Solutions

1. Solutions Contributions by: John L. Falconer & Will MedlinDepartment of Chemical and Biological EngineeringUniversity of ColoradoBoulder, CO 80309-0424 Supported by the National Science Foundation

2. Phase a and b each contain component A. The two phases are not in equilibrium. The direction of mass transport of component A is ________. from a to b from b to a Cannot tell from this information. No mass transfer occurs. a CA=0.001 b • CA=0.020

3. Phase a and b each contain component A. The two phases are not in equilibrium. What is the direction of mass transport of component A? From a to b From b to a Cannot tell from this information No mass transfer occurs a CA=0.005 mol/L b • CA=0.100 mol/L

4. Consider two immiscible mixtures. The concentration of A is much greater in the bottom solution. The direction of mass transfer of component A is _________. into mixture 1 into mixture 2 Could be in either direction. No mass transfer occurs. Mixture 1 CA=0.001 Mixture 2 • CA=0.200

5. The concentration of A is different in two liquids that do not mix. What determines the direction of mass transfer of component A? Concentration Pressure Solubility Energy Other A in B • A in C

6. Phases a and b are comprised of component A. The two phases are not in equilibrium. If the system is at constant temperature, which phase has the higher fugacity? Phase a Phase b Both phases have same fugacity Not enough information a CA=0.01 mol/L b • CA=0.50 mol/L

7. Two liquid phases are in equilibrium at 2 bar. The bottom liquid is pure A; the top liquid is a mixture of A and B with xA = 0.05. If PAsat = 0.5 bar, PBsat = 0.8 bar, the fugacity of liquid A in the mixture is _____ bar. 1.0 0.8 0.5 0.1 0.05 Mixture of A & B xA=0.05 Liquid A

8. Compounds A and B do not mix, and compound B is more dense. This figure shows the situation immediately after the 3 mol% C in A was added on top of the 4 mol% C in B solution. Over time, compound C will _________. move from liquid A to liquid B move from liquid B to liquid A remains as they are since A & B are immiscible 3 mol% C in A gC = 2 4 mol% C in B gC = 1.1

9. This system is not in equilibrium. Which happens to reach equilibrium? Liquid evaporates Vapor condenses Cannot predict without more information Vapor C1= 0.25 kg/m3 75°C Water C1= 975 kg/m3

10. For the system below, which only contains component A, what will happen next? Some vapor will condense All the liquid will vaporize All the vapor will condense Some liquid will vaporize Vapor fAGas= 0.4 bar Liquid fALiq= 0.6 bar

11. These tubes, with an aqueous BSA* solution on the left and pure water on the right are at equilibrium. When you add salt to the pure water on the right, __________________. the water level on the right increases the BSA solution level on the left increases no change in the levels occur Aqueous BSA Pure water H2O permeable membrane *BSA= bovine serum albumin protein

12. An aqueous BSA* solution on the left left and pure water on the right are at equilibrium. When you add more BSA to the solution on the left, ___________________. the water level on the right increases the BSA solution level on the left increases no change in levels occur Aqueous BSA Pure water H2O permeable membrane *BSA= bovine serum albumin protein

13. These tubes each have an aqueous BSA* solution on the left and pure water on the right. A membrane that is only permeable to water separates the two sides. Which one is at equilibrium? B C D A H2O + BSA H2O + BSA H2O + BSA H2O + BSA H2O H2O H2O H2O *BSA= bovine serum albumin protein

14. Which component (A or B) has the higher molecule weight? Neither A nor B dissociates. A B They are the same Need more information H2O + 10 g A H2O + 10 g B H2O H2O H2O permeable membrane H2O permeable membrane

15. Which component (A or B) has the higher molecule weight? Neither A nor B dissociates. A B They are the same Need more information H2O + 10g A H2O + 20g B H2O H2O H2O permeable membrane H2O permeable membrane

16. A container with water and NaCl is boiling at 105°C on a stove. The amount of NaCl in the water is half of the maximum amount of salt that can dissolve. Which is the correct plot of the chemical potential of the liquid water versus time as the water boils away to 10% of its initial volume. None of the above. μ(l) Time Time Time Time A B C D

17. 8 8 8 Liquids A and B are immiscible. When each liquid is present, it exerts its own vapor pressure. A vapor contains a mixture of A and B at low pressure. The pressure is increased at constant temperature. At 4 bar, liquid A appears; At 6 bar, liquid B appears. Which is the correct plot of the partial pressures of A and B vs. total pressure? 6 6 6 Pi (bar) 4 4 4 2 2 2 0 0 0 0 0 0 2 2 2 4 4 4 6 6 6 8 8 8 Pressure (bar) Pressure (bar) Pressure (bar) A B C

18. 8 8 8 Components A and B are immiscible. When each liquid is present, it exerts its own vapor pressure. A vapor contains 5 mol A and 5 mol B at low pressure. The pressure is increased at constant temperature. At 4 bar, liquid A appears; At 6 bar, liquid B appears. Which is the correct plot of the partial pressures of A and B vs. total pressure? 6 6 6 Pi (bar) 4 4 4 2 2 2 0 0 0 0 0 0 2 2 2 4 4 4 6 6 6 8 8 8 Pressure (bar) Pressure (bar) Pressure (bar) A B C

19. When component A is mixed with component B, the activity coefficient of component A is greater than one for all mixtures. When component A is mixed with component C, the activity coefficient of component A is less than one for all mixtures. Which plot is closest for the fugacity of A vs. the mole fraction of A for A-B mixtures (red) and for A-C mixtures (blue)? A B C D fA (bar) mole fraction xA mole fraction xA mole fraction xA mole fraction xA

20. When component A is mixed with component B, the activity coefficient of component A is greater than one for all mixtures. When component A is mixed with component C, the activity coefficient of component A is less than one for all mixtures. Which plot is closest for the fugacity of A vs. the mole fraction of A for A-B mixtures (red) and for A-C mixtures (blue)? A B C D fA (bar) mole fraction xA mole fraction xA mole fraction xA mole fraction xA

21. A liquid containing 60 mol% salt and 40 mol% wateris in equilibrium with water vapor at 0.5 atm. Which species has the higher fugacity in the liquid? Salt Water Their fugacities are equal Need more information

22. Sugar was dissolved in hot tea until it was saturated. When the tea was cooled, the solution was supersaturated with sugar and not at equilibrium. The chemical potential of the sugar in the solution is _____________ solid sugar at the same temperature . higher than lower than the same as Insufficient information.

23. Sugar was added to pure water until the water was saturated and the excess sugar settled to the bottom of the container. If the reference state for sugar is solid sugar at 1 bar, the activity of the dissolved sugar is ______________. Zero The mole fraction of sugar in water < 0.1 1.0 None of the above

24. A liquid mixture that is 25% A and 75% B is in equilibrium with an ideal gas at 1 bar that is 60% A and 40% B. The chemical potential of component A is ___________ component B in the liquid phase. greater than less than the same as

25. If you add salt to water, what happens to the fugacity of the water? It increases It decreases It remains the same

26. When 10 mL of liquid water and 10 mL of liquid ethanol are mixed, the resulting solution has a volume of about 19 mL. Heat is also released during the mixing process. Which of the following statements is true? Water and ethanol form an ideal solution Water and ethanol are immiscible (i.e. separate into two layers) Water and ethanol repel each other in liquid mixtures Water and ethanol experience attractive interactions

27. Water and ethanol form an azeotrope at approximately 90% ethanol. From a 50/50 mixture of water-ethanol, which is currently below its bubble T, your aim is to produce a phase containing 95% ethanol. What can you do? Heat up the mixture to the bubble T Heat up the mixture to the dew T Heat up the mixture to a very high T (above the dew T) None of the above

28. Mixing two liquid compounds results in a decrease in the total Gibbs free energy of the system. Which of the following MUST be true? The solution is not ideal The two components attract each other The enthalpy of mixing is negative None of the above

29. For a 50/50 binary mixture, the activity coefficients in a modified Raoult’s law model of each component will be closest to ____________. one as the solution is more ideal one if the two components attract each other strongly zero if the components repel each other

30. Consider a 95/5 mixture of the acetone(1) ‐ acetic acid(2) system. Which component will have an activity coefficient closer to 1? Acetone Acetic acid Both should be close to 1.

31. Which of the following statements is true? For an ideal solution, __________. ΔHmix = 0 but HE > 0 ΔGmix = 0 but GE > 0 ΔSmix > 0 but SE = 0 ΔGmix < 0 but GE = 0 Answers C and D

32. When 1 mol ethylamine and 1 mol acetylacetone are mixed adiabatically, starting at 15°C, the mixture would be __________ 15oC. The excess enthalpy plot is shown in the figure. greater than less than equal to Depends on SE 0.30 0.25 0.20 0.15 HE 0.10 0.05 0.00 0 0.25 0.5 0.75 1 x1

33. Which curve is for component 1 of a binary mixture? A B A or B B 2.6 A 2.2 Activity coefficients 1.8 1.4 1.0 0 0.25 0.5 0.75 1 x1

34. A A A A A yi yi yi yi yi Which is the correct plot of Helmholtz free energy vs. the mole fraction for a binary, ideal liquid solution at constant temperature? A B C D E

35. As the mole fraction of a species in an ideal solution approaches one, its partial molar Gibbs free energy ____________. increases decreases remains the same depends on the mole fraction

36. As the mole fraction of a species in an ideal solution approaches one, its partial molar entropy _______. increases decreases remains the same

37. Which statement is most likely correct if molecule 1 is represented by blue and molecule by red? A = 1 B = 2 a22 = a11 a21 > a12 a12 > a22 & a12 > a11 a12 < (a11a22)½ a12 = a11a22