1. Fugacity 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. Which of the following will increase the fugacity of a component, A?
Convert from solid to liquid
Convert from liquid to solid
Decrease pressure
Dilute with component B
None of the above
ANSWER: E. None of the above.

3. What is the driving force for component A to move from liquid to vapor to reach equilibrium?
A. Pressure B. Entropy C. Enthalpy D. Concentration E. Gibbs free energy
Vapor yA
ANSWER:
Liquid xA

4. One component exists in two phases at the same temperature, but the phases are not in equilibrium. Which phase has the higher fugacity? α β
Same fugacity in each phase.
Not enough information.
0.1 mol/L
0.5 mol/L
α phase
ANSWER: D. Not enough information
ᵦ phase

5. One component exists in two phases at the same temperature, but the phases are not in equilibrium. What is the direction of mass transfer?
From α to β.
From β to α.
No mass transfer occurs.
Cannot predict direction.
0.005 mol/L
0.10 mol/L
α phase
ANSWER: D. Cannot predict direction.
ᵦ phase

6. Two identical flasks at 45°C are connected by a tube
Two identical flasks at 45°C are connected by a tube. Flask A contains water and flask B contains 50% more water plus it contains ethanol. As the system approaches equilibrium, _______________________.
H2O A B
H2O + EtOH
water moves from A to B
ethanol moves from B to A
water moves to B and ethanol moves to A
both water and ethanol move to A
there is no change in solution levels
ANSWER: C. water moves to B and ethanol moves to A. The components move in direction of lowest fugacity.

7. Two identical flasks are connected by a tube
Two identical flasks are connected by a tube. Flask A contains water at 40°C. Flask B contains 50% more water at 35°C. As the system approaches equilibrium, _______________.
H2O
40°C A B
35°C
water moves from A to B
water moves from B to A
no change occurs
ANSWER: A. water moves from A to B. The fugacity of water is higher at 40°C than 35°C so it moves to lower fugacity.

8. Two identical flasks are connected by a tube
Two identical flasks are connected by a tube. Flask A contains water at 40°C. Flask B contains 50% more water at 40°C. As the system approaches equilibrium, _______________.
H2O
40°C A B
water moves from A to B
water moves from B to A
no change occurs
ANSWER: C. no change occurs. The fugacity of water is the same in both containers so no driving force for mass transfer.

9. Two identical flasks contain water at 40°C and are connected by a tube
Two identical flasks contain water at 40°C and are connected by a tube. NaCl is added to flask B. As the system approaches equilibrium, ______________.
water moves from A to B
water moves from B to A
no change in levels occur
H2O
40°C A B
+ NaCl
ANSWER: A. water moves from A to B. The fugacity of water was lowered when salt was added so water moves to lower fugacity.

10. Two identical flasks are connected by a tube
Two identical flasks are connected by a tube. Flask A contains water at 45°C. Flask B contains twice the volume of A but is a 98% H2O/ 2% ethanol mixture at 55°C. As the system approaches equilibrium, _______.
H2O
45°C A B
98% H2O
+ 2% EtOH
55°C
water moves from A to B
ethanol moves from B to A
water moves to B and ethanol to A
both water and ethanol move to A
no change in levels occur
ANSWER: D. both water and ethanol move to A. The higher temperature in flask B increases the water’s fugacity. The temperature has a greater effect on the fugacity than the ethanol that slightly lowers the water’s fugacity. Both the water and ethanol fugacities are higher in flask B.

11. PH2Osat(25°C) = 3.2 kPa PH2Osat(22°C) = 2.6 kPa
Flask A contains a NaCl solution at 25°C in equilibrium with the pure water at 22°C in flask B.
PH2Osat(25°C) = 3.2 kPa PH2Osat(22°C) = 2.6 kPa
Estimate the fugacity of water in the NaCl solution.
3.2 kPa
2.6 kPa
< 2.6 kPa
> 3.2 kPa
> 2.6 kPa
NaCl
Solution
25oC A B
Pure H2O
22oC
ANSWER: B. 2.6 kPa. The fugacity of the water in the two solutions must be the same at equilibrium. The fugacity is essentially the same as the vapor pressure of the pure water at such a low pressure.

12. Two flasks at 45°C are connected by a tube
Two flasks at 45°C are connected by a tube. Flask A contains H2O, and flask B contains the same amount of an 80/20 mixture of H2O and NaCl. After 5 hours, ________.
H2O
45°C A B
80% H2O
+ 20% NaCl
Beaker A has more water
Beaker B has more water
The amounts of water do not change since they are at the same temperature
All the salt moves to beaker A
ANSWER: B. Beaker B has more water. The fugacity of the water in beaker B is lower, so water transfers from A to B.

13. Two flasks at 45°C are connected by a tube
Two flasks at 45°C are connected by a tube. Flask A contains water and NaCl. Flask B contains 50% more water and also contains NaCl. The system is at equilibrium. When 5 g of KCl is added to Flask B, _________________.
H2O
45°C
NaCl A B
45°C NaCl +
5 g KCl
water moves from B to A
water moves from A to B
KCl moves from B to A
nothing changes
ANSWER: B. water moves from A to B. The KCl lowers the water fugacity in B, so water moves from A to B.

14. Porous zeolite crystals
Adsorption concentrates a molecule on a surface from another phase. Consider hexane liquid and
vapor. The hexane concentration in the zeolite pores is ____________.
Vapor
Liquid A
Liquid
Vapor B
higher in A
higher in B
the same in both
Insufficient information
Porous zeolite crystals
ANSWER: C. the same in both. Fugacity is the same in both phases so the adsorbed concentration is the same.

15. Porous zeolite crystals
Two systems have acetone/hexane in vapor-liquid equilibrium at the same temperature. Acetone is enriched in the vapor phase. Both molecules adsorb on the zeolite surface, where they have a higher concentration than in the gas phase. Which arrangement will have a
higher concentration of
acetone adsorbed on the
zeolite crystals?
Porous zeolite crystals
Vapor
50/50
Liquid A B
ANSWER: A. Higher in A. The fugacity of the acetone is the same for the liquid and vapor when in equilibrium, so in container A the vapor has greater than 50% acetone. The fugacity of acetone is therefore greater in container A.
Higher in A
Higher in B
The same in both
Insufficient information

16. Porous zeolite crystals
Two systems have acetone/hexane in vapor-liquid equilibrium at the same temperature. Acetone is enriched in the vapor phase. Both molecules adsorb on the zeolite surface, where they have a higher concentration than in the gas phase. Which arrangement will have a
higher concentration of
acetone adsorbed on the
zeolite crystals?
Porous zeolite crystals
50/50 Vapor
Liquid A
50/50 Liquid
Vapor B
ANSWER: B. Higher in B. The fugacity of the acetone is the same for the liquid and vapor for a given container when in equilibrium. The vapor in container B no has greater than 50% acetone. The fugacity of acetone is therefore greater in container B.
Higher in A
Higher in B
The same in both
Insufficient information

17. A B As the pressure increases from point 1 to 2,
which figure shows an area proportional to the change
in Gibbs free energy? A B P V 1 2 P V 1 2
ANSWER: A. Delta G is the integral of VdP. Only the actual pressure change from point 1 to 2 should be included.

18. Which plot represents f vs. P for an ideal gas?B P f P f C D P f P f
ANSWER: B. For an ideal gas, fugacity is equal to pressure, and at zero pressure the fugacity is zero.

19. For the H-xA diagram at 80°C, what is the maximum value of the partial molar enthalpy of component A at 80°C?
100
100
50 cal/mol
22 cal/mol
85 cal/mol
100 cal/mol
0 cal/mol
H (cal/mol) 50 50
ANSWER: C. 85 cal/mol.
0.5
1.0 xA

20. An isotherm for a cubic equation of state is shown below
An isotherm for a cubic equation of state is shown below. Which line corresponds to a vapor-liquid equilibrium? A B C D E
Pressure
ANSWER: C. The fugacities are equal when the area above and below the pressure line are equal.
n/V

21. When both vapor and liquid are present, the fugacity at x1 = 0
When both vapor and liquid are present, the fugacity at x1 = 0.1 will be ________ at x1 = 0.3.
greater than
less than
equal to the value P
ANSWER: B. less than at x1 = 0.3 because the mol fraction is lower at x1 = 0.3.
0.1
0.3
0.5

22. When both vapor and liquid are present, the fugacity at x1 = 0
When both vapor and liquid are present, the fugacity at x1 = 0.1 will be ________ at x1 = 0.3, because ________.
greater than; pressure is higher
less than; mole fraction is lower
less than; partial pressure is higher
equal to the value; its at equilibrium. P
ANSWER: B. less than at x1 = 0.3, because the mole fraction is lower.
0.1
0.3
0.5

23. A metal box of fixed volume contains CO2 at a pressure of 2 bar
A metal box of fixed volume contains CO2 at a pressure of 2 bar. Through a valve you add CH4 at a constant rate and at constant temperature. Which plot represents how CH4 fugacity changes with time up to a total pressure of 20 bar? Assume ideal gases.
2 bar
Time
20 bar A
Time B
Time C
Time D
fugacity
ANSWER: D. The relationship of fugacity vs. time is linear, and at time = 0, the CH4 fugacity is 0.
0 bar
None of the above.

24. A metal box of fixed volume contains CO2 at 2 bar pressure
A metal box of fixed volume contains CO2 at 2 bar pressure. Methane was added at a constant rate and at constant temperature. Which is the most likely plot of CH4 fugacity vs. time up to a total pressure of 20 bar? Assume ideal gases.
2 bar
Time
20 bar A B C D
10 bar
ANSWER: B. The relationship of fugacity vs. time is linear, and at time = 0, the CH4 fugacity is 0.

25. Liquid water is in equilibrium with water vapor and air.
Ptot = 1.2 bar
PH2O = 0.1 bar
The fugacity of water is about __________.
0.1 bar.
1.2 bar.
1.00 (dimensionless).
Cannot be determined.
ANSWER:

26. The boiling point of water at 1 bar is 100°C.
At 150°C the boiling point is 4.7 bar. The fugacity of water at 150°C and 100 bar is closer to ______ bar. 1 5 50
100
ANSWER: B. 5 bar. As the pressure increases for a liquid, its fugacity does not change much. The fugacity would increase just slightly, so the fugacity at 150°C and 100 bar would be closest to the vapor pressure of water at 150°C.

27. When comparing steam at 100°C to water at 100°C, steam has a higher enthalpy, _______, and ________.
higher entropy, higher Gibbs free energy
higher entropy, the same Gibbs free energy
the same entropy, the same Gibbs free energy
lower entropy, lower Gibbs free energy
ANSWER: B. higher entropy, and the same Gibbs free energy.

28. 1 kg of ice and 1 kg of liquid water are at equilibrium at 0°C
1 kg of ice and 1 kg of liquid water are at equilibrium at 0°C. When liquid ethanol is added and the temperature is kept at 0oC, _______________.
some ethanol freezes
some water freezes
some ice melts
all the ice melts
all the ethanol freezes
ANSWER: D. all the ice melts. The fugacity of the liquid water decreases when ethanol is added, so the ice has higher fugacity. The driving force is then driven to the lower fugacity of the liquids.

29. Air is bubbled through a tank of water at 25oC and atmospheric pressure. The solubility of O2 in water is about mol% at 25oC. Estimate the fugacity of oxygen in the water.
1 bar
0.2 bar
0.5 bar
2 bar
bar
ANSWER: B. 0.2 bar. The partial pressure of oxygen in air is about 0.2 atm, which is also equal to the fugacity for this ideal gas. Since the fugacity of O2 in the liquid is equal to the fugacity in the vapor at equilibrium, the answer is B.

30. 1) V = 0.080 L/mol ; fugacity = 11 bar
A pure-component fluid is at 10 bar and 350 K. The Peng-Robinson equation of state has three real roots:
1) V = L/mol ; fugacity = 11 bar
2) V = 8 L/mol ; fugacity = 9 bar
The fluid is a ____________.
liquid
gas
2-phase mixture
supercritical fluid
ANSWER: B. gas. The lower fugacity is the stable state. This corresponds with the larger volume per mol, which is the vapor state.

31. 1) density = 25 mol/L; fugacity = 11 bar
A pure-component fluid is at 10 bar and 350 K. The Peng-Robinson equation of state has three real roots:
1) density = 25 mol/L; fugacity = 11 bar
2) density = 0.2 mol/L; fugacity = 9 bar
The fluid is a ____________.
liquid
gas
2-phase mixture
supercritical fluid
ANSWER: B. gas. The lower fugacity is the stable state. This corresponds with the lower density, which is the vapor.

32. Boiling point of water: Psat = 1.0 bar; Tsat = 100°C
The fugacity of water at 150°C and 100 bar is closer to __________.
1 bar
5 bar
50 bar
100 bar
ANSWER: B. 5 bar. The fugacity at saturation is close to 4.7 bar, and raising the pressure of the liquid does not increase the fugacity much.

33. Which of the following will increase the fugacity of a component, A?
Convert from solid to liquid
Convert from liquid to solid
Decrease pressure
Dilute with component B
None of the above
ANSWER: E. None of the above.

34. If you were to boil water on a stove in a small room for an hour, the fugacity of the ______________.
liquid increases
water vapor increases
liquid decreases
water vapor decreases
water stays the same in the vapor
H2O
ASNWER: B. water vapor increases.

35. Soda (liquid water with a low concentration of dissolved CO2) at 0°C is compressed to 5 bar so only a liquid phase remains. In the liquid phase, the fugacity of ___________.
water is higher
CO2 is higher
water and CO2 are the same
ANSWER: B. CO2 is higher. This is because in the gas phase, CO2 has a pressure orders of magnitude higher than the water pressure. If it is an ideal gas, the partial pressure is equal to the fugacity and the fugacity is the same in the liquid and the vapor.

36. A can of soda at 0°C contains liquid water with a low concentration of dissolved CO2. If the CO2 pressure in the can is slightly above 1 bar, which has a higher fugacity in the liquid phase?
Water
CO2
Fugacities of water and CO2 are equal
ANSWER: B. CO2. This is because in the gas phase, CO2 has a pressure orders of magnitude higher than the water pressure. If it is an ideal gas, the partial pressure is equal to the fugacity and the fugacity is the same in the liquid and the vapor.

37. When salt is added to pure water, what happens to the fugacity of the water?
increases
decreases
stays the same
ANSWER: B. Decreasing the mol fraction of water in the liquid phase decreases the fugacity of the water.

38. Pure NaCl was added to pure water until the water was saturated and the excess salt settled to the bottom of the container. What happened to the fugacity of the salt?
Increased
Decreased
Did not change
ANSWER:

39. Compared to the fugacity of pure water, the fugacity of water in a saline solution will be _________.
higher
lower
the same
ANSWER: B. Decreasing the mol fraction of water in the liquid phase decreases the fugacity of the water.

40. Pure NaCl was added to pure water until the water was saturated and the excess salt settled to the bottom of the container. The fugacity of the dissolved salt is __________ the fugacity of the pure NaCl.
higher
lower
the same as
ANSWER: C. the same as. Since the dissolved salt is in equilibrium with pure sodium chloride, they must have the same fugacities

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

42. Which component has the highest fugacity?
A sealed container of water is at high enough pressure so that no vapor is present. The water contains 0.2 mol% salt and 0.2 mol% CO2.
Which component has the highest fugacity?
Water
CO2
Salt
Same for all
ANSWER: