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