Phase Equilibrium:Two Components

in Piston-CylindersContributions by:

John L. Falconer & Will MedlinDepartment of Chemical and Biological Engineering

University of ColoradoBoulder, CO 80309-0424

Supported by the National Science Foundation

A mixture of ethanol and propanol are at 60°C. Both liquid and vapor are present. How many additional variables can be specified before the system is completely determined?

A. 0

B. 1

C. 2

D. 3

E. System is already over-specified

A mixture of ethanol and propanol are at 60°C. Both liquid and vapor are present. The pressure is 1 bar. How many additional variables can be specified before the system is completely determined?

A. 0

B. 1

C. 2

D. 3

E. System is already over-specified

A 2-componet system is at 98oC and 90 kPa. How many different equilibrium phase conditions are possible for this system (for example: liquid, vapor, liquid and vapor)?

A. 1

B. 2

C. 3

D. 1 or 2

E. 1 or 3

A mixture of ethanol and propanol are at 60°C. Both liquid and vapor are present. The pressure is 1 bar and the liquid mole fraction of ethanol is 0.5. How many additional variables can be specified before the system is completely determined?

A. 0

B. 1

C. 2

D. 3

E. System is already over-specified

Which of the following is not possible:

A. 2 components in VLE equilibrium, both temperature and pressure are specified.

B. 1 component in three phases: solid, liquid, gas.

C. 2 solids in equilibrium at a specified temperature.

D. 2 components as solid and liquid, with temperature, pressure, and mole fractions specified.

E. 1 component as a gas, temperature and mole fractions specified.

A piston-cylinder system contains components A and B

in vapor-liquid equilibrium. Assume ideal solution and ideal gas, with xA = 0.25, yA = 0.50. A small weight

was added to the piston, while temperature was held constant. What happens?

A. xA increases, yA decreases

B. xA increases, yA increases

C. xA decreases, yA decreases

D. xA decreases, yA increases

VaporyA=0.50

LiquidxA=0.25

One mole of pure hexane is in vapor-liquid equilibrium at 1 bar and 70°C in a piston-cylinder. After 0.2 mole of heptane liquid is injected, the system returns to equilibrium at the same temperature and pressure.

What are the final contents of the system?

A. All liquid

B. All vapor

C. Liquid and vapor with yhexane > xhexane

D. Liquid and vapor with yhexane < xhexane

Psat(hexane) > Psat

(heptane)

HexaneVapor

HexaneLiquid

0.2 moleHeptane (l)

One mole of pure hexane is in vapor-liquid equilibrium at 1 bar and 70°C in a piston-cylinder. After 0.2 mole of heptane vapor is injected, the system returns to equilibrium at the same temperature and pressure.

What are the final contents of the system?

A. All liquid

B. All vapor

C. Liquid and vapor with yhexane > xhexane

D. D. Liquid and vapor with yhexane < xhexane

Psat(hexane) > Psat

(heptane)

HexaneVapor

HexaneLiquid

0.2 moleHeptane (v)

Hexane liquid is in equilibrium with N2 gas at 50°C in a

piston-cylinder. Some heptane liquid is added to the system at constant temperature and pressure. What happens?

A. Some hexane vapor condenses

B. Some hexane liquid vaporizes

C. All the hexane vapor condenses

D. All the hexane liquid vaporizes

E. No change in the hexane in the 2 phases

Psat(hexane) > Psat

(heptane)

N2

Gas

HexaneLiquid

Heptane (l)

Hexane liquid is in equilibrium with N2 gas at 50°C in a

piston-cylinder. Some heptane vapor is added to the system at constant temperature and pressure. What happens?

A. Some hexane vapor condenses

B. Some hexane liquid vaporizes

C. All the hexane vapor condenses

D. All the hexane liquid vaporizes

E. No change in the hexane in the 2 phases

Psat(hexane) > Psat

(heptane)

N2

Gas

HexaneLiquid

Heptane (v)

Hexane liquid is in equilibrium with N2 gas at 50°C in a

piston-cylinder. Some heptane vapor is added to the system at constant temperature and pressure. What happens?

A. The heptane remains in the vapor phase

B. Some heptane condenses

C. All the heptane condenses

D. All the hexane liquid vaporizes

Psat(hexane) > Psat

(heptane)

N2

Gas

HexaneLiquid

Heptane (v)

Hexane liquid is in equilibrium with N2 gas at 50°C in a

piston-cylinder. Some heptane liquid is added to the system at constant temperature and pressure. What happens?

A. The heptane remains in the liquid phase

B. Some heptane vaporizes

C. All the heptane vaporizes

D. All the hexane liquid vaporizes

Psat(hexane) > Psat

(heptane)

N2

Gas

HexaneLiquid

Heptane (l)

Two components (A & B) are in VLE in a piston-cylinder container. Initially, 1.0 mol of liquid (xA = 0.4) and 0.1

mole of vapor (yA = 0.7) are present. If 0.5 mole of liquid

A is added to the system and it returns to equilibrium at the same temperature and pressure as before:

A. the amount of liquid increases

B. the amount of liquid decreases

C. the concentration of A in the gas phase increases

D. the concentration of A in the liquid phase increases

VaporyA=0.7

LiquidxA=0.4

Two components (A & B) are in VLE in a fixed volume container. Initially, xA = 0.3 and yA = 0.6. 1.0 cm3 of air

is injected into the system. The temperature and pressure are constant. The liquid solution is ideal. If liquid and vapor phases are still present, there is _______ before the injection of air.

A. more liquid than

B. less liquid than

C. the same amount of liquid as

VaporyA=0.6

LiquidxA=0.3

1 cm3 air

Two components (A & B) are in VLE in a piston-cylinder. One mole of liquid (xA=0.2) is in equilibrium

with one mole of vapor (yA =0.6). The liquid phase

does not possess an azeotrope.10 mol liquid A are added at constant temperature and pressure. What phase(s) are present at equilibrium?

A. All liquid

B. All vapor

C. More vapor, less liquid, same compositions

D. More liquid, less vapor, same composition

E. More vapor, less liquid, different compositions

VaporyA = 0.6

LiquidxA = 0.2

10 mol A

liquid

Two components (A & B) are in VLE at 60oC and 1 bar in a piston-cylinder. One mole of liquid (xA=0.2) is in

equilibrium with one mole of vapor (yA =0.6). The liquid

phase does not possess an azeotrope. When 0.3 mol liquid B is added at 60oC and 1 bar, what phase(s) are present at equilibrium?

A. All liquid

B. All vapor

C. More vapor, less liquid, same compositions

D. More liquid, less vapor, same composition

E. More vapor, less liquid, different compositions

VaporyA = 0.6

LiquidxA = 0.2

0.3 mol B

liquid

Two components (A & B) are in VLE in a fixed volume container. Initially, xA = 0.3 and yA = 0.6. 1.0 cm3 of air

is injected into the system. The temperature and pressure are constant. The liquid solution is ideal. If liquid and vapor phases are still present, xA _______.

A. increases

B. decreases

C. remains the same

VaporyA=0.6

LiquidxA=0.3

1 cm3 air

Two components (A & B) are in VLE in an adiabatic piston-cylinder. Assume ideal solution and ideal gas.

If 0.2 mole of liquid A is rapidly injected into the system, the temperature at equilibrium is _______ before the injection of A.

A. higher than

B. lower than

C. the same as

xA = 0.2, yA = 0.7

VaporyA = 0.7

LiquidxA = 0.2

0.2 mole A

liquid

Two components (A & B) are in VLE in a fixed volume container with 2 moles vapor and 1 mole liquid.

You add 30 moles of liquid B at constant temperature and pressure. This system does not have an azeotrope. What happens?

A. Some liquid evaporates

B. All the liquid evaporates

C. Some vapor condenses

D. All the vapor condenses

xA = 0.2, yA = 0.7

VaporyA=0.7

LiquidxA=0.2

30 moles B(l)

Two components (A & B) are in VLE in a fixed volume container with 2 moles vapor and 1 mole liquid.

You add 30 moles of vapor A at constant temperature and pressure. This system does not have an azeotrope. What happens?

A. Some liquid evaporates

B. All the liquid evaporates

C. Some vapor condenses

D. All the vapor condenses

xA = 0.3, yA = 0.8

VaporyA=0.8

LiquidxA=0.3

30 moles A(v)

A fixed container, with components A and B, is in chemical and phase equilibrium (xA = 0.6, yA = 0.2).

For the reaction (A B), the addition of liquid B _______ the mole fraction of A in the liquid.

A. increases

B. decreases

C. remains the same

VaporyA=0.2

LiquidxA=0.6

B(l)

A liquid mixture is in equilibrium in a piston-cylinder system with a gas phase. The N2 does not dissolve in

the liquid. If N2 is removed completely isothermally

using a selective membrane at constant pressure, then xA ________.

A. increases

B. decreases

C. remains the same

xA = 0.4, xB = 0.6

yA = 0.5, yB = 0.3, and yN2 = 0.2Vapor

yA = 0.5yN2 = 0.2

LiquidxA = 0.4

N2

A liquid mixture is in equilibrium in a piston-cylinder system with a gas phase. The N2 does not dissolve in

the liquid. If N2 is removed completely isothermally

using a selective membrane at constant pressure, then xA ________.

A. increases

B. decreases

C. remains the same

xA = 0.4, xB = 0.6

yA = 0.5, yB = 0.3, and yN2 = 0.2Vapor

yA = 0.5yN2 = 0.2

LiquidxA = 0.4

N2

Water liquid and vapor are in equilibrium in a piston-cylinder. An insoluble polymer containing a salt is in the liquid. The salt slowly diffuses out of the polymer and dissolves in the water. Temperature and pressure are constant. What happens?

A. All the water condenses

B. All the water evaporates

C. Some water condenses

D. Some water evaporates

1 kg

Vapor

Water

Polymer

A container with 5 cm3 of benzene liquid and 1 cm3 of benzene vapor is in equilibrium. You inject 1 cm3 of toluene vapor. Which of the following mole fractions of toluene in the vapor composition at equilibrium will be closest to the correct value:

A. 90 %

B. 50 %

C. 10 %

D. 1 %

Vapor1 cm3

Benzene5 cm3

1 cm3

Toluene

A fixed-volume tank contains two components in VLE. 1.0 mole of N2 is added. Assume N2 is not soluble in

the liquid. The vapor phase is an ideal gas. The amount of component A in the liquid phase ____________.

A. increases

B. decreases

C. stays the same

VaporyA = 0.6

Liquid

1 mole N2

A fixed-volume tank contains two components in VLE. 1.0 mole of N2 is added. Assume N2 is not soluble in

the liquid. The vapor phase is an ideal gas. The amount of component A in the vapor phase ____

A. increases

B. decreases

C. stays the same

VaporyA = 0.6

Liquid

1 mole N2

A fixed-volume tank contains two components in VLE. 1.0 mole of N2 is added. Assume N2 has no solubility in

the liquid. The vapor phase is an ideal gas. The partial pressure of component A ________.

A. increases

B. decreases

C. stays the same

VaporyA = 0.6

Liquid

1 mole N2

Acetone and chloroform form a maximum temperature azeotrope. A piston-cylinder contains pure chloroform at 55°C and 0.95 bar. It has 0.9 mole vapor, 0.1 mole liquid. What is the final condition when 0.1 mole acetone is added at constant temperature and pressure?Tb (chloroform) = 60°C @ 0.95 bar

Tb (acetone) = 55°C @ 0.95 bar

A. All liquid

B. All vapor

C. Vapor-liquid mixture

Vapor0.9 mole

CHCl3

Liquid0.1 mole

0.1 mole

Acetone

0.1 mole of A vapor is in VLE with 10 mol liquid A at 70°C in a piston-cylinder. After 0.1 mol of liquid B is injected, the system returns to equilibrium at the same temperature and pressure. PA

sat = 2 bar ; PBsat = 1.3 bar

The liquid is non-ideal and the system has a maximumpressure azeotrope. What are the final contents of thesystem?

A. All liquid

B. All vapor

C. Liquid and vapor with yA > xA

D. Liquid and vapor with yA < xA

0.1 mole A

10 mole A

0.2 mole B

1.0 mole of pure hexane is in VLE at 1 bar and 70°C in a piston-cylinder. After 0.2 mole of octane liquid is injected, the system returns to equilibrium at the same temperature and pressure. If octane has a lower vapor pressure than hexane, what are the final contents of the system?

A. All liquid

B. All vapor

C. Liquid and vapor with yhexane > xhexane

D. Liquid and vapor with yhexane < xhexane

HexaneVapor

HexaneLiquid

A binary mixture is in VLE in a piston-cylinder with 10x more moles in the vapor phase than in the liquid phase with yA = 2xA. You push down on the piston until

the volume is half its original value. Temperature is constant. What happens?

A. Pressure increases

B. Pressure remains the same

C. All vapor condenses, pressure is constant

D. All vapor condenses, pressure is higher

E. Nothing changes

A binary mixture is in VLE in a piston-cylinder with 10x more moles in the vapor phase than in the liquid phase with yA = 2xA. You push down on the piston until

the volume is half its original value. Temperature is constant. What happens?

A. Vapor and liquid at same pressure

B. Vapor and liquid at higher pressure

C. Some vapor condenses

D. xA increases, yA decreases

E. xA and yA increase

A sealed 15-L tank contains 5 L of liquid water and 10 L of water vapor at 50°C. Two liters of liquid glycerol are injected into the tank. Glycerol is soluble in water but it has a negligible vapor pressure compared to water. The system is isothermal. What happens?

A. Some water condenses, pressure does not change

B. Some water condenses, pressure decreases

C. All the water condenses

D. Amount of water in the vapor phase does not change

A piston-cylinder contains 5 L of liquid water and 10 L of water vapor at 50°C. Two liters of liquid glycerol are injected into the tank. Glycerol is soluble in water and it has a negligible vapor pressure compared to water. The system is isothermal and at constant pressure. What happens?

A. Some liquid water evaporates

B. Some water vapor condenses

C. All the liquid water evaporates

D. All the water vapor condenses

E. Amount of water in the vapor phase does not change