1. Phase Equilibrium: Two Components
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. The pressure increases for a 50/50 vapor mixture of A and B that is initially at a low pressure. The liquid is ideal. Which plot corresponds to how xA and yA change with pressure at constant temperature if PAsat > PBsat ? A B C D E
0.5
1.0 P yA xA
ANSWER: B. Composition has to be equal to the bulk composition at the endpoints, and satisfy a mass balance such that y and x straddle the bulk composition.

3. The pressure increases for a 50/50 vapor mixture of A and B that is initially at a low pressure. The liquid is ideal. Which plot corresponds to how xB and yB change with pressure if PAsat > PBsat ?
0.5
1.0 P yB xB yB xB
0.5
1.0 P
0.5
1.0 P yB xB A B C yB xB
0.5
1.0 P yB xB
0.5
1.0 P
ANSWER: C. Composition has to be equal to the bulk composition at the endpoints, and satisfy a mass balance such that y and x straddle the bulk composition. D E

4. Isotherm for 60-40 benzene/hexane mixture
Which is the VLE line that most likely connects liquid and vapor phases in equilibrium for a benzene-hexane mixture? x
Isotherm for benzene/hexane mixture A B C
None of these A P B C
ANSWER: B. Equal-area rule applies for equal fugacities. V

5. Which is the VLE line that most likely connects liquid and vapor phases in equilibrium for a pentene-octene mixture?
Isotherm for pentene/octene mixture A B C
None of these A x P x B x x x x C x x
ANSWER: B. B. The line has to be at constant pressure. Also, pentene will be enriched in the vapor phase so the red line would be the vapor and the black the liquid so line B D
Isotherm for pentene/octene mixture V

6. Which of these diagrams are not possible?
xA, yA P
P-x
P-y
xA, yA P
P-y
P-x 1 2
2 & 6
1, 4, & 6
2 & 5
2, 3, & 5
3 & 5
xA, yA P
P-x
P-y
xA, yA P
P-x
P-y 3 4
ANSWER: D. 2, 3, and because higher pressure causes formation of vapor, 3 because it implies separation into two vapor phases, 5 because high P at compositions greater than 40% A or so leads to formation of vapor.
xA, yA P
P-x
P-y
xA, yA P
P-x
P-y 5 6

7. Mg and Si form the compound Mg2Si
Mg and Si form the compound Mg2Si. At constant pressure, what is the composition of the system when xSi= 0.4 and T = 1000 K?
T (K)
1600
1200
800
1.0
0.5
mole fraction of Si
liquid Mg Si
Mg2Si
One solid phase
Pure Si and Mg
Si and Mg2Si
ANSWER: C. Si and Mg2Si

8. Mg and Si form the compound Mg2Si
Mg and Si form the compound Mg2Si. At constant pressure, what is the composition of the system when xSi= 0.6 and T = 1000 K?
T (K)
1600
1200
800
1.0
0.5
mole fraction of Si
liquid Mg Si
One solid phase containing Mg and Si
Two solid phases: 40% Si, 60% Mg2Si
Two solid phases: 60% Si, 40% Mg2Si
Two solid phases: each contain Si & Mg
Mg2Si
ANSWER: B. Two solid phases: 40% Si, 60% Mg2Si. Apply lever rule.

9. This figure shows saturated liquid and saturated vapor lines for a 2-component system. Which of these are equilibrium compositions and temperature?
x1= 0.6, y1=0.9, 245°C
x1= 0.6, y1=0.3, 210°C
x1= 0.9, y1=0.6, 200°C
x1= 0.6, y1=0.3, 250°C
ANSWER: B. x1= 0.6, y1=0.3, 210°C. Equilibrium must be at the same P and T so needs to be a point when vapor line of one compostion intersects liquid line of another compostion. Also, the saturation pressure of component 1 (x1=1 line ) is lower than the saturation pressure of component 2 (x1 = 0 line), so y1,x1
At 210C, the solid line for x1=0.6 ,which is the liquid, interests the dashed line for y1-0.3, which is the vapor.

10. the mole fraction of A in the liquid phase __________.
A tank contains a 50/50 mixture of A and B (yA = 0.6). As the vapor is removed and the liquid boils away,
the mole fraction of A in the liquid phase __________.
increases
decreases
remains the same
ANSWER: B. decreases because A is enriched in the vapor phase

11. (Note: Tsat(methanol) = 65°C, Tsat(ethanol) = 78°C)
A closed system has methanol and ethanol in vapor-liquid equilibrium at 1 bar and 65°C. The temperature of the system is raised to 70°C at 1 bar. If two phases are still present, how do the methanol mole fractions change for each phase?
(Note: Tsat(methanol) = 65°C, Tsat(ethanol) = 78°C)
xm increases, ym decreases
xm increases, ym increases
xm and ym do not change
xm decreases, ym decreases
xm decreases, ym increases
ANSWER: D. xm increases, ym increases. Refer to a Txy diagram

12. We want to separate 50/50 mixtures of C6 isomers in the gas phase
We want to separate 50/50 mixtures of C6 isomers in the gas phase. As the temperature was lowered, your technician observed that n-hexane (n-C6) condensed before 2,2, dimethylbutane (DMB). Can this happen?
Yes, if n-C6 has a lower vapor pressure than DMB
Yes, if n-C6 has a higher vapor pressure than DMB
No, because both species have to condense
It depends on the system pressure as to whether one or two species condense.
ANSWER: C. No, because both species have to condense

13. A mixture of n-hexane and acetone were in the liquid phase in a piston-cylinder at 1 bar pressure. As the temperature increased, your technician observed that acetone evaporated first. Can this happen?
Yes, if acetone has the higher Psat
Yes, if n-hexane has the higher Psat
No, both species evaporate
It depends on the system pressure as to whether one or two species evaporate
ANSWER: C. No, both species have to evaporate

14. A mixture of n-hexane and acetone were in the liquid phase in a piston-cylinder at 1 bar pressure. As the pressure decreased, your technician observed that acetone evaporated first. Can this happen?
Yes, if acetone has the higher Psat
Yes, if n-hexane has the higher Psat
No, both species evaporate
It depends on the system pressure as to whether one or two species evaporate
ANSWER: C. No, both species evaporate

15. A mixture of water and acetone was placed in an open beaker in a room
A mixture of water and acetone was placed in an open beaker in a room. The next morning, 90% of the acetone had evaporated, but none of the water had evaporated. Can this happen?
Yes, if acetone has the higher Psat
Yes, if n-hexane has the higher Psat
No, both species evaporate
It depends on the system pressure as to whether one or two species evaporate
ANSWER: C. No, both species evaporate

16. Will this system exhibit an azeotrope at 100°C?
At 100°C, PAsat = PBsat.
Will this system exhibit an azeotrope at 100°C?
Yes No
Maybe…need more information.
ANSWER: A. Yes. Not possible to have vapor and liquid compostion the same for the entire compostion range so the pressure above the liquid must be above or below horizontal

17. Which statement is not correct?
A binary mixture that has a minimum boiling point azeotrope ____________.
has a maximum pressure azeotrope
has one composition where the boiling point does not change as liquid evaporates
cannot be modeled by a modified Raoult’s Law
allows for either component 1 or 2 to be enriched in the vapor phase, depending on the liquid composition
has activity coefficients greater than one
ANSWER: C. cannot be modeled by a modified Raoult’s Law.

18. A liquid mixture of 50 mol% n-pentane (Psat = 5 bar) and 50 mol% n-heptane (Psat = 1 bar) is at high pressure. The mixture is partially vaporized by isothermally lowering the pressure to just below 3 bar. Which statement is correct?
n-heptane is enriched in the gas phase
n-pentane is enriched in the gas phase
The gas phase has a 50/50 composition
No vapor forms
ANSWER: B. n-pentane is enriched in the gas phase.

19. Often, wine or beer is added to soup that is then
simmered. When the soup is ready to be served,
what has happened to the alcohol?
It all evaporates
It all remains in the soup
Some of it evaporates
ANSWER: C. VLE for a liquid of water and alcohol would have the vapor enriched in alcohol but it would not all evaporate.

20. ________ is the driving force for component A to move from liquid to vapor in order to reach equilibrium.
Pressure
Entropy
Enthalpy
Concentration
Gibbs free energy
ANSWER: E. Gibbs free energy. The fugactiy or chemial potential or the Gibbs free energy represent driving forces for mass transfer

21. 1. 0 mol of CH4 at 1 atm and 50°C is mixed with 1
1.0 mol of CH4 at 1 atm and 50°C is mixed with 1.0 mol of O2 at 1 atm and 50°C. The final mixture is at 2.0 atm and 50°C. Assume ideal gases. The Gibbs free energy change is _______.
positive
negative
zero
ANSWER: C. The enthalpy does not change since ideal gases. (G = H-TS)
The entropy does not change because the partial pressure of CH4 does not change and the partial pressure of O2 does not change and the entropy change is related to the ln of of the ratio of partial pressures.

22. An n-butane/n-heptane mixture is in vapor-liquid equilibrium
An n-butane/n-heptane mixture is in vapor-liquid equilibrium. The liquid composition is 30% n-butane. Which of these vapor compositions (% n-butane) are not possible?
20%
40%
60%
80%
All of these compositions are possible
ANSWER: A. 20%. The vapor pressure of n-butane is lower than that of n-heptane so the vapor must be enriched in n-butane

23. Consider a system at equilibrium that contains n-hexane and water, which are immiscible in the liquid phase. Which set of phases could not exist?
Two Liquids (hexane + H2O)
Hexane liquid and two vapors (hexane + H2O)
Two Liquids (hexane + H2O) and hexane vapor
H2O liquid and two vapors (hexane + H2O)
None of the above
ANSWER: C. Not possible to have liquid water and vapor space above it and no water vapor.

24. Consider a 1 L constant-volume container with n-hexane in VLE
Consider a 1 L constant-volume container with n-hexane in VLE. If half the volume is liquid and 0.1 L of liquid H2O is added to the container, what happens? Assume constant temperature and that water is immiscible with n-hexane.
Some hexane evaporates
Some hexane condenses
All the H2O evaporates
Some water evaporates and some hexane condenses
All the hexane evaporates
ANSWER: D. The two components do not interact in liquid phase so they each exert their own vapor pressure. Some n-hexane will condense because less vapor volume available. Some water will evaporate to get to VLE but not all because 0.1 L of liquid water would occupymuch more than 0.4 L of vapor volume.
ALTERNATIVE:
1) another answer: some hexane evaporates and some water evaporates

25. PAsat > PBsat > PCsat
An ideal liquid solution that is 30% A, 30% B, and 40% C is heated at a constant temperature until 80% of the original liquid has evaporated. Which component would you expect to have completely evaporated at that point?
PAsat > PBsat > PCsat
Component A
Component B
Component C
None of them
ANSWER: D. None of them. Must have each component in each phase for equilibrium

26. PAsat = 1.5; PBsat = 1.0 bar ; T = 70°C
Assume ideal gas and ideal solution behavior for the A-B system:
PAsat = 1.5; PBsat = 1.0 bar ; T = 70°C
What is the total pressure at equilibrium above a liquid that is 60% A and 40% B
2.5 bar
1.5 bar
1.2 bar
1.0 bar
None of the above
ANSWER: C bar.

27. Which of the following statements is NOT true at an azeotrope?
xA = yA
xA = xB
None of the above
ANSWER: B. xA = xB

28. One mole of component A is in VLE at 1 bar and 75°C
One mole of component A is in VLE at 1 bar and 75°C. One mole of B is added to form a mixture, and the pressure is isothermally increased to 2 bar. What is the state of the system? The vapor pressure of B at 75°C is 2 bar. Assume A and B form an ideal solution.
VLE
All liquid
All vapor
ANSWER: B. All liquid.

29. Which of the following is true for a binary azeotrope at low pressure?
The activity coefficients of the two components are the same
The vapor pressures of the two components are the same
The value of the vapor pressures multiplied by the activity coefficients are the same
None of these
ANSWER: C. The value of the vapor pressures multiplied by the activity coefficients are the same

30. Are there conditions in which liquid water (or solid ice) at atmospheric pressure will not have a vapor phase partial pressure when in contact with nitrogen? (Assume the system is below the normal boiling point of nitrogen).
No.
Yes, if the temperature is low enough
Yes, if the temperature is high enough
ANSWER: B. Yes, if the temperature is low enough

31. At 105°C: P1sat = 1.8 bar, P2sat = 1.2 bar
You want to completely condense a vapor containing
50% methanol(1) and 50% ethanol(2). What is the minimum pressure at which the condenser must operate at 105°C?
 At 105°C: P1sat = 1.8 bar, P2sat = 1.2 bar
3.0 bar
1.8 bar
1.5 bar
1.2 bar
ANSWER: C. 1.5 bar

32. At what temperature is 58.7 mol% ethane liquid not in equilibrium with a vapor?
T (°F) P
700
100
300
500 M
88.7 mol% ethane
77.1 mol% ethane
26.5 mol% ethane
Critical locus
CC2H6
CC7H16
58.7 mol% ethane
335 °F
275 °F
315 °F
400 °F
ANSWER: D. Both phases are not present at 400F.

33. 58.7 mol% ethane liquid is in equilibrium with what ethane mol% vapor composition?
T (°F) P
700
100
300
500 M
88.7 mol% ethane
77.1 mol% ethane
26.5 mol% ethane
Critical locus
CC2H6
CC7H16
58.7 mol% ethane
77.1
88.7
26.5
All of those shown
A & B
ANSWER: E. The liquid phase intersects with the other two compositions.

34. When the binary interaction parameter, kij, increases, for a fixed liquid phase, fixed temperature system, the equilibrium pressure ________.
increases
decreases
remains the same
ANSWER: A.

35. A liquid mixture containing species A & B is boiled by increasing the temperature at constant pressure. The saturation pressure is greater for A than for B. What happens?
xA increases and yA increases
xA increases and yA decreases
xA decreases and yA decreases
xA decreases and yA increases
ANSWER: C. Observing a Txy diagram for this system, as temperature is increased from liquid phase to eventual vapor phase, the more volatile component A will decrease its molar composition in the liquid and vapor phases as T is increased.

36. What is the fraction of this mixture that is liquid?
1/3
2/3 70 80 90
100
110
120
130
140
0.2
0.4
0.6
0.8 1 X
, Y
Temperature
T-x
T-y
ANSWER: A. Lever rule applies at equilibrium composition.