phase equilibrium: two components contributions by: john l. falconer & will medlin department of...
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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 PAsat > PB
sat ?
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 PAsat > PB
sat ?
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
xx
x
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
C
DIsotherm for 40-60
pentene/octene mixture
xx xB
x xxx
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. 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 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?
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
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°C
What 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
E. None of the above
Which of the following statements is NOT true at an azeotrope?
A. xA = yA
B. xA = xB
C.
D.
E. None of the above
VA
LA ˆˆ
VA
LA ff ˆˆ
Which of the following statements is NOT true at an azeotrope?
A. xA = yA
B.
C.
D.
E. None of the above
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
E. None of the above
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%
E. None of the above
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 1
X1, 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
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