EXPERIMENT 1 SOLID LIQUID PHASE DIAGRAM Important: bring a formatted 3.5 floppy diskette/usb flash drive for this laboratory you will need it to save your data files! Introduction The 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 chosen for study here, the two components, although miscible with one another in the liquid phase, are of limited solubility in one another as solids. Thus, we can consider them as pure solids, plus a twocomponent liquid. Such systems exhibit an eutectic temperature at which the three phases can coexist in equilibrium at a fixed pressure. Solid-liquid equilibria differ from liquid-vapour equilibria in that they are essentially independent of pressure changes on the order of a few atmospheres, owing to the small molar volume 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: [1] [2] [3] where: X A and X B are the mole fractions of components A and B, respectively, H A and H B are the heats of fusion of components A and B, respectively, and T A and T B are the melting points of the pure components. Equations [1] and [2] can be represented in the following phase diagram: [4] 15
Figure 1.1 The eutectic composition (X E ) and eutectic temperature (T E ) 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 of the cooling curves in a system of this kind. The curves in graph (b) are plots of temperature against time 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 to form. The temperature then remains constant until solidification is complete, where upon it falls again. It is said that the curve shows a thermal arrest. When a liquid having the eutectic composition is cooled, the behaviour is similar in that a thermal arrest is obtained. However, when a liquid of some other composition for example, X 1 (see graph (a)) is cooled, solid A begins to form at temperature T 1. This tends to deplete the liquid of component A, so that its composition passes through X 2, X 3,... and the temperature falls as long as solid A alone continues 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 X E, solid B begins to form together with solid A and the two solids continue to separate from solution at the temperature T E until no liquid remains, and thus an arrest occurs. The binary solid-liquid phase diagram for the naphthalene-diphenylamine system will be constructed from cooling curves. Several mixtures of different ratios of the two components will be melted, and temperature versus time curves will be plotted as the mixtures cool. The temperatures at which these breaks and arrests occur are plotted as a function of composition of the mixtures to obtain the phase diagram. 16
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 (C 10 H 8 ) diphenylamine (C 12 H 11 N) Procedure The 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 construct these 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 chips to prevent bumping. 2. Fill the plexiglass container with cold water and maintain the temperature between 10-20 EC throughout 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 magnetic stirrer to ensure that the sample is continually stirring. 17
temperature probe 600 ml beaker to Labpro plexiglass container and lid hotplate medium test tube ice water bath stir bar jumbo magnetic stirrer Figure 1.2 7. Click on on the Logger Pro software. This will provide a real time plot of the changing temperature in the sample. The collection will continue for a maximum of 1000 seconds. However, if you observe a distinct arrest or break in the pattern, you may terminate the acquisition and begin a new run. Note: keep the water bath cold, especially for the later runs! Remember that the pure compounds and the eutectic mixture should have only 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 process this 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 the eutectic arrest for two of the latter. Calculations 1. 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 thermodynamic temperature scale (i.e., Kelvin) and use these units for all of the calculations. 2. Determine the mole fraction, X naphthalene, for all of the mixtures. Determine the mole fraction of diphenylamine, X diphenylamine, for runs 6, 7 and 8. 18
3. Using the break and arrest temperatures of these mixtures, plot the two limbs of the solidliquid 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 each area of the diagram. 5. Determine the eutectic composition and eutectic temperature from the phase diagram. 6. Using [1] and [2], plot ln X naphthalene against 1/T for runs 1-5 and plot ln X diphenylamine against 1/T for runs 6-8. The plots should be linear with: slope = - H i /R and -slope/intercept = T i (the melting temperature of the pure component.) 7. Calculate the enthalpy of fusion and the melting point for each component, assuming that an ideal liquid solution is formed. Compare to literature values by calculating the percent error for fus H and temperature, as well as the absolute error for the temperature. Lab Questions 1. 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 Excel spreadsheet) for the Ni-Mn system. Label the different components and number of phases in each part of the phase diagram. Mn-Rich mixtures: T/( o C) 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/( o C) 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 and Mn at 1000 o C? What is this point designated as? References 1. Atkins, Peter and Julio de Paula. Physical Chemistry. 7 th ed. New York: W. H. Freeman, 2002. 144-148. 2. Shoemaker, David P., Garland, Carl W., and Joseph W. Nibler. Experiments in Physical Chemistry. 6 th ed. New York: McGraw Hill, 1996. 215-221. 3. Silbey, Robert J., and Robert A. Alberty. Physical Chemistry. 3 rd ed. Wiley, 2001. Chapter 6, Section 6.9. 19