Phase Equilibrium:
Two Components
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
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 > PBsat ?
1.0
1.0
xA
0.5
0.5
0
A
yA
P
0
1.0
yA
xA
0.5
0
yA
0.5
B
1.0
1.0
xA
0.5
D
P
0
xA
P
yA
yA
C
0
P
xA
E
P
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 > PBsat ?
1.0
1.0
xB
0.5
0
0.5
yB
A
P
1.0
0
1.0
yB
xB
B
P
0
xB
C
P
1.0
xB
yB
0.5
0.5
yB
0
0.5
yB
D
P
0
E
xB
P
Which is the VLE line that most likely connects liquid
and vapor phases in equilibrium for a benzene-hexane
mixture?
Isotherm for 60-40
benzene/hexane
mixture
A. A
B. B
C. C
D. None of these
P
A
x
x
B
x
x
C
x
x
V
4
Which is the VLE line that most likely connects liquid
and vapor phases in equilibrium for a pentene-octene
mixture?
Isotherm for 70-30
pentene/octene mixture
A. A
B. B
C. C
D. None of these
P
Ax
Bx
C x
x
x
x
x
x
D
Isotherm for 40-60
pentene/octene mixture
V
Which of these
diagrams are not
possible?
P-x
P
P
P-y
P-x
2
1
xA, yA
A. 2 & 6
B. 1, 4, & 6
P-y
xA, yA
P-x
P-x
P
P
P-y
P-y
C. 2 & 5
3
4
xA, yA
D. 2, 3, & 5
xA, yA
P-x
E. 3 & 5
P-x
P
P
P-y
P-y
5
xA, yA
6
xA, yA
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
1600
liquid
1200
Mg2Si
C. Si and Mg2Si
T (K)
B. Pure Si and Mg
800
0
Mg
0.5
mole fraction of Si
1.0
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?
160
0
C. Two solid phases:
60% Si, 40% Mg2Si
D. Two solid phases:
each contain Si & Mg
liquid
1200
Mg2Si
B. Two solid phases:
40% Si, 60% Mg2Si
T (K)
A. One solid phase
containing Mg and Si
800
0
Mg
0.5
mole fraction of Si
1.0
Si
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 closed system has methanol and ethanol in vaporliquid 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 = PBsat.
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 then
simmered. 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 atm and 50°C is mixed with 1.0
mol of O2 at 1 atm and 50°C. The final mixture is at
2.0 atm 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 nhexane 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 nhexane 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?
PAsat > PBsat > PCsat
A. Component A
B. Component B
C. Component C
D. None of them
Assume ideal gas and ideal solution behavior for the
A-B system:
PAsat = 1.5; PBsat = 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
ˆ A  ˆ
L
C.
D.
V
A
ˆf L  fˆ V
A
A
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 at
low 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 atmospheric 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 must
operate at 105°C?
At 105°C: P1sat = 1.8 bar, P2sat = 1.2 bar
A. 3.0 bar
B. 1.8 bar
C. 1.5 bar
D. 1.2 bar
At what temperature is 58.7 mol% ethane liquid not in
equilibrium with a vapor?
M
88.7 mol% ethane
A. 335 °F
77.1 mol% ethane
58.7 mol% ethane
B. 275 °F
CC2H6
Critical locus
C. 315 °F
D. 400 °F
P
CC7H16
26.5 mol% ethane
0
100
300
T (°F)
500
700
58.7 mol% ethane liquid is in equilibrium with what
ethane mol% vapor composition?
M
88.7 mol% ethane
77.1 mol% ethane
A. 77.1
58.7 mol% ethane
CC2H6
B. 88.7
C. 26.5
Critical locus
P
D. All of those shown
CC7H16
E. A & B
26.5 mol% ethane
0
100
300
T (°F)
500
700
When the binary interaction parameter, kij, increases,
for a fixed liquid phase, fixed temperature system, the
equilibrium pressure ________.
A. increases
B. decreases
C. remains the same
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
140
Temperature
130
T-y1
120
110
T-x1
100
90
80
70
0
0.2
0.4
0.6
X1, Y1
0.8
1