769 0.6249 0.6760 0.7305 0.7885 0.8503 0.9159 0.9856 1.0001 1.000 0.886 0.775 0.673 0.579 0.490 0.408 0.331 0.259 0.192 0.128 0.068 0.011 0.000 1.000 0.953 0.899 0.840 0.776 0.706 0.630 0.548 0.459 0.363 0.259 0.146 0.025 0.000 Plots of y-x and T-x-y based on the above table from Raoult's law calculations are shown on the next page. When the y-x plot is compared to the previous y-x plot based on a constant relative volatility, it is seen that, for a given value of x for benzene, the values of y for benzene are in fairly close agreement. From the above table, the Raoult's law αA,B = PAs / PBs ranges from 2.62 at 80.1oC to 2.32 at 110.5oC. Analysis: (continued) Exercise 4.8 (continued) Exercise 4.8 (continued) Analysis: (continued) (a) To find the temperature at 25 mol% vaporization, starting with a liquid mixture of 70 mol% benzene and 30 mol% toluene, extend a dashed, vertical line upward from point M on the T-y-x diagram on the previous page until point B is reached. At this point, using the inverse lever-arm rule, the ratio of the AB line length to the BC line length is 25/75. The temperature is 88oC. The benzene mole fraction of the equilibrium vapor when condensed is the same as the equilibrium vapor at point C or 0.88. The benzene mole fraction in the residue liquid is the same as the equilibrium liquid at point A or 0.65. (b) The Raoult's law K-values are included in the above table, and are plotted below. Exercise 4.9 Subject: Vapor-liquid equilibrium for n-heptane (A) - toluene (B) system at 1 atm Given: Vapor pressure data for n-heptane and toluene, and experimental T-y-x data. Assumptions: Raoult's and Dalton's laws Find: (a) x-y plot based on n-heptane, the most volatile component. (b) T-x bubble-point...
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