In the process of distillation, a mixture of two (or more) volatile liquids is first heated to convert the volatile materials to the vapor state. Then the vapor is condensed, reforming the liquid. The net result of this liquid n vapor n liquid conversion is to enrich the fraction of a more volatile component in the mixture in the condensed vapor. We can describe how this occurs using Raoult’s law. Imagine that you have a mixture of 12% (by weight) ethanol and water (as formed, for example, by fermentation of grapes).
(a) What are the mole fractions of ethanol and water in this mixture?
(b) This mixture is heated to 78.5°C (the normal boiling point of ethanol). What are the equilibrium vapor pressures of ethanol and water at this temperature, assuming Raoult’s law (ideal) behavior? (You will need to derive the equilibrium vapor pressure of water at 78.5°C from data in Appendix G.)
(c) What are the mole fractions of ethanol and water in the vapor?
(d) After this vapor is condensed to a liquid, to what extent has the mole fraction of ethanol been enriched? What is the mass fraction of ethanol in the condensed vapor?

Data given in Appendix G

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TABLE 15 Temperature (°C) -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Vapor Pressure of Water at Various Temperatures Vapor Pressure (torr) 2.1 2.3 2.5 2.7 2.9 3.2 3.4 3.7 4.0 4.3 4.6 4.9 5.3 5.7 6.1 6.5 7.0 7.5 8.0 8.6 9.2 9.8 10.5 11.2 12.0 12.8 13.6 14.5 15.5 16.5 17.5 Temperature (°C) 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Vapor Pressure (torr) 18.7 19.8 21.1 22.4 23.8 25.2 26.7 28.3 30.0 31.8 33.7 35.7 37.7 39.9 42.2 44.6 47.1 49.7 52.4 55.3 58.3 61.5 64.8 68.3 71.9 75.7 79.6 83.7 88.0 92.5 Temperature (°C) 51 7839 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 Vapor Pressure (torr) 97.2 102.1 107.2 112.5 118.0 123.8 129.8 136.1 142.6 149.4 156.4 163.8 171.4 179.3 187.5 196.1 205.0 214.2 223.7 233.7 243.9 254.6 265.7 277.2 289.1 301.4 314.1 327.3 341.0 355.1 Temperature (°C) 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 Vapor Pressure (torr) 369.7 384.9 400.6 416.8 433.6 450.9 468.7 487.1 506.1 525.8 546.1 567.0 588.6 610.9 633.9 657.6 682.1 707.3 733.2 760.0 787.6 815.9 845.1 875.1 906.1 937.9 970.6 1004.4 1038.9 1074.6