Binary Solid-Liquid Phase Diagram Thermochemistry
Chemistry 4581
University of Colorado
Department of Chemistry and Biochemistry
- 1 -
Binary Solid-Liquid Phase Diagram
In this lab, the heterogeneous equilibrium between solid and liquid phases of a
two-component naphthalene-diphenylamine system is investigated. The binary phase
diagram is constructed by measuring the cooling curves of the mixture at different overall
compositions. From the phase diagram, the eutectic temperature and composition of the
mixture, as well as the melting points and heats of fusion for both naphthalene and
diphenylamine, are determined.
For a pure substance, phase transitions occur at a characteristic temperature for a
given pressure. At this transition temperature, the two phases are in equilibrium. A phase
diagram shows the thermodynamically allowed regions of pressure and temperature for
which a given phase can exist. The phase boundaries, designated by lines on the phase
diagram, are pressure-temperature points where the two phases are in equilibrium. The
triple point of a substance (point A in Figure 1) is the temperature and corresponding
pressure coordinate for which all three phases are in equilibrium. The critical point
(point B in Figure 1) is the point at which a supercritical fluid forms. A supercritical
fluid is a state in which gas and liquid cannot be distinguished from one another.
Figure 1. General phase diagram for a pure substance. Solid, liquid, and gas phases are separated by
phase boundaries (lines). Point A designates the triple point. Point B designates the critical point. Thermochemistry
Chemistry 4581
University of Colorado
Department of Chemistry and Biochemistry
- 2 -
A two-component system can have a much more complex phase diagram. In this case the
stability of a certain phase depends on the pressure, temperature, and the composition of
the solution.
The binary solid-liquid phase diagram in Figure 2 shows the stability of different
phases as a function of temperature and composition at a given pressure. This particular
example shows a case where the solid components are partially miscible. In this figure,
(s) represents a solid state mixture predominantly composed of substance A, with B
present as an impurity, and (s) represents the opposite case where A is an impurity.
When a substance is dissolved in a liquid and the freezing point of the liquid is lowered,
this is called freezing point depression. The shape of the phase boundaries between the
+ liquid region and + liquid region (the liquidus curves) describes the freezing point
depression for this mixture. The equation for the liquidus curves can be derived from the
Clausius-Claperyon equation under the assumption that the solution behaves ideally:
T(X
A
) T
f,A
+ ln(X
A
) RT
f,A2
/H
A
= T
A
((1-X
A
) + (1-X
A
)
2
/2 + ) RT
f,A2
/H
A
(2)
T
f,A
is the freezing point of compound A, and is also shown in Figure 2. H
A
is the heat
of fusion for compound A and X
A
is the mole fraction of compound A. An analogous
equation can be written for compound B. The two liquidus curves intersect at the eutectic
point, C.
Below the liquidus curves are two regions,
+ liquid and + liquid. The +
liquid region represents a mixture of
dissolved in liquid A and B, while the +
liquid region is a mixture of solid dissolved in liquid A and B. The bottom-most
region
(s) + (s) is a solid solution of and . The regions at the edges of the phase
diagram denoted
(s) and (s) are present because the solids are partly miscible. For
compounds that are less miscible, these regions are smaller, whereas for solids that are
completely immiscible these regions would not exist. In the latter case, the regions of the
phase diagram corresponding to the solid states
and would be replaced by regions
corresponding to pure A and pure B. Thermochemistry
Chemistry 4581
University of Colorado
Department of Chemistry and Biochemistry
- 3 -
Figure 2. A general phase diagram for a two-component system in which the solids are partially miscible
as a function of mole fraction of A (X
A
) and temperature. Point C represents the eutectic point. T
f,A
represents the freezing point of pure A, while T
f,B
represents the freezing point of pure B. (s) represents a
solid state composed predominantly of A, with B present as an impurity; (s) represents a solid state
composed predominantly of B, with A present as an impurity.
The phase diagram can be constructed from observed changes in slope of the
temperature versus time profile, or a cooling curve. In the absence of a phase change, the
rate of change of the temperature obeys Newton's Law of cooling, which predicts an
exponential approach to the ambient temperature. When a solid is formed, the rate of
cooling is changed because part of the heat exchanged with the surroundings contributes
to the phase transition. During the freezing process of a pure substance, the temperature
remains constant, which is called a thermal arrest. In a two-component system, as the
temperature is lowered, one component begins to freeze while the other component
remains in the liquid state. During this type of freezing process, the concentration of the
liquid mixture changes as more and more solid forms, which consequently changes the
freezing point. For this reason, the rate of cooling is not constant, but is different from
the rate of cooling of the original liquid mixture. This change in the rate of cooling is
known as a thermal break. When the remaining liquid reaches a certain ratio of the two
components, a thermal arrest is observed. This temperature and concentration point is Thermochemistry
Chemistry 4581
University of Colorado
Department of Chemistry and Biochemistry
- 4 -
known as the eutectic point. A common example of a eutectic mixture is solder, which is
the eutectic mixture of tin (67%) and lead (33%) which melts at 183
o
C.

Figure 3. Example cooling curves and a corresponding phase diagram. W, Y and Z denote thermal arrests,
and X denotes a thermal break.
EXPERIMENTAL
The binary system will be naphthalene-diphenylamine. The temperature measurements
will be made with a thermocouple system. A thermocouple system produces a voltage
proportional to the temperature difference between the two junctions. One junction is
kept at 0°C by immersing it in a slushy mixture of distilled water and ice. The
thermocouple system is attached to a chart recorder to plot voltage as a function of time
to see the thermal arrests and breaks. Charts will be available in the lab to convert the
voltage reading to temperature. A diagram of the apparatus is attached to the end of this
document. Thermochemistry
Chemistry 4581
University of Colorado
Department of Chemistry and Biochemistry
- 5 -
Make up the first mixture in as specified in Table 1 in a small test tube. Make sure to
record exactly how much of each compound you add to the tube.
First Run
% Wt. N
Add to tube
100
0.50g N
90.9
0.05 g D
83.3
0.05 g D
76.9
0.05 g D
66.7
0.10 g D
58.8
0.10 g D
50.0
0.15 g D
40.0
0.25 g D
33.0
0.25 g D
Second Run
% Wt. N
Add to tube
0
0.50 g D
9.0
0.05 g N
16.7
0.05 g N
20.6
0.03 g N
25.0
0.037g N
28.0
0.03 g N
31.0
0.03 g N
34.0
0.03 g N
Table 1. Mixture details. Here, N stands for naphthalene and D stands for diphenylamine.
Next, it is necessary to obtain a cooling curve. To do this, one must first heat the
mixture in a beaker of water until it is completely liquified. Remove the test tube from
the hot water bath and insert a thermocouple. It is possible that some of the liquid
mixture may have solidified on the tip of the thermocouple upon its insertion. If this is
the case, return the test tube to the hot water bath until the solid mixture is completely
remelted. Turn the chart recorder on. The small test tube can then be transferred to rest
inside a beaker and allowed to slowly cool. While it is cooling, the mixture must be
agitated.
When the mixture has completely solidified, the chart recorder can be turned off.
You should see at the least a single arrest on the chart. Continue to add to the mixture as
specified in Table 1. After adding a large amount of impurity to your original sample,
it may be necessary to have an ice bath to cool the mixture.
CALCULATIONS
On each cooling curve, determine the break and/or arrest temperatures using the
thermocouple chart.
Calculate mole fractions.
Plot break/arrest temperatures vs. mole fraction. Find the liquidus curves by
fitting with a po