Fugacity Contributions by: John L. Falconer & Will Medlin Department of Chemical and Biological Engineering University of Colorado Boulder, CO 80309-0424 Supported by the National Science Foundation

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.

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

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

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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

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.

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.

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

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

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

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

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.

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.

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:

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.

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.

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.

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. 1 bar 0.2 bar 0.5 bar 2 bar 0.0005 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.

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 = 0.080 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.

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.

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.

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.

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.

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.

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.

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.

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:

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.

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

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:

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: