Download The Liquid-Vapor Phase Diagram for Ethanol

CHEM 331L
Physical Chemistry Laboratory
Revision 2.0
The Liquid-Vapor Phase Diagram for Ethanol-Cyclohexane
In this laboratory exercise we will construct a liquid-vapor phase diagram for the EthanolCyclohexane system. This is basically a temperature-composition diagram for mixtures of these
two substances. To do this, we will produce Ethanol-Cyclohexane mixtures, bring them to a boil
and then determine the composition of both the liquid and the vapor. This data can then be used
to generate the desired phase diagram. This data can also be used to calculate the activity
coefficients for each component in the mixtures, the activity coefficients being the gateway to all
other thermodynamic quantities.
Water Vapor in Equilibrium with Its Liquid
(http://www.photoeverywhere.co.uk/britain/ukwild/slides/english_rain0254.htm)
A phase diagram for the Propanol-Water system (J. Chem. Ed.) is provided below. This is an
example of a system that exhibits a minimum boiling azetrope. Note that a system of an overall
Propanol composition of 0.8 mole fraction at a boiling temperature of 365K produces a vapor of
composition 0.7 mole fraction and a liquid of composition 0.85.
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We would like to consider two things in this regard. First, how are the compositions of the liquid
and the vapor actually measured? Second, is there a theoretical construct that will allow us to
understand liquid-vapor equilibria? We will start with the second question first.
If a solution is Ideal, and the above system is not, then the compositions of the vapor and liquid
are governed by Raoult’s and Dalton’s Laws. Suppose we have a Binary mixture of components
“A” and “B” whose pure state vapor pressures are PAo and PBo. Further, we will suppose “A” is
the lower boiling component; so, PAo > PBo. According to Dalton’s Law:
PTot = PA + PB
(Eq. 1)
where the partial pressures of the components in the vapor above the mixture (Pi) are given by
Raoult’s Law:
PA = xA PAo
(Eq. 2)
PB = xB PBo = (1 – xA) PBo
(Eq. 3)
xi represents the mole fraction of the component in the liquid:
xi =
(Eq. 4)
Inserting the Raoult’s Law expressions into Dalton’s Law, and rearranging, we obtain the
following result:
PTot = PBo + (PAo - PBo) xA
(Eq. 5)
From this we can see there is a linear relationship between the total pressure and the composition
in the liquid.
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Now, what about the vapor? The composition variables are again given by Dalton’s Law:
yA =
yB =
(Eq. 6)
Inserting the Raoult’s Law results and inverting to find the total pressure gives us:
PTot =
(Eq. 7)
We can add this “inverse” relationship between PTot & yA to our above Phase Diagram. Here we
plot PTot vs. xA and PTot vs. yA on the same diagram, letting zA represent both xA and yA.
To understand this diagram, suppose we start with a piston filled with a liquid of composition zII
at Point 1. As we lower the total pressure by expanding the piston, we will reach a point where
the liquid begins to vaporize. At Point 2, we have established a liquid-vapor equilibrium; the
composition of the liquid is zI and that of the vapor is zIII. Notice that the vapor is enriched in
component A; zIII > zII. This is as we expect since A is the lower boiling component. As we
continue to expand the piston, the remaining liquid is converted entirely to vapor. At Point 3 all
the liquid has been converted to vapor with a composition again at zII.
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Unfortunately, this has provided us with a Pressure-Composition diagram. From a practical
point of view, Temperature-Composition diagrams are more useful because they can be used in
analyzing distillation processes. It is much easier to vaporize a liquid in a Distilling Pot by
raising the temperature of the liquid and boiling it than it is to vaporize the liquid by expanding a
piston and lowering the pressure.
Our P vs. z Phase Diagram can be converted to a T vs. z Diagram via the use of a modified form
of the Clausius-Clapeyron Equation called the Antoine equation:
(Eq. 8)
where A, B and C are empirical constants for a particular liquid i.
At intermediate compositions between xA = 1 (PAo) and xA = 0 (PBo), the vapor pressure for each
component Pio can be calculated for the desired temperature t. This will allow us to determine
the liquid and vapor compositions using (Eq. 5) and (eq. 6):
(Eq. 9)
In conceptual terms, liquids with a high vapor pressure will have a low boiling point. So,
component A will have a lower boiling point TAo than will component B, which will boil at TBo
when pure. So, our P vs. z diagram will be inverted.
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Of course, this assumes the liquid is behaving Ideally; i.e., follows Raoult’s Law. If it is not
behaving ideally, then a minimum boiling or a maximum boiling Azeotrope can form.
In this case, Raoult’s Law must be modified with an Activity Coefficient i:
Pi = i xi Pio
(Eq. 10)
Under the mild conditions we are working with, we will assume the vapor can still be treated as
Ideal and hence Dalton’s Law still holds:
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Pi = yi P
(Eq. 11)
A good model for the non-Ideal behavior of the liquid is that of van Laar. Here, the activity
coefficients can be estimated from:
log A =
(Eq. 12)
log B =
(Eq. 13)
where AL and BL are van Laar constants that are relatively insensitive to Pressure and
Temperature. If the activity coefficients A and B are known, then the van Laar equations can be
inverted to determine AL and BL:
AL
= log A
(Eq. 14)
BL
= log B
(Eq. 15)
Once a phase diagram has been constructed, the azeotropic point for the system can be
determined. This will allow us to then determine the activity coefficients for this mixture using
equations (10) and (11) because at this point xi = yi. Hence:
i,az = P/Pio
(Eq. 16)
Once A,az and B,az have been determined, the van Laar coefficients AL and BL can be calculated
from equations (14) and (15). Now equations (12) and (13) can be used to calculate model values
for A and B at any other system composition. These model coefficients can then be used to
model the entire phase diagram.
Unfortunately the van Laar model typically exhibits three extrema in the liquid curve of the
model phase diagram; one at the azeotrope, as expected. The other two extrema are artifacts of
the van Laar model and do not satisfy the stability requirements of the Second Law. These
artifacts do not seriously distort the graphs if the experimental azeotropic data is good. If the
azeotropic data is poor, then the van Laar theoretical curves can be bizarre.
Recall, we desire activity coefficient data because this leads to information about the chemical
potential i for each component in the mixture:
i(T,P,xi) = (T,P) + RT ln(ixi)
(Eq. 17)
where i* is defined as the chemical potential of pure liquid i at T and P. It should be noted this
differs only slightly from component i's Standard State chemical potential io:
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i*(T,P) = io(T,Po) +
because the parital molar volume of the liquid
(Eq. 18)
is typically very small.
From the chemical potential, the Gibbs Free Energy for the mixture can be determined:
G(T,P,xi) =
(Eq. 19)
On a molar basis, for a binary liquid mixture, we then have:
(T,P) = x11 + x22
(Eq. 20)
= x11* + x1RT ln(x1) + x22* + x2RT ln(x2)
+ x1RT ln(1) + x2RT ln(2)
(Eq. 21)
This can then be used to determine the Gibbs Free Energy of Mixing:

mxg
=
=
pure
- x11* - x22*
= x1RTln(x1) + x2RT ln(x2) + x1RT ln(1) + x2RT ln(2)
(Eq. 22)
The first two terms in Equation 22 represent the mixing Free Energy for an Ideal Solution. The
"Excess" Free Energy is then given by:
E
= + x1RT ln(1) + x2RT ln(2)
(Eq. 23)
Now, onto how to generate the phase diagram
experimentally. To do this, we will need a
method to sample and measure the
composition of both the vapor and the liquid
once equilibrium has been established between
them. We will establish our Liquid-Vapor
equilibrium in a standard distilling apparatus
operated under reflux. The Claissen Head will
be modified so that as the vapor condenses it
can be trapped and collected.
Our method of determining the composition of
the collected liquid and trapped vapor will be
to determine the Refractive Index of these
mixtures and to compare this measurement
with an appropriate calibration curve.
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During the first week of the lab, we will prepare the calibration curve. During the second week
we will generate the phase diagram.
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Procedure
Week 1
To obtain data for the calibration curve, you will need a series of 10 samples approximately
evenly spaced over the full range of mole fractions from 0 to 1. Prepare the calibration samples
by weight, using two burets to deliver approximate amounts into 25 mL Erlenmeyer flasks.
Weigh the flasks empty and after the addition of each component. The volumes to be used in
preparing these samples should be computed from density and molecular weight data. The total
volume should be 5 – 10 mL. Stopper the flasks promptly to prevent evaporation, which can
cause serious errors. Be sure each sample is thoroughly mixed, then measure the refractive
index. Include measurements for the two pure liquids. Your always helpful laboratory instructor
will demonstrate the use of the Abbe Refractometer.
Week 2
Set-up the Still as pictured in the background material above. Use a heating block on a hot plate
as a heat source. To begin the equilibrium measurements, introduce about 50 mL of Ethanol into
the clean, dry distilling flask. Add a boiling stone to the liquid. Adjust the heat source so that
the liquid boils vigorously, with the vapor condensing well below the top of the reflux
condenser. Continue boiling until the temperature has become stable, that is, until it fluctuates
about a mean value rather than showing an upward trend. It is quite useful to record temperature
readings periodically as the system approaches a steady state, as this makes it easier to decide
when this condition has been reached.
For the first series of measurements on mixtures, make successive additions of Cyclohexane of,
for example, 4, 8, 14, 20 and 20 mL. Do not empty the flask between additions.
With pure liquids, the steady state is reached within a few minutes, but with mixtures a much
longer time is required because a steady-state composition difference must be established
between the Claissen Head and the distilling flask. To expedite reaching a steady state with
mixtures, flush out the distillate collected in the Claissen Head several times by inserting a
disposable pipet with a squeeze bulb attached and forcing Air through it.
After a steady temperature has been reached, record the temperature. Withdraw a sample of
about 1 mL from the condenser pocket and another from the distilling flask. Use a dry pipet for
each sample, and stopper the samples promptly.
After the first series of measurements has been completed, drain and dry the flask and introduce
about 50 mL of Cyclohexane for a boiling point determination. Additions of Ethanol (0.4, 1, 2,
10, 10 and 10 mL) may then be made for the remaining series of measurements.
Be sure and make a measurement of the atmospheric pressure for the day.
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Data Analysis
1.
Construct your Refractive Index calibration curve.
2.
Determine the composition of the Liquid and Vapor at each recorded boiling temperature
using your calibration curve results.
3.
Construct a T-Z Phase Diagram for the Ethanol-Cyclohexane system at the recorded
atmospheric pressure. Use a French Curve to smoothly connect your data points.
Determine the temperature and composition of the azeotrope for this system. Include an
error estimate for each determination. Compare this with literature values.
4.
Calculate the van Laar constants AL and BL. Include appropriate error estimates.
5.
Compute the activity coefficients EtOH and Cyc at 0.1 mole fraction intervals over the entire
composition range. Include appropriate error estimates. Plot your results on a single
graph.
6.
Use the van Laar model to reconstruct the T-Z phase diagram. For each composition used
above (Calc. 5), use the determined activity coefficients and the atmospheric pressure to
determine the temperature at which the system should boil via Dalton’s Law:
P = PEtOH + PCyc = EtOH xEtOH PEtOHo + Cyc xCyc PCyco
(Eq. 24)
The Pio’s can be determined using the Antoine equation. Equation parameters for our
system are:
Substance
A
Ethanol
8.11220
Cyclohexane 6.84941
B
1592.864
1206.001
C
226.184
223.148
Some numeric technique will be require to determined the desired temperatures. The vapor
composition can be determined using (Eq. 11).
7.
Include a phase diagram which compares the van Laar model results with the experimental
results.
8.
Calculate  mxg and E as a function of composition for both the experimental case as well
as the van Laar model case. Comparative plots of each of these quantities should be
constructed.
P a g e | 11
References
Hala, E., Pick, J., Fried, V., and Vilim, O. (1967) “Vapor-Liquid Equilibrium”, 2nd Ed.
Pergamon Press, New York.
Sime, Rodney J. (1990). “Physical Chemistry: Methods, Techniques and Experiments.”
Saunders College Publishing, Philadelphia.
Vaughan, Worth and Turner, Ed. “Liquid-Vapor Equilibrium Laboratory”. University of
Wisconsin-Madison. Personal Communication.