Solid-Liquid Phase Diagram

of Naphthalene-Diphenylamine Two-Component System

Michael Go, Nate Manaloto, Ronald Reyes*

*Faculty, Ateneo de Manila University; email: ron_rxn24@yahoo.com

Abstract. The experiment aims to be able to construct a phase diagram of

Naphthalene-Diphenylamine two-component system at constant atmospheric

pressure for thermal analysis. From the phase diagram, the eutectic composition

(XE) and eutectic temperature (TE) are determined and are compared with the

literature value. Commercial Naphthalene is used to undergo this test, and see if it

is of the same caliber as the standard Naphthalene.

Keywords. Naphthalene-Biphenylamine. Eutectic point. Newton’s Law of Cooling. Thermal Arrest. Thermal Break.

Introduction. In investigating the heterogeneous

equilibrium between solid and liquid phases of a two-

component system, a phase diagram is constructed. In

constructing phase diagrams, cooling curves forms

the basis for “thermal analysis”. From the phase

diagram, the eutectic composition (XE) and eutectic

temperature (TE) are determined.

Figure 1. A Phase Diagram for a two component system in

which the solids are partially miscible and the liquids are

complete miscible.

The binary solid-liquid diagram in Figure 1 shows the

stability of different phases as a function of

temperature and composition. This example (Figure

1) shows a case where the solid components are

partially miscible, α+β. α(s) represents a solid state

mixture predominantly composed of substance A,

with B present as an impurity, and β(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

pint depression, a colligative property that depends on

the number of solute particles present in the solvent.

The shape of the phase boundaries between the (α +

liquid region) + (β + liquid region), the liquidus

curves, describes the freezing point depression for

this mixture. The equation of the liquidus curves can

be derived from the Clausius-Claperyon equation

under the assumption that the solution behaves

ideally:

T(XA) = Tf.A. + ln(XA)RTFA2/dHA = TA-((1-XA) + (1-XA)2/2 + …) RTf.A

2/dHA

Tf.A is the freezing point of compound A, and is also

shown in Figure 2. dHA is the heat of fusion for

compound A and XA 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.

In the absence of a phase change, the rate of change

in temperature follows Newton’s Law of cooling. The

Newton’s Law of cooling predicts that there is an

exponential approach to the ambient temperature. A

solid is formed because the rate of cooling is changed

as part of the heat exchanged with the surroundings

that contributes to the phase transition. During the

freezing point of a pure substance, when the

temperature remains constant, this is called thermal

arrest. In a two-component system, as the temperature

is lowered, one component begins to freeze while the

other component still remains in the liquid state. In

this freezing process, the liquid’s concentration

mixture changes as more and more solid forms, and

this 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. This change in the rate of cooling is known as

thermal break. When the liquid reaches a certain ratio

of the two components, a thermal arrest is observed.

This temperature and concentration point is also

known as the eutectic point.

Experimental. The binary system will be

naphthalene-diphenylamine. Make two series of runs:

a Naphthalene-rich series beginning with pure

Naphthalene followed by successive additions of

Diphenylamine to the previous run; and a

Diphenylamine-rich series similarly prepared with the

Naphthalene-rich series*. Heat the mixture in water

bath until completely melted, and then, remove the

water bath and measure the temperature periodically

(e.g. every 15 seconds for the first 5 minutes, 30

seconds for the next five minutes, and every minute

for the latter parts until the eutectic temperature is

reached) until the system is essentially solid.

Table 1. Approximate range of composition for the two-component Naphthalene-Diphenylamine mixture

Approximate Range of CompositionPure A -

Naphthalene: 10 g.Pure B -

Diphenylamine: 10 g.Run B (g) Wt. % A Run A (g) Wt. % B

1A 0.0 100 1B 0.0 100

2A 1.5 87 2B 1.5 87

3A 2.0 74 3B 2.0 74

4A 2.5 63 4B 2.5 63

5A 3.0 51 5B 3.0 51

Results.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

R² = 0.936158860842965

R² = 0.996134484802076

Temperature vs. Mole Fraction

mole fraction (XB)

Tem

pera

ture

Figure 2. The constructed phase diagram with the

freezing points plotted, temperature (y-axis) and mole

fraction of Naphthalene (x-axis). The best fitted curve

is used and the eutectic point and temperature were

determined.

Eutectic composition (XE) = 0.76381045

Eutectic temperature (TE) = 21.8121115

Discussion: In the constructed phase diagram, a few

changes were made. The best fitted curve was used in

order to get the eutectic point. The experimental value

of the eutectic point is 0.764 mole fraction

composition of Naphthalene and 21.81⁰C for the

temperature. Comparing it with the values taken by

other studies, it was found that the eutectic point is

around 0.36-0.38 mole fraction of naphthalene, and

the temperature roughly 31⁰C. The high deviation of

the results from the previous one can be seen in the

experimental procedure, and the result itself. As can

be seen in the results, the points were not successive

and not complete. As such, there was a huge break

and empty space between the 0.3 and 0.8 mole

fraction of Naphthalene interval. As such, the eutectic

point can only be roughly estimated by extending the

best fitted curves. Having more points can lead to a

more visualize-able and more accurate results. The

recommendation for the experiment is that it can add

more solutes for each runs that can extend the points

further nearer the eutectic point, or if not change the

five runs where the solute are added 1.5 g. each run

instead of adding in a 0.5g increment.

The major source of error in the experiment is

temperature reading. Since the temperature is read not

automatically by a machine, but manually by the

experimenter. Furthermore, when the system is not

stirred, the whole solution is not in equilibrium which

leads to a deviation in temperature reading that

eventually leads to supercooling of the system.

Although this will eventually be eliminated, however,

this could have been prevented if the system was

stirred consistently. The recommendation is that an

automatic stirrer can be used rather than a manual

one.

Acknowledgement.

We would like to acknowledge the Chemistry

Department of the Ateneo de Manila University for

supporting our project and providing us the

equipments necessary for the completion of the

project.

References.

University of Colorado. “Binary Solid-Liquid Phase

Diagram.” Accessed on October 6, 2010.

<http://www.colorado.edu/Chemistry/chem4581_91/

BSL.pdf>

Williams College. “Binary Solid-Liquid Phase

Diagram.” Accessed on October 6, 2010.

<http://www.williams.edu/chemistry/epeacock/EPL_

CHEM_366/366_LAB_WEB/

Expt_5_BinaryPhases.pdf>

Figure 1. A Phase Diagram for a two component system in which the solids are partially miscible and the

liquids are complete miscible.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

R² = 0.936158860842965

R² = 0.996134484802076

Temperature vs. Mole Fraction

mole fraction (XB)

Tem

pera

ture

Figure 2. The constructed phase diagram with the freezing points plotted, temperature (y-axis) and mole

fraction of Naphthalene (x-axis). The best fitted curve is used and the eutectic point and temperature were

determined.

0 100 200 300 400 500 600 700 800 9000

10

20

30

40

50

60

70

80

Diphenylamine + 3.0 g Naphthalene

Time (s)

Tem

pera

ture

Figure 3. A run of Diphenylamine with 3 grams of Naphthalene as impurity, the graph illustrates the thermal

break and the thermal arrest.