The Solid-Liquid Phase Diagram Experiment Updated for the Physical Chemistry Laboratory Kathryn R. Williams and Sean E. Collins University of Florida, Gainesville, FL32611 The determination of a solid-liquid phase diagram is a valuable part of the physical chemistry laboratory curriculum. Not only does the exercise aid in the understanding of the fundamental concepts of phase equilibria, the results often are industrially significant. For these reasons the experience is useful to majors in both chemistry and chemical engineering. However, the acquisition of the data by the method described in standard texts and laboratory manuals is tedious and t i e consuming, and the results oRen are poor as well. Fortunately, these problems are alleviated hv use of modem instrumentation to obtain the this paper describes a student experidata. ~~ehfically, ment usine differential scannine calorimetrv and fusion microscop~todetermine the diagram for a eutectic system. Asample phase diagram for two species exhibitingeutectic behavior, shown in Figure 1,is a plot of temperature versus composition at constant ambient pressure. According to the Gihhs Phase Rule there are three invariant ~ o i n ton s the dianam. .. Two of these are the melting ~ o i n t s bf each of the pure omponents rTAand To,at the exiremities of the lot. The two liauidus lines. which separate the area of to&lly liquid from the iiquid-solid regions, orieinate from these ~ o i n tand s corres~ondto the freezing depression c-es for the two c~mponents.The two mutually exclusive curves cross a t the eutectic, which is the third invariant point; both the temperature, TE,and composition,X~,of the eutectic are fixed. The eutectic temperature defines the solidus line, the border between the totally solid and liquid-solid regions. To DreDare the ~ h a s ediaeram the tem~eraturesof the solidh ind liquidus lines &st be detemked for a series of A-B mixtures. A prominent laboratory manual (1) and recent physical chemistry texts (2) still specify the cooling curve method. in which a liauified mixture of known composition is allowed to cool, &d the temperature is monitored as a function of cooline time. Ideally. the lot of temperature versus time changes slope at the liq&dus point and levels offat the cutcmic. However. although the acauisition of the cooling cuwes can be compute&ed (31, the
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Figure 1. Phase diagram for a simple eutectic system.
evaluation of the break and arrest points is tedious and suffers from difficultiesdue to indistinct slope changes and supercooling. As a result, liquidus and solidus temperatures can he highly uncertain and quite inaccurate, especially when evaluated by novice students. Because phase transitions are equilibrium processes, the solidus and liquidus lines also can he ohsewed when solid A-B mixtures are heated. Superheating of solids usually is not a problem, and the transitions can be determined accurately, ifa detection method other than direct temperature measurement is available. The experiment devised for the physical chemistry laboratory uses two techniques: differential scanning calorimetry and optical microscopy with a programmable heating stage. Experimental Method Previously in this laboratory the binary mixtures consisted of two metals, tin and lead. The system was desirable for the teaching lab because of its commercial importance as soft solders. However, the two metals show some deviation from simple eutectic behavior (41, and more importantly, they are opaque, and cannot he viewed with the microscope in the transmission mode. It was, therefore, necessary to change to two organic compounds, phenacetin and benzamide, which show simple eutectic behavior throwhout the entire com~ositionrange. The crvstals are semi&ansparent, and, as-described bilow, the& melting behavior can be observed easily with a polarizing microscope. To save time and materials, the mixtures are prepared by the teaching staff, before the students come to the lahoratorv. Each of the two ~0mDoundSare recrvstallized from ethanol and drled in a vackm de~iceator.~~es~red ratlos arc: wrlehed into small beakers and oremelted \nth a hot plate o;oven to assure uniformity. small portions of 3-5 mg each are then sealed in aluminum DSC pans. To reduce the possibility of sample loss, the hermetic pan design is preferred. Another series is prepared by fusing a few milligrams of each mixture between a microscope slide and cover slip. In addition, for the measurement of enthalpies of fusion a microhalance is used to prepare DSC pans containing precise (f3pg) masses of the two pure compounds. The principles of differential scanning calorimetry can be found in many instrumental analysis texts (5).Figure 2 shows the plot of differential heat input versus temperature for the 20180 wffwt phenacetinhnzamide mixture. For the DSC in the University of Florida teaching laboratories (TAInstmments 2910 module with model 2000 computer) endothermic changes are plotted in the negative direction. The sharp negative peak at 98 "C corresponds to the eutectic temperature, at which crystals of the two solids melt together in the eutectic ratio. After all the solid Presented at the43rd Southeast Reaional Meeiina of the- American -~~ - - Cnemical Socery. 1991, the Ann~alMeet ng oftnefor'oa Secuon of the Amerlcan Chemcal Soclety. 1992,an0 tne Annua Meefing of the Nortn Amef can Thermal Ana fsis Society.Atlanta. GA. 1992. ~~~
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Volume 71 Number 7 July 1994
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PhmaeetlnlB.nzamlda Phase Dlagram 110.0
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Figure 2. DSC output for the 20180 wtiwt phenacetinlbenzamide mixture. phenacetin (limiting component in this sample) is consumed, the eutectic peak ends, and a second broad transitmn 1s observed as the excess bcmamide continues to melt. The peak value. as shown in Firmre 2. mves the best estimate' for the li&dus temperatire. ~b;mixtures close to the eutectic the two peaks are not resolved. and the liquidus temperature is difficult to evaluate a$ a result. For this ex~erimentthe value mav be taken as the temperature wiere the signal just re&s to the flat baseline, but the students should be cautioned that this simple approach may lead to problems with more complex phase equilibria (e.g., those exhibiting peritectics). The transitions can be evaluated more accuratelv if a slow heating ramp 1s used, but tn complete the data acquisition in a reasonable time heating rates of 2 "C per minute are used throughout the experiment. The solidus and liquidus temperatures also can be obtained visuallv bv viewinr! the samples through a microscope as t h e i a r e heatedat a constant rate. &though a standard clinical microscope can be used, the transition data can be determined more precisely, if one with polarizerr; is available. Once a common tnol of the chemist, optical microscopy again is hemming a valued instrumental tcchnique for cenain applications. Thermal (or fusion, microscopy is important in drug analyses and investigations of crystallization processes, and it is especially applicable to the study of phase transitions (6).This usage also provides an opportun~tyto introduce the properties of polarized light and crystal optics. Although not included in common chemistry books, an introductory text is available from the McCrone Research Institute (71.and detailed descriotions are provided in any text on optical mineralogy.' When viewed between crossed polars isotropic materials (i.e., liquids, gases, crystals of the cubic class, as well as ordinary glass and amorphous solids) appear black, but anisotropic substances, such as crystalline phenacetin and benzamide, pass light. Depending on their thicknesses and orientations, the crystals appear white or display a variety of interference colors. The contrast between the crystals
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'Because ootical microscoov ~,~ ~~-~~ . ~is -, used ~-~~ so -~ heavilv , bv ~,minemloaists. ~" ~. tne geology fac~llymay oe helpful to cnemlslry inshnors des r ng accessto this instrunentation.An accessory forcontrol eo heat ng of tne m crosmpe s .oe s also needed. A man~allycontrolled devce can be constructed from a tin oxide coated slide, as described by Skirus and Moran (8, 9). The slides may be purchased from the McCrone Research Institute (10). Programmable heating stages are sold by several manufacturers (11). ~~~~~~
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Figure 3. Experimentalphase diagram for the phenacetinhenzamide system. The lines are extrapolations of least-squares fits to the points closest to the eutectic. and the melt is distinct and allows the transition temperatures to be determined with high precision. The temperature for the eutectic is recorded at the first sign of black regions or dulling of the interference colors. When the li&dus tempera& is reached, the field turns mmpletely black. To help save time and avoid eve fatieue the students are given a list of suggested observ&on ranges. Data Analysis and Results
When this experiment was performed by the cooling curve method, the most difficult pan of the data analysis was the evaluation oftheoften ill-defined break and arrest temperatures. By using the DSC and micmscope to acquire the data this time-consuming step is eliminated, and the students are able to d o t the Dhase d i m a m directlv.Asample plot is shown in'~igure'3 for a d s a set obtaiLed with the DSC. The solidus line is drawn as the average of the eutectic temperatures for the 11mixtures studied. Construction of the liauidus lines depends on the sophistication of the available software f&lities. If the students make use of nonlinear fitting routines, they may determine best-fit curves for the two sides of the diagram. However, a simpler approach was used for the data shown in Fikwre 3. G o lea;; squares hnes were constructed: one using the three data points closest to the euwnlcon the benzamide-rich side; the other using the corresponding three points on the phenacetin-rich side. The intersection of these two lines with each other gave the central value of the eutectic composition (0.366 mole fraction phenacetin). The upper and lower confidence limits were taken as the intersections of these lines with the eutectic line (0.355 and 0.374 mole fraction). Data obtained with the microscope were treated in like fashion. The data for the phase diagram also can be used to calculate the enthalpies of fusion for the two pure components ( I ) . The derivation, which is valid only for mole £ractions close to the extremities of the plot, assumes that Raoult's Law holds, and that there is no solid-solid solubility. For a general component A,
where T~ and BMAf are the melting point and enthalpy of fusion of A, and X is the mole fraction of the second component. A plot of ?he liquidus temperature versus XB should be linear for very small XB.dueswith slopegiven by and intercept m a 1 to TA.An analogous equation may be written for TB*AH&f, ,andXll The students are provided with several mixtures close in composition to pure benzamide and ~ u r ohenacetin. e Referrine to Fieure 3. a data set, consistiig of {he melting point of &re bekamide plus the liouidus tem~eraturesof the three closest mixtures. was sGbjected to feast-squares analysis, and another least: squares line was constructed for the four points on the far right side of the diagram. The slopes of these lines were used to evaluate the enthalpies of fusion of the two compounds. (Note that the lines plotted in Figure 3 are extrapolations of the ones used to cahulate theutectic composition.) For comparison, the AH& 's also are obtained directly from the calibrated (with an indium standard) DSC peak areas for the pure compounds. A summary of the results obtained from Figure 3 (plus the correspondingmicroscope results) are presented in the table. Although the uncertainty is greater for the eutectic composition calculated from the microscope data, the result is closer to the literature value. This tendency may be a consequence of the difficulty in evaluating the liquidus temperatures &om the DSC plots. As mentioned above, the peaks are resolved poorly for mixtures in the middle of the diagram. On the other hand, the eutectic temperature evaluated by the microscope method is slightly higher than the literature result. Students sometimes have trouble discerning the initial melting of the eutectic, thus leading to an elevated value by that method. The calculated enthalpies of fusion are all low compared tKthose obtained directly from the DSC. Because the values are evaluated by dividing RTA2by the negative of the slope, the slopes must be t w steep. This is expected, because of the curvature near the extremities of phase diagram. The data possibly could be improved by -analyzingmore mixtures inthese regions, but, considenh;: the time constraints, the observed results are acceptable.
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Addiiional Exercises
Because of its simplicity and direct interpretation by the theory of colligative properties, this experiment focusses on a eutectic phase diagram. However, simple eutectic behavior is somewhat rare. and students should be ex~osed to syswms that demonsbate other types of phase huilibrio. most notablv solidsolid solubilitv and formation of an addition comp&d. Considering the"time constraints of the usual laboratow schedule. it is not feasible to DreDare more than one com
