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1. Vapor-Liquid Equilibria
Back to previous section: Single Component Liquid
Continue to next section: Using VLE to Solve Mass Balances
Importance of VLE
Vapor-liquid equilibrium (VLE) undergirds the bulk of industrial separation processes, particularly
in distillation processes. We will consider only binary (two-component) mixtures here for simplicity.
The composition of the liquid phase will be designated by the mole fraction of the more volatile
component (lower boiling point), represented by x. The mole fraction of the other component in the
liquid is of course 1 - x. Likewise, the mole fraction of the vapor will be represented by y, with 1 - y
being the composition of the other component in the vapor phase. When the liquid mixture is heated
to its boiling point, the vapor produced will, in general, have a different composition than the liquid;
i.e., x will not equal y. Thus, boiling the mixture produces a partial separation of the components. If
the vapor is collected, it can be condensed and boiled again to further change the composition.
Distillation columns use this principle, effectively repeating
the separation process at individual trays within a column.
Such columns may have over a hundred trays on which
VLE is occurring. Depicted at the left is a cartoon cut-away
of a small section of a tray-type distillation column. Two
sieve trays are shown. Hot vapor (shown in white) flows up
through the holes in the sieve tray and vigorously bubbles
through the liquid (shown in blue). The vapor and liquid
mix on this tray and the new mixture boils. The composition
of the liquid, x, leaving the will be enriched in the less
volatile component while the composition of the vapor, y,
will be enriched in the more volatile component. The vapor
rises up to the next tray where it will contact a liquid of
larger x and mixing and re-equilibration will again occur.
The liquid leaving the tray will flow over the weir and down
the downcomer to the next tray where it will mix with the
vapor on that tray. In this way, x tends to become smaller at
each lower tray, while y tends to increase at each tray higher
in the column. VLE refers to the relationship between the x and y values on each tray.
At equilibrium, the temperature and pressure of the liquid and vapor phases will be equal, but the
compositions will not. Why is this? There are two main factors that make the vapor and liquid
compositions different at equilibrium: the pure component vapor pressures and the nonidealities in
the liquid phase. In this class, we will not deal with the nonidealities in the liquid; this topic will be
discussed in ChEn 373. We will focus only on ideal liquid mixtures for which Raoult's Law applies.
When we discussed the phase behavior of pure fluids, we found that the temperature and pressure
were constant when the two phases were in equilibrium. Thus, the saturated liquid and vapor points
were both at the same temperature. When the liquid is heated it will boil at the same temperature as
that at which the vapor will condense when it is cooled. Another way of saying the same thing is
that the bubble point (boiling point) and dew point are the same for a pure fluid.

2. When we have two components in both the vapor and liquid phases, the bubble point and dew points
no longer coincide. There is a difference in composition between the liquid and vapor phases that are
in equilibrium at the same T and P. This is extremely important! It means that when you raise the
temperature of a mixture until it boils, more of the more-volatile component ends up in the vapor
phase. The liquid phase is left enriched in the less-volatile component. Thus, you can achieve a
partial separation in the mixture. This is the principle behind distillation that accounts for most of
the separation done in the chemical industry.
Using Phase Diagrams to Understand VLE
This difference between the bubble-point and dew-point temperatures is probably best understood
from phase diagrams like those we presented for pure fluids. Unfortunately, with a binary mixture
we must add another independent variable, composition of component 1. This makes the phase
diagram four dimensional instead of three dimensional. We can greatly simplify the diagrams by not
including volumes, which reduces the figures to 3D. Furthermore, we will pick a particular pressure
in order to look at a specific T-x plane or we will pick a particular temperature and look at a specific
P-x plane.
The Txy graph below shows binary mixtures of n-pentane and n-heptane at a fixed pressure of 1.5
atm. Like all phase diagrams, areas outside of enclosed regions represent a single phase, and areas
enclosed by coexistence lines represent two phases in equilibrium, with the boundary lines
representing the two phases that are in equilibrium. The temperature is plotted as a function of x
(mole fraction of n-pentane in the liquid) and y (mole fraction of n-pentane in the vapor).
Everywhere above the red line we will have only vapor; everywhere below the blue line we will
have only liquid. Between the blue and red lines we will have both liquid and vapor coexisting.
The blue line represents the saturated liquid line, or bubble line. Suppose a liquid containing 12
mol% n-pentane is heated up at constant pressure. It would remain liquid until it reached 370 K (see
the green dotted line at the left), at which point it would boil. This is the boiling point temperature
of this mixture (12 mol% pentane) at this pressure (1.5 atm). The vapor that boils off will not be the
same composition of the liquid. Pentane is more volatile than heptane so there will be more pentane
in the vapor mixture. Remember, on these plots we are using x to represent the mole fraction of n-
pentane (the more volatile component) and 1-x to represent the mole fraction of n-heptane in the
liquid. Likewise, we use y to represent the mole fraction of n-pentane in the vapor and 1-y to
represent the mole fraction of n-heptane in the vapor. The two phases that are in equilibrium are at
the same temperature and pressure, so they can be thought of as being connected through the two
phase region by a horizontal line (the horizontal green dotted line on the graph). This horizontal line
connecting the two equilibrium phases is called a tie line. The plot therefore shows us that the vapor
that boils off at 370 K will be 40 mol% pentane (and 60 mol% hexane). This is found from the end
of the tie line where it intersects the saturated vapor or dew line (red line). Notice that at the right
and left ends of the graph that the bubble and dew points meet. For example, at x = 1.0 we have pure
n-pentane, which is seen from the graph to boil at 322 K. The vapor given off will also be pure n-
pentane and so the bubble and dew point temperatures are the same. Does it seem strange to you that
x = 1 and y = 1 at this point? If it does, then you are confusing the definitions of these terms.
Remember that x applies to the liquid and y to the vapor for the same component; the mole fraction
of the other component is 1-x in the liquid and 1-y in the vapor. When a pure pentane boils, of course
the vapor will also be pure pentane.
Summary:
A liquid containing 12 mol%
pentane (x = 0.12) could be
heated to 370 K at which
point it would start to boil

3. (blue line). The saturated
vapor (red line) in
equilibrium with the boiling
liquid is at the same
temperature, but is richer in
the more volatile component,
n-pentane. The composition
of this saturated vapor is 40
mol% n-pentane (y = 0.4).
Likewise a vapor containing
40 mol% n-pentane could be
cooled to 370 K before it
started to condense. At 370
K, the vapor is saturated and
the first liquid droplets
appear. The composition of
these liquid droplets will be
12 mol% n-pentane.
We could have chosen instead to plot the phase diagram on a constant temperature diagram and
allow the pressure to vary. The Pxy diagram for n-pentane + n-heptane mixtures at 400 K is shown
below. At 400 K, the vapor pressure of pure n-pentane is just over 10 atm while the vapor pressure
of n-heptane is just over 2 atm. Can you see these from the graph below? Note that on a constant
temperature graph the liquid is on top and the vapor on bottom, whereas the reverse was true for the
constant pressure plot. This is because liquids exist at high pressures; vapors at low pressures.
Likewise, vapors exist at high temperatures; liquids at low temperatures. Again, the blue line
represents the saturated liquid, and the red line represents the saturated vapor. The region between
the blue and red lines is where two phases exist, the compositions of which are given by the blue
and red lines themselves. Thus, if the pressure of a 400 K vapor containing 90 mol% n-pentane is
increased isothermally, it will remain a vapor until it reaches 7.5 atm. At this point, the pressure is
high enough that we reach the dew point, and it will begin to condense. The liquid that condenses
will have a composition of 65 mol% n-pentane, as given by the end of the tie line that links the
saturated vapor (red line) to the equilibrium saturated liquid (blue line).
Summary:
A vapor containing 90 mol%
pentane (y = 0.9) could be
compressed to 7.5 atm (at
400 K), at which point it
would be a saturated vapor
(red line), and it would begin
to condense. The saturated
liquid (blue line) in
equilibrium with the vapor
contains less of the more
volatile component, n-
pentane. The composition of

4. this saturated liquid is 65
mol% n-pentane (y = 0.65).
Likewise a liquid containing
65 mol% n-pentane could be
expanded to 7.5 atm before it
started to evaporate. The
vapor that begins to come off
from the liquid at this
pressure has a composition
of 90 mol% n-pentane.
The yx Plot
On the Txy and Pxy plots shown above, both the saturated liquid (blue line) and saturated vapor (red
line) phases were plotted on the same graph. Thus, when you read the composition for the saturated
vapor (any point on the red line), you are reading y values from the abscissa (horizontal axis), and
when you read the composition for the saturated liquid (any point on the blue line), you are reading
x values from the abscissa. The length of the tie line (green line) in the two-phase region is how
much different the composition of n-pentane will be in the vapor phase than in the liquid phase. For
each x value on the blue line there is a corresponding y value on the red line representing the
composition of the vapor in equilibrium with the liquid. For the purposes of identifying the
separation that occurs when we boil the mixture, it is convenient to plot y values versus the x value
with which it is equilibrium. This is done for this system on the yx plot below.
Summary:
The red line represents the vapor
composition of n-pentane (y) that is
in equilibrium with the liquid (x).
The diagonal black line represents y
= x. The deviation of the red line
from the diagonal line is therefore an
indication of how wide the tie lines
are, or the amount of separation that
will take place.
See if you can match x and y values
shown on this diagram with those
that you obtain from the ends of tie

5. lines on the Pxy or Txy diagrams
given above.
All of this new information can be somewhat confusing the first few time you look at these graphs.
Re-read this page and then go to the next page where some interactive drills and questions will help
clarify the concepts and fix them in your mind.
Continue to next section: VLE Practice