1. Solutions Contributions by:
John L. Falconer & Will Medlin Department of Chemical and Biological Engineering University of Colorado Boulder, CO
Supported by the National Science Foundation

2. Phase a and b each contain component A
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.
CA=0.001
CA=0.020 a b
ANSWER: C. Cannot tell from this information. No info is given on which phase has the higher fugacity of A.

3. Phase a and b each contain component A
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
CA=0.005 mol/L
CA=0.100 mol/L a b
ANSWER: C. Cannot tell from this information. . No info is given on which phase has the higher fugacity of A.

4. Consider two immiscible mixtures
Consider two immiscible mixtures. The concentration of A is much greater in the bottom solution. The direction of mass transfer of component A is _________.
CA=0.001
CA=0.200
Mixture 1
into mixture 1
into mixture 2
Could be in either direction.
No mass transfer occurs.
Mixture 2
ANSWER: C. Could be in either direction. Cannot tell direction without fugacity data.

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

6. Phases a and b are comprised of component A
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?
CA=0.01 mol/L
CA=0.50 mol/L a
Phase a
Phase b
Both phases have same fugacity
Not enough information b
ANSWER: D. Not enough info.

7. Two liquid phases are in equilibrium at 2 bar
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 = If PAsat = 0.5 bar, PBsat = 0.8 bar, the fugacity of liquid A in the mixture is _____ bar.
Mixture of
A & B
xA=0.05
Liquid A
1.0
0.8
0.5
0.1
0.05
ANSWER: C. 0.5 bar. Fugacity of liquid A is close to its vapor pressure and fugacity of A is the same in both phases when at equilibrium.

8. Compounds A and B do not mix, and compound B is more dense
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 _________.
3 mol%
C in A
gC = 2
4 mol%
C in B
gC = 1.1
move from liquid A to liquid B
move from liquid B to liquid A
remains as they are since A & B are immiscible
ANSWER: A. move from liquid A to liquid B. Fugacity of C is initially higher in solution A.

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
ANSWER: C. Cannot predict without more information. Fugacity, not concentration, is the driving force. Need more info such as the vapor pressure.
Water
C1= 975 kg/m3

10. For the system below, which only contains component A, what will happen next?
Liquid
fALiq =
0.6 bar
Vapor
fAGas =
0.4 bar
Some vapor will condense
All the liquid will vaporize
All the vapor will condense
Some liquid will vaporize
ANSWER: D. Some liquid will vaporize. Mass transfer takes place from high to low fugacity.

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
ANSWER: A. the water level on the right increases. Adding salt to the pure water decreases its fugacity, so water moves across the membrane from the BSA (high fugacity) to the water and salt (low fugacity).
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
ANSWER: B. the BSA solution level on the left increases. There is no change in fugacity of the water in the BSA solution by adding more of the same solution so only the level of the BSA solution increases.
H2O permeable
membrane
*BSA= bovine serum albumin protein

13. A B C D 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? A B C D
ANSWER: B. The water must have the same fugacity on both sides.
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
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
ANSWER: B. There are fewer moles for 10 g of B because the osmotic pressure is lower.
H2O permeable
membrane
H2O permeable
membrane

15. Which component (A or B) has the higher molecule weight
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
ANSWER: B. B, It takes twice as many grams of B to have the same osmotic pressure so its moleuclar weight is greater.
H2O permeable
membrane
H2O permeable
membrane

16. A container with water and NaCl is boiling at 105°C on a stove
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.
μ(l)
Time A
Time B
Time C
Time D
ANSWER: C. The chemical potential of the water will decrease as its mole fraction decreases, then will remain constant as solution becomes saturated with salt.
None of the above.

17. Liquids A and B are immiscible
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? 2 4 6 8
Pi (bar)
Pressure (bar) A 2 4 6 8
Pressure (bar) B 2 4 6 8
Pressure (bar) C
ANSWER: A.

18. Components A and B are immiscible
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? 2 4 6 8
Pi (bar)
Pressure (bar) A 2 4 6 8
Pressure (bar) B 2 4 6 8
Pressure (bar) C
ANSWER: A.

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
ANSWER: B.
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
ANSWER: B.
fA (bar)
mole fraction xA
mole fraction xA
mole fraction xA
mole fraction xA

21. Which species has the higher fugacity in the liquid?
A liquid containing 60 mol% salt and 40 mol% water is 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
ANSWER: B. Water. The fugacity of the water in its liquid state is equal to fugacity of water in its vapor state.

22. Sugar was dissolved in hot tea until it was saturated
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.
ANSWER: A. higher than. The chemical potential is higher because the driving force is for sugar to come out of solution and precipitate as a solid.

23. 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
ANSWER: A. greater than component B in the liquid phase. The partial pressure in the gas phase is equal to the fugacity for an ideal gas, and the fugacity of the gas is the same as the fugacity of the liquid.

24. If you add salt to water, what happens to the fugacity of the water?
It increases
It decreases
It remains the same
ANSWER: B. It decreases. Fugacity decreases as mole fraction decreases

25. 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
ANSWER: D. Water and ethanol experience attractive interactions. Smaller volume of mixture than the sum of the individual components because of the attractive interactions.

26. Water and ethanol form an azeotrope at approximately 90% ethanol
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
ANSWER: D. None of the above.

27. 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
ANSWER: D. None of the above. Gibbs free energy decreases when a mixture forms.

28. 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
ANSWER: A. one as the solution is more ideal.

29. Consider a 95/5 mixture of the acetone(1) ‐ acetic acid(2) system
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.
ANSWER: A. Acetone. As x approaches 1, approach Raoult's Law behavior.

30. 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
ANSWER: E Answers C and D.

31. 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.
0.25
0.5
0.75
0.10
0.15
0.30
0.00 1 HE x1
0.20
0.05
greater than
less than
equal to
Depends on SE
ANSWER: B. less than 15oC. If mixed isothermal, the product (the mixture) has more enthalpy than the starting materials. Since this is done adiabatically, must cool down the mixture to get the energy for mixing. That is, this same as an endothermic reaction, where products have more energy than reactants.

32. Activity coefficients
Which curve is for component 1 of a binary mixture?
0.25
0.5
0.75
1.8
2.6
1.0 1
Activity coefficients x1
2.2
1.4 B A
ANSWER: B. B. The pure component activity coefficient must approach one as its mole fraction goes to one. A B
A or B

33. Which is the correct plot of Helmholtz free energy vs
Which is the correct plot of Helmholtz free energy vs. the mole fraction for a binary, ideal liquid solution at constant temperature? yi A yi A yi A A B C
ANSWER: C. Helmholtz free energy (A)= U –TS. yi A yi A D E

34. 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
ANSWER: A. increases. Entropy change is minimized.

35. As the mole fraction of a species in an ideal solution approaches one, its partial molar entropy _______.
increases
decreases
remains the same
ANSWER: B. decreases. Partial molar entropy approaches minimum at pure component (no mixing).

36. Which statement is most likely correct if molecule 1 is represented by blue and molecule by red?
a22 = a11
a21 > a12
a12 > a22 & a12 > a11
a12 < (a11a22)½
a12 = a11a22
ANSWER: D. a12 < (a11a22)½