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Binary Solid-Liquid Phase Diagram
Introduction
The substances that we encounter in the material world are hardly ever pure chemical compounds
but rather mixtures of two or more such compounds. The individual substances in such a mixture
may behave more or less independent of each other but merely diluted, i.e. , an ideal solution or
mixture, or there may be substantial chemical interaction or complex formation between the
constituents. The study of such mixtures can lead to an understanding of the most fundamental
intermolecular interactions.
In the present experiment, the phase changes that occur in a two-component mixture will be
investigated. The three common phases of matter are the solid, liquid and vapor states. The
particular phase or phases in which a pure substance or mixture exists under a given set of
conditions, e.g. , temperature, pressure and composition, is obviously of utmost importance in our
use of or interaction with the myriad of material substances in the world. We take it for granted that
the mixtures air, ocean water and wood exist in the vapor, liquid and solid states at ambient
conditions. In the preparation of countless commercial chemical products, great effort is taken to
insure that the final product, usually a complex mixture, is in an attractive and practical physical
state. Solid toothpaste and liquid margarine would not sell!
While you may never have thought about it, when salt water freezes, as it must if the temperature is
sufficiently low, the solid substance is pure water with no NaCl or other dissolved solutes
incorporated into the ice lattice. The present experiment assumes in the first place that when solid
precipitates from a liquid mixture on cooling, the solid is a pure substance in equilibrium with the
remaining liquid solution. In the salt water analogy, the solid ice (pure H 2 O) is in equilibrium with
the liquid H 2 O that remains in the unfrozen salt water.
Mixtures of naphthalene and diphenylamine, both solids in the pure state at room temperature, will
be prepared and their phase transitions studied by means of a thermal analysis. The details of this
experiment are provided in Reference 1.
Secondly, the assumptions used in going from the Clapeyron equation
dP
dT
Δ H
T Δ V
relating the change in vapor pressure with temperature to the enthalpy and volume changes to the
integrated form of the Clausius-Clapeyron equation
ln
P
1
P
0
=
vap
H
R
T
0
T
1
are taken to be valid. In equation (2), Δ vap H is the enthalpy of vaporization of pure solvent which
has vapor pressures P 0 at T 0 , and P 1 at T 1
. These assumptions are that the vapor behaves as an
ideal gas, the volume of the condensed phase is negligible in contrast to the volume of the vapor and
finally, that the enthalpy change accompanying vaporization is independent of temperature.
Finally, it is assumed that Raoult's Law is obeyed, namely that in a mixture, the vapor pressure of
one component, P 1 is directly proportional to the mole fraction of that component in the mixture,
X
1 , and to the vapor pressure of the pure component, P 1
0
P
1
= X
1
P
1
0 (3)
where
X
1
+ X
2
for a two component systems.
Let us consider the situation of our mixtures of diphenylamine (A) and naphthalene (B). There are
four possible combinations, neglecting the vapors of the two substances, a reasonable assumption at
temperatures just above their melting points. We can have
I) liquid A mixed homogeneously with liquid B.
II) solid A in heterogeneous equilibrium with the solution.
III) solid B in heterogeneous equilibrium with the solution.
IV) solid A mixed with solid B.
It is interesting to note that II (and, in a reciprocal manner, III) can be viewed in either of two ways.
The appearance of solid A in II will begin to occur at a lower temperature than will solid A begin to
occur in pure melted A. This is an illustration of the freezing point (solidification) lowering of A as
the result of the presence of some B in mixture II. Alternatively, mixture II can be viewed as
representing the maximum solubility , at the given temperature, of component A in component B.
At the freezing point of this mixture, solid A and liquid A are in equilibrium and, therefore, the
chemical potentials, μ, or the molar Gibbs free energies, G , must be equal (definition of
equilibrium) for A (solid) and A (solution)
μ A
0 ( solid ) = μ A ( solution ) = μ A
0 ( liquid ) + RT ln( γ A
X
A
or
G
A
0 ( solid ) = G A ( solution ) = G A
0 ( liquid ) + RT ln( γ A
X
A
where γA is the mole-fraction-scale activity coefficient that, on the assumption of ideal behavior,
may be set equal to unity. The standard molar free energy of fusion would be
fus
G
A
0 = Δ G A
0 ( liquid ) – Δ G A
0 ( solid ) (7)
Remembering that in general
Δ G = Δ H – T Δ S (8)
or
Δ G
T
Δ H
T
– Δ S (9)
which leads to the Gibbs-Helmholtz equation
Δ G
T
∂ T
P
Δ H
T
2
Fig 1.- Phase diagram of the naphthalene-diphenylamine
mixture. Data taken by D. Carin '90.
Review the composition of the mixtures I-IV and study this diagram to be certain you understand
what is present in the different regions.
Application of equation (14) would give
Point C P F variable
P
A 1 2 1 pressure
D 2 2 2 pressure and temperature
or pressure and composition
E 2 3 1 pressure
Point E is referred to as a eutectic point with a characteristic
temperature T E, and mole fraction X B,E.
Procedure
Follow pp. 243-245 in Reference 1 (pp. 219-221 in 6
th edition).
The reading of the electronic thermometer is transferred to the
computer and continuously read by a data acquisition card running
under a LabVIEW VI. To run the software start LabVIEW and
open the file “Temperature Curve” in the Chem 366 folder. Click
the hallow arrow button in the top left to start the data acquisition,
and use the large “Stop” button on the front panel (see Fig. 2) to
end the data acquisition once you notice a break or arrest in the
cooling profile. Do not use the little stop-sign button which appears
next to the start button once the VI runs (if you do, your data will
Fig. 2: Front Panel
Fig 3: Save File Dialog
not be saved, but you can still read the break temperature off of
the plot using the cursor below). Upon quitting, the VI asks you
for a filename to save your data under. The file dialog is slightly
counter-intuitive: Click “New…” and enter your file name in the
input field which opens up (see Fig. 3) and click “File”
Typical data are shown below (Fig. 4). For a pure substance, usually an "arrest temperature" is
noted where the temperature remains constant on freezing (trace I). For a mixture, there will be a
brief diminution in the temperature drop, or a "break temperature." As one component in the
mixture freezes out, the remaining solution becomes richer in the other component and the freezing
point continues to drop (Trace II). This does not occur in a pure substance. Remember that in both
cases, the temperature drop is slowed because of the release of the enthalpy of solidification to the
surroundings. Melting is endothermic, solidification is exothermic.
Fig. 4. Sample cooling curves for binary mixtures.
I: pure substance, II: mixture, III: eutectic mixture
Suggested Compositions For Thermal Analysis 1
(A = D = diphenylamine; B = N = Nap = naphthalene)
Run Wt.% Prepare by ...to sample
No B adding... used in run no.
1 100 5g B = N
2 83.3 1g A = D 1
3 66.7 1.5g A = D 2
4 50.0 2.5g A = D 3
5 33.3 5g A = D 4
6 0 5g A = D
7 16.7 1g B = N 6
8 25.0 0.67g B = N 7
9 Eutectic (see text)
References
- D. P. Shoemaker, C. W. Garland, and J. W. Nibler, Experiments in Physical Chemistry, 5th
Edition, McGraw-Hill, New York, 1994, pp. 195-197, 238-246. (
th edition, pp 179-182, 215-
222.)
- G. P. Matthews, Experimental Physical Chemistry , Clarendon Press, Oxford, 1985, pp. 46-
48, 52-53.
- P. P. Blanchette, J. Chem. Ed. , 64, 267-269, 1987.
Safety Notes
Diphenylamine: Potential Health Effects
Eye:
Causes eye irritation.
Skin:
Causes skin irritation. May cause skin sensitization, an allergic reaction, which becomes
evident upon re-exposure to this material.
Ingestion:
May cause gastrointestinal irritation with nausea, vomiting and diarrhea.
Inhalation:
May cause respiratory tract irritation.
Chronic:
Prolonged or repeated exposure may cause adverse reproductive effects.
Napthalene
Health Rating: 1 – Slight
Flammability Rating: 2 – Moderate
Reactivity Rating: 0 – None
Contact Rating: 1 – Slight
Lab Protective Equipment: Goggles & Lab Coat
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