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FugacityContributions by:
John L. Falconer & Will MedlinDepartment of Chemical and Biological Engineering
University of ColoradoBoulder, CO 80309-0424
Supported by the National Science Foundation
Which of the following will increase the fugacity of a component, A?
A. Convert from solid to liquid
B. Convert from liquid to solid
C. Decrease pressure
D. Dilute with component B
E. None of the above
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
VaporyA
LiquidxA
0.1 mol/L
0.5 mol/L
One component exists in two phases at the same temperature, but the phases are not in equilibrium. Which phase has the higher fugacity?
A. α
B. β
C. Same fugacity in each phase.
D. Not enough information.
α phase
ᵦ phase
0.005 mol/L
0.10 mol/L
One component exists in two phases at the same temperature, but the phases are not in equilibrium. What is the direction of mass transfer?
A. From α to β.
B. From β to α.
C. No mass transfer occurs.
D. Cannot predict direction.
α phase
ᵦ phase
H2O
A B
H2O +EtOH
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, _______________________.
A. water moves from A to B
B. ethanol moves from B to A
C. water moves to B and ethanol moves to A
D. both water and ethanol move to A
E. there is no change in solution levels
H2O
40°C
A B
H2O
35°C
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, _______________.
A. water moves from A to B
B. water moves from B to A
C. no change occurs
H2O
40°C
A B
H2O
40°C
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, _______________.
A. water moves from A to B
B. water moves from B to A
C. no change occurs
H2O
40°C
A B
H2O
40°C+
NaCl
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, ______________.
A. water moves from A to B
B. water moves from B to A
C. no change in levels occur
H2O
45°C
A B
98% H2O +
2% EtOH55°C
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, _______.
A. water moves from A to B
B. ethanol moves from B to A
C. water moves to B and ethanol to A
D. both water and ethanol move to A
E. no change in levels occur
NaClSolution
25oC
A B
Pure H2O22oC
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.
A. 3.2 kPa
B. 2.6 kPa
C. < 2.6 kPa
D. > 3.2 kPa
E. > 2.6 kPa
H2O
45°C
A B
80% H2O
45°C+
20% NaCl
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,
________.
A. Beaker A has more water
B. Beaker B has more water
C. The amounts of water do not change since they are at the same temperature
D. All the salt moves to beaker A
H2O
45°CNaCl
A B
H2O
45°CNaCl
+5 g KCl
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, _________________.
A. water moves from B to A
B. water moves from A to B
C. KCl moves from B to A
D. nothing changes
Adsorption concentrates a molecule on a surfacefrom another phase. Consider hexane liquid andvapor. The hexane concentration in the zeolite pores is ____________.
A. higher in A
B. higher in B
C. the same in both
D. Insufficient information
Porous zeolite crystals
Vapor
Liquid
A
Liquid
Vapor
B
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?
A. Higher in A
B. Higher in B
C. The same in both
D. Insufficient information
Porous zeolite crystals
Vapor
50/50Liquid
A
Liquid
50/50Vapor
B
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?
A. Higher in A
B. Higher in B
C. The same in both
D. Insufficient information
Porous zeolite crystals
50/50Vapor
Liquid
A
50/50Liquid
Vapor
B
As the pressure increases from point 1 to 2, which figure shows an area proportional to the changein Gibbs free energy?
P
V
1
2
P
V
1
2
A B
Which plot represents f vs. P for an ideal gas?
P
f
P
f
P
f
P
f
A B
DC
For the H-xA diagram at 80°C, what is the maximum
value of the partial molar enthalpy of component A at 80°C?
A. 50 cal/mol
B. 22 cal/mol
C. 85 cal/mol
D. 100 cal/mol
E. 0 cal/mol
xA
H (
cal/m
ol)
0 0.5 1.0
100
50
0
100
50
0
An isotherm for a cubic equation of state is shown below. Which line corresponds to a vapor-liquid equilibrium?
AB
C D
E
Pre
ssu
re
n/V
When both vapor and liquid are present, the fugacity at x1 = 0.1 will be ________ at x1 = 0.3.
A. greater than
B. less than
C. equal to the value
0.1 0.3 0.5
P
When both vapor and liquid are present, the fugacity at x1 = 0.1 will be ________ at x1 = 0.3, because
________.
A. greater than; pressure is higher
B. less than; mole fraction is lower
C. less than; partial pressure is higher
D. equal to the value; its at equilibrium.
0.1 0.3 0.5
P
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.
E. None of the above.
2 bar
Time
20 bar
Time Time Time
A B C D
fug
acit
y
0 bar
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
Time Time Time
A B C D
10 bar
Liquid water is in equilibrium with water vapor and air.Ptot
= 1.2 bar
PH2O = 0.1 bar
The fugacity of water is about __________.
A. 0.1 bar.
B. 1.2 bar.
C. 1.00 (dimensionless).
D. Cannot be determined.
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.
A. 1
B. 5
C. 50
D. 100
When comparing steam at 100°C to water at 100°C, steam has a higher enthalpy, _______, and ________.
A. higher entropy, higher Gibbs free energy
B. higher entropy, the same Gibbs free energy
C. the same entropy, the same Gibbs free energy
D. lower entropy, lower Gibbs free energy
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, _______________.
A. some ethanol freezes
B. some water freezes
C. some ice melts
D. all the ice melts
E. all the ethanol freezes
Air is bubbled through a tank of water at 25oC and atmospheric pressure. The solubility of O2 in water is
about 0.005 mol% at 25oC. Estimate the fugacity of oxygen in the water.
A. 1 bar
B. 0.2 bar
C. 0.5 bar
D. 2 bar
E. 0.0005 bar
A pure-component fluid is at 10 bar and 350 K. The Peng-Robinson equation of state has three real roots:
1) V = 0.080 L/mol ; fugacity = 11 bar 2) V = 8 L/mol ; fugacity = 9 bar
The fluid is a ____________.
A. liquid
B. gas
C. 2-phase mixture
D. supercritical fluid
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 ____________.
A. liquid
B. gas
C. 2-phase mixture
D. supercritical fluid
Boiling point of water: Psat = 1.0 bar; Tsat = 100°CPsat = 4.7 bar; Tsat = 150°C
The fugacity of water at 150°C and 100 bar is closer to __________.
A. 1 bar
B. 5 bar
C. 50 bar
D. 100 bar
Which of the following will increase the fugacity of a component, A?
A. Convert from solid to liquid
B. Convert from liquid to solid
C. Decrease pressure
D. Dilute with component B
E. None of the above
If you were to boil water on a stove in a small room for an hour, the fugacity of the ______________.
A. liquid increases
B. water vapor increases
C. liquid decreases
D. water vapor decreases
E. water stays the same in the vapor
H2O
Soda (liquid water with a low concentration of dissolved CO2) at 0°C is compressed to 5 bar soonly a liquid phase remains. In the liquid phase, the fugacity of ___________.
A. water is higher
B. CO2 is higher
C. water and CO2 are the same
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?
A. Water
B. CO2
C. Fugacities of water and CO2 are equal
When salt is added to pure water, what happens to the fugacity of the water?
A. increases
B. decreases
C. stays the same
Pure NaCl was added to pure water until thewater was saturated and the excess salt settled to the bottom of the container. What happened to the fugacity of the salt?
A. Increased
B. Decreased
C. Did not change
Compared to the fugacity of pure water, the fugacity of water in a saline solution will be _________.
A. higher
B. lower
C. the same
Pure NaCl was added to pure water until thewater was saturated and the excess salt settled to the bottom of the container. The fugacity of the dissolvedsalt is __________ the fugacity of the pure NaCl.
A. higher
B. lower
C. the same as
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?
A. Salt
B. Water
C. Their fugacities are equal
D. Need more information
A sealed container of water is at high enough pressureso that no vapor is present. The water contains 0.2 mol% salt and 0.2 mol% CO2.
Which component has the highest fugacity?
A. Water
B. CO2
C. Salt
D. Same for all