phase equilibrium: two components

Phase Equilibrium:Two Components

Contributions by:John L. Falconer & Will Medlin

Department of Chemical and Biological EngineeringUniversity of Colorado

Boulder, CO 80309-0424

Supported by the National Science Foundation

The pressure increases for a 50/50 vapor mixture of A and B that is initially at a low pressure. The liquid is ideal. Which plot corresponds to how xA and yA change with pressure at constant temperature if PA

sat > PBsat ?

A B C

D E

0

0.5

1.0

P

yA

xA

P0

0.5

1.0

xAyA

0

0.5

1.0

P

yA

xA

0

0.5

1.0

P

yA xA

0

0.5

1.0

P

yA

xA

A B C

D E

The pressure increases for a 50/50 vapor mixture of A and B that is initially at a low pressure. The liquid is ideal. Which plot corresponds to how xB and yB change with pressure if PA

sat > PBsat ?

0

0.5

1.0

P

yB

xB

yB xB

0

0.5

1.0

P0

0.5

1.0

P

yB xB

yB

xB

0

0.5

1.0

P

yB

xB

0

0.5

1.0

P

Which is the VLE line that most likely connects liquid and vapor phases in equilibrium for a benzene-hexane mixture?

A. A

B. B

C. C

D. None of these

4

xxx

x

x

x

Isotherm for 60-40 benzene/hexane

mixture

P

V

AB

C

Which is the VLE line that most likely connects liquid and vapor phases in equilibrium for a pentene-octene mixture?

A. A

B. B

C. C

D. None of these

x

Isotherm for 70-30 pentene/octene mixture

P

V

A

CD

Isotherm for 40-60 pentene/octene mixture

xx xBx x

xx

1 2

43

5 6

Which of these diagrams are not possible?

A. 2 & 6

B. 1, 4, & 6

C. 2 & 5

D. 2, 3, & 5

E. 3 & 5

xA, yA

P

P-x

P-y

xA, yA

PP-x

P-y

xA, yA

P

P-x

P-y

xA, yA

P

P-y

P-x

xA, yA

P

P-x

P-y

xA, yA

PP-x

P-y

Mg and Si form the compound Mg2Si. At constant pressure, what is the composition of the system when xSi= 0.4 and T = 1000 K?

A. One solid phase

B. Pure Si and Mg

C. Si and Mg2SiT

(K)

1600

1200

8000 1.00.5

mole fraction of Si

liquid

Mg Si

Mg 2

Si

Mg and Si form the compound Mg2Si. At constant pressure, what is the composition of the system when xSi= 0.6 and T = 1000 K?

A. One solid phase containing Mg and Si

B. Two solid phases: 40% Si, 60% Mg2Si

C. Two solid phases:60% Si, 40% Mg2Si

D. Two solid phases:each contain Si & Mg

T (K

)

1600

1200

8000 1.00.5

mole fraction of Si

liquid

Mg SiM

g 2S

i

This figure shows saturated liquid and saturated vapor lines for a 2-component system. Which of these are equilibrium compositions and temperature?

A. x1= 0.6, y1=0.9, 245°C

B. x1= 0.6, y1=0.3, 210°C

C. x1= 0.9, y1=0.6, 200°C

D. x1= 0.6, y1=0.3, 250°C

A tank contains a 50/50 mixture of A and B (yA = 0.6). As the vapor is removed and the liquid boils away, the mole fraction of A in the liquid phase __________.

A. increases

B. decreases

C. remains the same

A liquid mixture (x1 = 0.4) evaporates at constant pressure by increasing the temperature. The first bubble has a composition of y1 = 0.7 because component 1 is more volatile and preferentially evaporates. As the last drop of liquid is evaporating, which is correct about the mole fraction of component 1 in the vapor phase?

A. y1 = 0.7

B. y1 = 0.4

C. y1 > 0.7

D. 0.4 < y1 < 0.7

A liquid mixture (x1 = 0.4) evaporates at constant pressure by increasing the temperature. The first bubble has a composition of y1 = 0.7 because component 1 is more volatile and preferentially evaporates. As the last drop of liquid is evaporating, which is correct about the mole fraction of component 1 in the liquid phase?

A. x1 = 0.4

B. x1 > 0.4

C. x1 < 0.7

D. x1 <<< 0.4

A closed system has methanol and ethanol in vapor-liquid equilibrium at 1 bar and 65°C. The temperature of the system is raised to 70°C at 1 bar. If two phases are still present, how do the methanol mole fractions change for each phase? (Note: Tsat

(methanol) = 65°C, Tsat(ethanol) = 78°C)

A. xm increases, ym decreases

B. xm increases, ym increases

C. xm and ym do not change

D. xm decreases, ym decreases

E. xm decreases, ym increases

We want to separate 50/50 mixtures of C6 isomers in the gas phase. As the temperature was lowered, your technician observed that n-hexane (n-C6) condensed before 2,2, dimethylbutane (DMB). Can this happen?

A. Yes, if n-C6 has a lower vapor pressure than DMB

B. Yes, if n-C6 has a higher vapor pressure than DMB

C. No, because both species have to condense

D. It depends on the system pressure as to whether one or two species condense.

A mixture of n-hexane and acetone were in the liquid phase in a piston-cylinder at 1 bar pressure. As the temperature increased, your technician observed that acetone evaporated first. Can this happen?

A. Yes, if acetone has the higher Psat

B. Yes, if n-hexane has the higher Psat

C. No, both species evaporate

D. It depends on the system pressure as to whether one or two species evaporate

A mixture of n-hexane and acetone were in the liquid phase in a piston-cylinder at 1 bar pressure. As the pressure decreased, your technician observed that acetone evaporated first. Can this happen?





A mixture of water and acetone was placed in an open beaker in a room. The next morning, 90% of the acetone had evaporated, but none of the water had evaporated. Can this happen?





At 100°C, PAsat = PB

sat. Will this system exhibit an azeotrope at 100°C?

A. Yes

B. No

C. Maybe…need more information.

Which statement is not correct? A binary mixture that has a minimum boiling point azeotrope ____________.

A. has a maximum pressure azeotrope

B. has one composition where the boiling point does not change as liquid evaporates

C. cannot be modeled by a modified Raoult’s Law

D. allows for either component 1 or 2 to be enriched in the vapor phase, depending on the liquid composition

E. has activity coefficients greater than one

A liquid mixture of 50 mol% n-pentane (Psat = 5 bar) and 50 mol% n-heptane (Psat = 1 bar) is at high pressure. The mixture is partially vaporized by isothermally lowering the pressure to just below 3 bar. Which statement is correct?

A. n-heptane is enriched in the gas phase

B. n-pentane is enriched in the gas phase

C. The gas phase has a 50/50 composition

D. No vapor forms

Often, wine or beer is added to soup that is thensimmered. When the soup is ready to be served, what has happened to the alcohol?

A. It all evaporates

B. It all remains in the soup

C. Some of it evaporates

________ is the driving force for component A to move from liquid to vapor in order to reach equilibrium.

A. Pressure

B. Entropy

C. Enthalpy

D. Concentration

E. Gibbs free energy

1.0 mol of CH4 at 1 bar and 50°C is mixed with 1.0 mol of O2 at 1 bar and 50°C. The final mixture is at 2.0 bar and 50°C. Assume ideal gases. The Gibbs free energy change is _______.

A. positive

B. negative

C. zero

An n-butane/n-heptane mixture is in vapor-liquid equilibrium. The liquid composition is 30% n-butane. Which of these vapor compositions (% n-butane) are not possible?

A. 20%

B. 40%

C. 60%

D. 80%

E. All of these compositions are possible

Consider a system at equilibrium that contains n-hexane and water, which are immiscible in the liquid phase. Which set of phases could not exist?

A. Two Liquids (hexane + H2O)

B. Hexane liquid and two vapors (hexane + H2O)

C. Two Liquids (hexane + H2O) and hexane vapor

D. H2O liquid and two vapors (hexane + H2O)

E. None of the above

Consider a 1 L constant-volume container with n-hexane in VLE. If half the volume is liquid and 0.1 L of liquid H2O is added to the container, what happens? Assume constant temperature and that water is immiscible with n-hexane.

A. Some hexane evaporates

B. Some hexane condenses

C. All the H2O evaporates

D. Some water evaporates and some hexane condenses

E. All the hexane evaporates

An ideal liquid solution that is 30% A, 30% B, and 40% C is heated at a constant temperature until 80% of the original liquid has evaporated. Which component would you expect to have completely evaporated at that point?

A. Component A

B. Component B

C. Component C

D. None of them

PAsat > PB

sat > PCsat

Assume ideal gas and ideal solution behavior for the A-B system:

PAsat = 1.5; PB

sat = 1.0 bar ; T = 70°CWhat is the total pressure at equilibrium above a liquid that is 60% A and 40% B?

A. 2.5 bar

B. 1.5 bar

C. 1.2 bar

D. 1.0 bar


Which of the following statements is NOT true at an azeotrope?

A. xA = yA

B. xA = xB

C.

D.


VA

LA ˆˆ

VA

LA ff ˆˆ

Which of the following statements is NOT true at an azeotrope?

A. xA = yA

B.

C.

D.


VA

LA ˆˆ

VA

LA ff ˆˆ

1ˆ A

At VLE,

Which is the correct equation to use when solving for the liquid phase fugacity of component 2 using an equation of state?

A. x2*g2*P

B. x2*f2L*P

C. x2*f2L*Psat

D. x2*g2*Psat


One mole of component A is in VLE at 1 bar and 75°C. One mole of B is added to form a mixture, and the pressure is isothermally increased to 2 bar. What is the state of the system? The vapor pressure of B at 75°C is 2 bar. Assume A and B form an ideal solution.

A. VLE

B. All liquid

C. All vapor

Which of the following is true for a binary azeotrope atlow pressure?

A. The activity coefficients of the two components are the same

B. The vapor pressures of the two components are the same

C. The value of the vapor pressures multiplied by the activity coefficients are the same

D. None of these

Are there conditions in which liquid water (or solid ice) at barospheric pressure will not have a vapor phase partial pressure when in contact with nitrogen? (Assume the system is below the normal boiling point of nitrogen).

A. No.

B. Yes, if the temperature is low enough

C. Yes, if the temperature is high enough

You want to completely condense a vapor containing 50% methanol(1) and 50% ethanol(2). What is the minimum pressure at which the condenser mustoperate at 105°C?

At 105°C: P1sat = 1.8 bar, P2

sat = 1.2 bar

A. 3.0 bar

B. 1.8 bar

C. 1.5 bar

D. 1.2 bar

At what temperature is 59 mol% ethane liquid not in equilibrium with a vapor?

A. 335 °F

B. 275 °F

C. 315 °F

D. 400 °F

T (°F)

P

700100 300 5000

M89 mol% C2

77 mol% C2

27 mol% C2

CC2H6

CC7H16

59 mol% C2

59 mol% ethane liquid is in equilibrium with what ethane mol% vapor composition?

A. 77

B. 89

C. 27

D. All of those shown

E. A & B

T (°F)

P

700100 300 5000

M89 mol% C2

77 mol% C2

27 mol% C2

CC2H6

CC7H16

59 mol% C2

A vapor with 59% ethane is in equilibrium with which phase?

A. 89%

B. 77%

C. 59%

D. 27%


T (°F)

P

700100 300 5000

M89 mol% C2

77 mol% C2

27 mol% C2

CC2H6

CC7H16

59 mol% C2

When the interaction parameter, kij, increases, for a fixed liquid phase, fixed temperature system, the equilibrium pressure ________.

A. increases

B. decreases

C. remains the same

𝒂𝒊𝒋=√ (𝒂𝒊𝒊𝒂 𝒋𝒋 ) (𝟏−𝒌𝒊𝒋 )

A liquid mixture containing species A & B is boiled by increasing the temperature at constant pressure. The saturation pressure is greater for A than for B.What happens?

A. xA increases and yA increases

B. xA increases and yA decreases

C. xA decreases and yA decreases

D. xA decreases and yA increases

What is the fraction of this mixture that is liquid?

A. ¼ B. 1/3 C. 2/3 D. ¾

70

80

90

100

110

120

130

140

0 0.2 0.4 0.6 0.8 1X1, Y1

Tem

pera

ture

T-x1

T-y1

In a bubble pressure calculation using a EOS, the mole fractions of liquid are known, and the mole fractions of vapor must be calculated by iteration by guessing the pressure. After the first iteration, Syi > 1. For the next iteration, _______________.

A. raise the pressure

B. lower the pressure

C. keep the pressure the same but change the composition

A EOS spreadsheet is used to calculate VLE for a binary mixture (x1= 0.9) with a non-ideal liquid phase and a non-ideal gas. Which statement about the fugacity coefficients is most likely to be correct?

A. =

B. =

C. <

D. >

6 mol A and 4 mol B are in equilibrium at 100°C and3.0 bar. A and B are completely immiscible in theliquid phase. Their vapor pressure at 100°C are:

Which phases are present?

A. Liquid B and vapor of A + B

B. Two liquids

C. Two liquids in equilibrium with vapor

D. All vapor

E. Liquid A and vapor of A + B

bar 0.2PsatA bar 5.0Psat

B

6 mol A and 4 mol B are in equilibrium at 100°C and2.0 bar. A and B are completely immiscible in theliquid phase. Their vapor pressure at 100°C are:

Which phases are present?

A. Liquid B and vapor of A + B

B. Two liquids

C. Two liquids in equilibrium with vapor

D. All vapor

E. Liquid A and vapor of A + B

bar 0.2PsatA bar 5.0Psat

B

A gas phase mixture at 100°C is 75 % A and 25 % B. As pressure increases isothermally, liquid A starts to condense at 1.6 bar. At 2.4 bar liquid B starts to condense. What are the vapor pressures of A and B?

A. PAsat = 1.6 bar, PB

sat = 2.4 bar

B. PAsat = 1.2 bar, PB

sat = 1.6 bar

C. PAsat = 1.6 bar, PB

sat = 1.2 bar

D. PAsat = 1.8 bar, PB

sat = 0.6 bar

E. PAsat = 1.2 bar, PB

sat = 1.2 bar

phase equilibrium: two components

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