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[1]

[2]

[3]

[4]

EXPERIMENT 1SOLID – LIQUID PHASE DIAGRAM

Important: bring a formatted 3.5” floppy diskette/USB flash drive for this laboratory – you willneed it to save your data files!

IntroductionThe relation of cooling curves to phase diagrams form the basis of “thermal analysis”, an

important technique for constructing phase diagrams. In the solid-liquid phase equilibrium chosenfor study here, the two components, although miscible with one another in the liquid phase, are oflimited solubility in one another as solids. Thus, we can consider them as pure solids, plus a two-component liquid. Such systems exhibit an eutectic temperature at which the three phases cancoexist in equilibrium at a fixed pressure.

Solid-liquid equilibria differ from liquid-vapour equilibria in that they are essentiallyindependent of pressure changes on the order of a few atmospheres, owing to the small molarvolume change associated with fusion. This is a consequence of the Clapeyron equation:

We shall be concerned here with temperature-composition diagrams at p = 1 atm.If the liquid solution behaves ideally, the “solubility” of each component in the liquid

depends on temperature, according to:

where:XA and XB are the mole fractions of components A and B, respectively,∆HA and ∆HB are the heats of fusion of components A and B, respectively, andTA and TB are the melting points of the pure components.

Equations [1] and [2] can be represented in the following phase diagram:

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Figure 1.1The eutectic composition (XE) and eutectic temperature (TE) are given by the intersection of

the two liquid curves. With the aid of graph (a) in Figure 1.1, we can predict the general nature ofthe cooling curves in a system of this kind. The curves in graph (b) are plots of temperature againsttime obtained when liquid solutions of various compositions are allowed to cool.

When a liquid consisting of pure A is cooled, the temperature falls until solid A begins toform. The temperature then remains constant until solidification is complete, where upon it fallsagain. It is said that the curve shows a thermal arrest. When a liquid having the eutecticcomposition is cooled, the behaviour is similar in that a thermal arrest is obtained.

However, when a liquid of some other composition – for example, X1 (see graph (a)) iscooled, solid A begins to form at temperature T1. This tends to deplete the liquid of component A,so that its composition passes through X2, X3, ... and the temperature falls as long as solid A alonecontinues to come out of solution.

The abrupt change in slope, which occurs when solid A begins to form, is called a break.When the composition of the solution finally reaches XE, solid B begins to form together with solidA and the two solids continue to separate from solution at the temperature TE until no liquid remains,and thus an arrest occurs.

The binary solid-liquid phase diagram for the naphthalene-diphenylamine system will beconstructed from cooling curves. Several mixtures of different ratios of the two components willbe melted, and temperature versus time curves will be plotted as the mixtures cool. Thetemperatures at which these breaks and arrests occur are plotted as a function of composition of themixtures to obtain the phase diagram.

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Materials

• 1 – 600 mL beaker• 1 – 200 mL beaker• 1 – plexiglass container and lid• 1 – large test tube• 1 – medium test tube• 1 – jumbo magnetic stirrer• 1 – magnetic stirring bar

• 1 – hot plate• 1 – rubber sleeve• boiling chips• Vernier with temperature probe• naphthalene (C10H8)• diphenylamine (C12H11N)

ProcedureThe apparatus will be set up as shown in Figure 1.2, and time-temperature curves should be

measured for the mixtures outlined in Table 1.1. Follow the procedure outlined below to constructthese curves. Instruction on the use of the Logger-Pro software will be provided by your TA.

Table 1.1

Run diphenylamine (g) naphthalene (g) made by

1 0 5

2 1 5 run (1) + 1.0 g diphenylamine

3 2.5 5 run (2) + 1.5 g diphenylamine

4 5 5 run (3) + 2.5 g diphenylamine

5 10 5 run (4) + 5.0 g diphenylamine

6 5 0

7 5 1 run (6) + 1.0 g naphthalene

8 5 1.67 run (7) + 0.67 g naphthalene

1. Fill the 600 mL beaker 3/4 full with water and bring to a boil. Be sure to use boiling chipsto prevent bumping.

2. Fill the plexiglass container with cold water and maintain the temperature between 10-20 ECthroughout the course of the lab.

3. Weigh all samples to an accuracy of 0.01 g.4. Transfer the first sample into the inner test tube. Insert the temperature probe and magnetic

stirring bar into the inner test tube as well.5. Place the test tube into a hot water bath and heat until the solid is completely melted.6. Dry the test tube and insert through the rubber sleeve of the large test tube contained within

the cold water bath in the plexiglass container (Figure 1.2). Turn on the jumbo magneticstirrer to ensure that the sample is continually stirring.

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jumbo magnetic stirrer

ice water bath

to Labpro

temperature probe

stir bar

plexiglasscontainerand lid

medium test tube

600 mL beaker

hotplate

Figure 1.2

7. Click on on the Logger Pro software. This will provide a real time plot of thechanging temperature in the sample. The collection will continue for a maximum of 1000seconds. However, if you observe a distinct arrest or break in the pattern, you mayterminate the acquisition and begin a new run. Note: keep the water bath cold, especiallyfor the later runs! Remember that the pure compounds and the eutectic mixture should haveonly one arrest! Be sure to pull out the stir bar before dumping waste!

8. Save a file for this run by exporting the data as a text file. Excel can later be used to processthis data. Make sure to use file names that will clearly distinguish your data sets.

9. Find the arrests on the curves for the pure compounds, the breaks on all mixtures, and theeutectic arrest for two of the latter.

Calculations1. Extract the break and arrest temperatures from the cooling curves. Print out plots of your

cooling curves (Excel can be used). Convert all temperatures to the thermodynamictemperature scale (i.e., Kelvin) and use these units for all of the calculations.

2. Determine the mole fraction, Xnaphthalene, for all of the mixtures. Determine the mole fractionof diphenylamine, Xdiphenylamine, for runs 6, 7 and 8.

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3. Using the break and arrest temperatures of these mixtures, plot the two “limbs” of the solid-liquid phase diagram (i.e., temperature as a function of the mole fraction of naphthalene).Runs 1-5 will constitute one “limb”, and runs 6-8 will make up the other.

4. Draw the liquidus curves, identify the eutectic line and identify the phases present in eacharea of the diagram.

5. Determine the eutectic composition and eutectic temperature from the phase diagram.6. Using [1] and [2], plot ln Xnaphthalene against 1/T for runs 1-5 and plot ln Xdiphenylamine against 1/T

for runs 6-8. The plots should be linear with:slope = -∆Hi/R and-slope/intercept = Ti (the melting temperature of the pure component.)

7. Calculate the enthalpy of fusion and the melting point for each component, assuming thatan ideal liquid solution is formed. Compare to literature values by calculating the percenterror for ∆fusH and temperature, as well as the absolute error for the temperature.

Lab Questions1. A series of Ni-Mn mixtures were prepared and allowed to reach equilibrium at various

temperatures. Use the following data to plot a phase diagram (preferably on an Excelspreadsheet) for the Ni-Mn system. Label the different components and number of phasesin each part of the phase diagram.

Mn-Rich mixtures:

T/(oC) 1260 1200 1150 1100 1050 1000

w(Ni)sol 0.00 0.04 0.08 0.13 0.22 0.45

w(Ni)liq 0.00 0.07 0.12 0.18 0.29 0.45

Ni-Rich mixtures:

T/(oC) 1050 1100 1150 1200 1250 1300 1350 1400 1450

w(Ni)sol 0.58 0.64 0.70 0.75 0.80 0.85 0.90 0.96 1.00

w(Ni)liq 0.54 0.62 0.68 0.73 0.78 0.83 0.88 0.94 1.00

2. What is the composition of the solid solution in equilibrium with a liquid mixture of Ni andMn at 1000 oC? What is this point designated as?

References1. Atkins, Peter and Julio de Paula. Physical Chemistry. 7th ed. New York: W. H. Freeman,

2002. 144-148.2. Shoemaker, David P., Garland, Carl W., and Joseph W. Nibler. Experiments in Physical

Chemistry. 6th ed. New York: McGraw–Hill, 1996. 215-221.3. Silbey, Robert J., and Robert A. Alberty. Physical Chemistry. 3rd ed. Wiley, 2001.

Chapter 6, Section 6.9.