Solutions to Exam 3 - Chemistry Engineering Thermodynamics | CHE 344, Exams of Chemistry

Download Solutions to Exam 3 - Chemistry Engineering Thermodynamics | CHE 344 and more Exams Chemistry in PDF only on Docsity! ChE 344 Spring 2008, Exam III Closed Everything. Be neat. Number of questions 3, Total Points 80 1. (35 points) The following questions are based on these phase diagrams. There is a Pxy and a Txy diagram for a binary, ideal gas/ideal liquid system and a Pxy diagram at a fixed temperature where the gas mixture behaves ideally, but the liquid mixture is non-ideal (the labels for the y axes have been deliberately left out, in some cases) 1. For the ideal gas/ideal liquid system, what is the vapor pressure of the less volatile component? Solution: Look at the Pxy diagram, since we want a vapor pressure. The answer is 60. 2. You are watching a binary vapor mixture being cooled down, the temperature at which the first liquid appears is 75 and that at which the last vapor disappears is 73. What is the composition of the more volatile component? (this is an ideal gas/ideal liquid system) Solution: 3. At a given temperature, you are lowering the pressure. The first liquid appears at a pressure of about 93 and it condenses completely at a pressure of 80. Are your observations right? if not, tell me why. 4. In an non-ideal liquid, ideal gas system, at a pressure of 70, write down the com- position of the liquid and vapor phase that are in equilibrium with each other. Is there more than one pair? 5. You have a mixture that is 50 % vapor, 50 % liquid, at a pressure of 60. What is the composition of the liquid that was flashed to get this 50/50 mixture? 6. In the non-ideal liquid/ideal gas system, as you lower the pressure, you notice that all of the vapor suddenly turns into a liquid. At what pressure does this transformation occur? 7. You have a vapor phase in equilibrium with a liquid phase in the non ideal liq- uid/ideal gas system. You determine that the mole fraction of the less volatile component in the vapor phase is 0.6. Can you calculate the activity coefficients? 3. Consider now a binary mixture flashed at 75 kPa and 90oC. Someone tells you that the composition of the liquid stream, x1 = 0.1604 and that of the vapor stream y1 = 0.2919. Can this be correct? If not, why not? Solution: var (’y1’) A1 = 13.7819 B1 = 2726.81 C1 = 217.572 A2 = 13.9320 B2 = 3056.96 C2 = 217.625 T = 90.0 x1 = 0.1604 P1S = exp(A1 - B1/(T + C1)) P2S = exp(A2 - B2/(T + C2)) y1 = x1*P1S/75.0 We get y1 = 0.291921121143910 Solution: 3. (15 points) If Raoult’s law is valid, show that the equilibrium mole vapor-phase fraction y1 corresponding to an equimolar liquid mixture is y1 = P S1 P S1 + P S 2 . Show that this is also valid for vapor liquid equilibrium described by xiγiP S i = yiP where ln(γ1) = Ax 2 2 and ln(γ2) = Ax 2 1 Solution: var(’P1S P2S P y1’) eq1 = 0.5*P1S + 0.5*P2S == P eq2 = y1*P == 0.5*P1S solutions = solve([eq1,eq2],y1,P,solution_dict=True) for solution in solutions: print solution[y1] myy1 = solution[y1] We get y1 = P1S P2S + P1S var(’P1S P2S gamma1 gamma2 P y1’) eq1 = 0.5*P1S + 0.5*P2S == P eq2 = y1*P == 0.5*P1S solutions = solve([eq1,eq2],y1,P,gamma1,gamma2,solution_dict=True) for solution in solutions: print solution[y1] myy1 = solution[y1] And we get y1 = P1S P2S + P1S 126 116 4186 fF 96 fF 58 4.4 Hole Fraction 6.6 ts or y} 4,8