Theory

Figure 1. Logarithm of the solubility of naphthalene in benzene as a function of inverse temperature. (S. U.  Pickering, J. Chem. Soc., London 63, 998 (1893))

The system naphthalene-benzene forms an ideal solution. The initial dependence is linear, as predicted by Equation (1). There is, however a sudden break in the curve at the point corresponding to T = 269.8 K (-3.4 °C) at a mole fraction of 0.133 naphthalene. The reason for this sudden break becomes more apparent if the data is treated in a slightly different way.

Figure 2.  The data of Figure 1 plotted as a phase diagram.

Figure 2 shows the same data plotted as a phase diagram. The experiment points correspond to the freezing points of the mixtures. By general convention, component on the left (in this case naphthalene) is known as component “A,” and that on the right (in this case benzene) is known as component “B.”; The components shall be referred  to by these designations.  At the left, the curve intersects the ordinate at the melting point of pure A; and at the right, it intersects the ordinate at the melting point of pure B. The minimum in the freezing-point curve is called the eutectic, and a horizontal line has been drawn along the eutectic temperature. The curve to the left of the eutectic can be considered a freezing-point-depression curve for component B dissolved in A, and the curve to the right of the eutectic a freezing-point-depression curve for A dissolved in B. This type of phase diagram is found for numerous binary systems in which the liquids are completely miscible and the solids completely insoluble in each other. (To be sure, there will always be some slight solubility of the solid phases in one another; but if the solubility is sufficiently small, it can be neglected.) For purposes of discussion, it will be useful to consider the sketch of the phase diagram shown in Figure 3, where the freezing-point-depression curves have been approximated by straight lines.

The phase diagram can be experimentally constructed by using cooling curves, as depicted in Figure 4. Samples containing known amounts of both components are placed in containers and heated until complete dissolution occurs. The samples are then allowed to cool slowly and the temperature of each sample is noted as a function of time until the entire sample has solidified. Cooling curve (i) is for pure A.  As the liquid sample cools, heat is lost through radiation and convention, and the temperature of the sample decreases at a rate indicated by the first portion of the cooling curve. When the melting point of pure A is reached, there is a sudden break in the curve; the temperature remains constant while the heat of fusion is released, as indicated by the horizontal portion of the cooling curve. When the last liquid has solidified, the sample, now a solid, begins to fall in temperature once again.

Now consider cooling curve (ii) along the line of constant composition indicated as (ii) on the phase diagram of Figure 3. The system has two components; hence the number of degrees of freedom is f = 4 - p. The pressure has been specified for this phase diagram, reducing f by unity and leaving f = 3 - p on the phase diagram.

Initially curve (ii) is a one-phase liquid region; f = 2 in the melt, since p = 1 in that region. The first break in cooling curve (ii) occurs at T = T², where some pure solid A begins to precipitate from the melt. Since two phases (liquid and pure solid A) are in equilibrium, the number of degrees of freedom falls to f = 3 - 2 = 1. As pure solid A precipitates, its latent heat of fusion is released, and the rate of cooling slows, as indicated by the sudden change in slope of the cooling curve. The melt becomes richer in component B as component A is removed, and the freezing point of the melt decreases along the freezing-point-depression curve.

Figure 4.  Sample cooling curves.

Now let’s examine point X in the two-phase region on the phase diagram. The overall composition is given by point X. The system is composed of two phases, a pure solid A phase, indicated by Y and a liquid phase, whose composition is given by point Z. The line YXZ is a tie line connecting the two phases, and the lever rule applies. The ratio of the amount of solid present to the amount of liquid is XZ/XY.  The composition of the melt has moved from the point indicated by T^” to the point Z.

A second break in the cooling curve appears at T_E, the eutectic temperature. The horizontal portion of the cooling curve corresponds to the solidification of the eutectic mixture. It has the same appearance as the curve for the solidification of the pure compound. In fact, eutectic mixtures give the appearance of pure compounds. They have constant freezing points, and the solid eutectic mass is a very fine grained mixture of the two components. The horizontal portion corresponding to the freezing of the eutectic is known as the eutectic halt. When the last of the eutectic has solidified, the cooling curve again begins its downward trend.

At the eutectic point, there are three distinct phases in equilibrium: liquid solution, pure solid A, and pure solid B. At constant pressure, the eutectic point is fixed and has no degrees of freedom remaining.

Cooling curve (iii) is for a mixture somewhat richer in component B and resembles (ii). The first break occurs at a somewhat lower temperature, and the eutectic halt is longer, since there is more eutectic present when T_E is reached. The cooling curve for the eutectic composition is shown by curve (iv). Now there is only one break, that break occurring at T_E. To complete the series of cooling curves, the curves (v) and (vi) have also been shown. Curve (v) is for an isopleth (a curve of constant composition) to the right of the eutectic and is completely analogous to curves (ii) and (iii). Curve (vi) is for pure component B and is similar to curve (i); the horizontal portion occurs at T_B, the melting point of pure B. With enough cooling curves, a complete phase diagram like that in Figure 2 can be constructed by plotting the points corresponding to the breaks in the cooling curves and connecting these points by smooth curves.

COMPOUND FORMATION

Suppose we have two components A and B that can combine to form the compound AB. Suppose further that solid A and solid AB are insoluble in each other and that liquid A and liquid AB are completely miscible. In addition, solid AB and solid B are completely insoluble in each other, and liquid AB and liquid B are completely miscible.  A complete phase diagram for the system A-B can be constructed simply by juxtaposing two phase diagrams, A – AB and AB – B, as shown in Figure 5. For the compound AB, the central maximum occurs at 0.5 mole fraction B. If the compound were of the form AB₂, this central maximum would occur at X_B = 0.667; whereas for a compound of the formula A₂B, the peak would occur at X_B = 0.333. The system Mg-Si forms the compound Mg₂Si; the phase diagram for this system is shown in Figure 5. Note that the eutectic Mg-Mg₂Si is only 0.012 mole fraction Si and melts slightly below the melting point of pure Mg.

In some cases a series of compounds may be formed. This is often the case for salts and water, when several different hydrates are formed. An extreme example of this is the system FeCl₃-H₂O, which forms four hydrates. It can be split into five simple phase diagrams. The four peaks correspond to the melting points of the successive hydrates.

Figure 5. Eutectic phase diagrams with compound formation. (a) The system A-AB. ( b) The phase diagram for the system Mg-Si, which forms the compound Mg₂Si.

Experiment

Apparatus

Ten 6-inch Pyrex test tubes and one larger Pyrex test tube to serve as jacket (S); magnetic stirrer- hot plate combination (S); beaker (D); ring stirrer constructed of nichrome wire (S); test tube rack; timer (S); temperature probe (S); Dewar (S); ice (L); disposable plastic gloves (S); two (2) large finger clamps (S); and one ring clamp (S).

Chemicals

40 grams naphthalene (S) and 40 grams o-nitrophenol (S); or 40 grams naphthalene (S) and 40 grams p-dichlorobenzene (S).

The following system may be substituted at the discretion of the instructor: naphthalene, m-nitrophenol.

The experiment, except for the weighings, is to be performed entirely in the hood!

Set up the temperature probe as described in the “serial box” write-up given in the Sensor section. Calibrate the temperature probe in an ice bath and a steam bath.

A total of six grams weight is sufficient for each binary mixture. Melt the mixture in the beaker of boiling H₂0.  NO FLAMES!  Obtain several cooling curves for each mixture.

At the conclusion of the experiment, remelt all samples and pour into labeled jar provided for collection of waste!

This experiment illustrates the use of cooling curves to establish the phase diagram for a binary system. It illustrates also the use of the temperature probe.

PROCEDURE. Phase relationships can be illustrated by use of mixtures of organic compounds as well as metal-alloy systems. For example, compound formation between the components is shown by the system phenol-p-toluidine.

Caution: These compounds must be handled with great care to avoid contact with the skin.

For the system assigned, a set of about 10 freezing-point tubes should be prepared to cover the composition range from one pure component to the other. The compounds are weighed out carefully into 1 by 6-in. test tubes; about 6 g total mixture weight is sufficient. One of the tubes is heated with hot water or a bunsen burner until the mixture is barely, but completely, melted. It may be necessary to insert the test tube in a larger test tube, with the help of a cork ring, to reduce the rate of cooling. To do this a small glass tube, closed at the bottom, is fitted into a cork and set so that it reaches near the bottom of the melted material. The temperature probe fits into this well. The probe is calibrated in an ice bath and a steam bath (with corrections for barometric pressure) and at intermediate temperatures with one or two other materials with sharp melting points.

A ring stirrer is used to keep the cooling mixture at a uniform temperature. The stirrer may be made from thin glass rod or nichrome wire or other chemically inert wire.   The temperature probe and the stirrer should be in the test tube when it is in the hot water so that the insertion of these objects does not cool the mixture too quickly at the start of the experiment.  It is most important to make sure that at the beginning of each cooling curve the system is at equilibrium and in the molten state, otherwise the first break in the cooling curve will be misted.  Also, it is important to cool each mixture until the plateau where everything is in the solid state is obtained.  An outer jacket is not needed for the systems used here because the cooling rate at the temperature used is slow.

A time-temperature graph is obtained by recording the temperature as a function of cooling time.  A sampling rate of 0.2 times per seconds and total time of 2000 seconds is recommended for recording the results using the temperature probe.

The mixture may be melted again, and a check determination made. The test tube should be thoroughly cleaned before inserting in the next sample. The procedure is repeated with each of the mixtures. It is important to use pure materials for preparing the mixtures.

For mixtures with low freezing points the test tube and its outer jacket may be immersed in an ice bath or an ice-salt mixture. If the compounds are subject to air oxidation or tend to absorb moisture or carbon dioxide from the air, they may be sealed off in an all-glass tube. The thermometer well is sealed into the top of the tube and extends nearly to the bottom of the tube. The sample is introduced through a side tube, which is then sealed off. It is more difficult to avoid supercooling in this apparatus in which shaking is the means of stirring.

A major experimental problem in all this work is supercooling, i.e., failure of crystallization to take place at the proper temperature. Actually, a small extent of supercooling is useful, since then, when crystallization does start, the crystals formed are dispersed widely through the liquid, and equilibrium between the solid and liquid phases is more easily maintained. If supercooling seems too great, the experiment is repeated, with more vigorous stirring at the appropriate stages. Supercooling may usually be avoided by dropping in a “seed crystal” of the solid material.

The collection of  picture during a sample cooling curve is given below:

Naphthalene and dichlorobenzene form miscible liquids at higher temperatures and insoluble solid phases at lower temperature. To study this phenomena 3.640 grams of naphthalene and 2.878 grams of p-dichlorobenzene were place in a tube and heated to around 100 ^oC in boiling water. The mixture was calculated to have a 0.59 mole fraction of naphthalene. A Vernier direct temperature probe and a metal stirrer were added to the mixture, the assemble allowed to reach a temperature equilibrium, and the entire assemble removed from the boiling water. The temperature was monitored using the Vernier logger pro software with an initial temperature around 67 ^oC as seen in Figure 6.

Figure 6. Initial cooling curve for p-dichlorobenzene-naphthalene mixture.

This mixture was allowed to cool in air with continual temperature monitoring. The temperature of the sample decreased at a steady rate to a temperature of 51 ^oC (see figure 7). There is little or no change in the physical appearance of the sample.  At a slightly lower temperature crystals began to form (see figure 8).  They first appear as a blur, but as seen in figure 9 & 10 the crystallization is soon apparent. The physical appearance of crystallization is a very strong function of temperature at this point.  However, there is a small time lag before this crystallization has an effect on the cooling curve. The heat released during the crystal formation and supersaturation caused the temperature to rise from 49.6 to 50.5 ^oC, and the rate of cooling to slow as can be seen in figure 10 & 11 . Then there was a constant rate of cooling until the temperature reached 27.9 ^oC upon which crystallization was completed and a slight temperature rise to 29.6 occurred as can be observed in Figure 9.  The temperature as a function of time data was exported as a text file, imported into excel, and graphed as a scatter plot (see Figure 12). The

Figure 7. Cooling curve for p-dichlorobenzene-naphthalene mixture to around 51 ^oC.

Figure 8. Cooling curve for p-dichlorobenzene-naphthalene mixture at around 50 ^oC.

Figure 8. Cooling curve for p-dichlorobenzene-naphthalene mixture at close to 50 ^oC.

Figure 9. Cooling curve for naphthalene p-dichlorobenzene mixture at close to 50 ^oC.

Figure 10. Cooling curve for a naphthalene p-dichlorobenzene mixture at close to 50 ^oC

Figure 11. Cooling curve from 80 to 28 ^oC for a 0.59 mole fraction naphthalene p-dichlorobenzene mixture

liquidus temperature was determined to be 50.4 ^oC and the eutectic temperature 29.6 ^oC at the points circled in Figure 12.

Figure 12.  Excel plot of temperature for the p-dichlorobenzene – Naphthalene cooling as a function of time obtained using temperature probe.

THEORY. The purpose of the experiment is to obtain data by thermal analysis for constructing a phase diagram which indicates the solid and liquid phases that are present at each temperature and composition. The temperatures at which solid phases appear upon cooling various solutions of the two components are detected by observation of the changes in slope of the plot of temperature versus time. A slower rate of cooling is obtained while a solid phase is separating out because the heat evolved by solidification partly offsets the heat lost by radiation and conduction to the colder surroundings.

CALCULATIONS.

For each mixture studied, the cooling curve is examined to determine the temperatures at which abrupt changes in slope or complete arrests occur. The former signify changes in the number of phases present, and the latter indicate systems which are invariant under the condition of constant pressure.

A phase diagram is then prepared by plotting these temperatures against the compositions of the mixtures. For each mixture, all the data points corresponding to changes in the number of phases present should be put on the graph. Lines are drawn through the points to complete a phase diagram, and each area labeled according to the phases present. The various types of one-, two-, and three phase systems possible for the particular system studied are listed by identifying the phases present in each case, and the properties of each are discussed in terms of the variance calculated from the phase rule under the assumption of constant pressure.

A plot of ln X as a function of 1/T should be made for both naphthalene and p-dichlorobenzene and DH^o_fus calculated.  Also, the limiting slopes of the observed freezing-point curves can be calculated theoretically on the assumption that the solid phases are the pure substances. Thus, for a two-component system, with mole fractions X_A and X_B, the freezing point depression near X_A = 1 is given by                             

where T_f = melting point of solution of mole fraction X_B

           T_o = melting point of pure component A

           DH^o_fus = standard molar enthalpy of fusion for pure component A

The limiting slopes are estimated from the phase diagram, and the corresponding heats of fusion are then calculated and compared with values obtained from the literature.

Practical applications. The method of thermal analysis illustrated in this experiment is a basic procedure in the study of phase relationships. A maximum in the freezing-point-composition curve indicates the existence of an intermediate compound, and the Composition of the compound is given by the highest point on the composition temperature curve, for this represents the melting point of the pure compound.

Temperature-composition curves and other phase diagrams are of great value in the technical study of alloys and ceramics and in the recovery of a salt by crystallization from a mixture of salts.

Fractional crystallization is an effective method of purification.

The constancy of the freezing point through the whole solidification from start to finish is one of the best criteria for purity. If the substance is impure, the impurities become concentrated in the mother liquor as the liquid freezes out, and the freezing point is lowered more and more by the impurities.

Suggestions for further work. The following pairs of organic compounds are suitable for study: urea, phenol; naphthalene, nitrophenol; acetamide, B-naphthol; ,B-naphthol, p-toluidine; phenol, a-naphthylamine; diphenylamine, naphthalene. A number of phase diagrams in organic systems are discussed by Kofler and Kofler[4] and by Skau and Wakeham.[5]

References3

1. A. Findlay, A. N. Campbell, and N. O. Smith, “The Phase Rule and Its Applications,” Dover Publications, Inc., New York, 1951.

2. Reference Tables for Thermocouples, Natl. BUT. Std. U.S. Circ. 561, 1955.

3. Methods of Testing Thermocouples and Thermocouple Materials, Natl. Bar. Std. U.S. Circ 590, 1958.                                                                                        

4. L. Kofler and A. Kofler, “Thermo-Mikro-Methoden,” Verlag Chemie GmbH, Weinheim,  Germany, 1954.

5. E. L. Skau and H. Wakeham in A. Weissberger led.), “Technique of Organic Chemistry,”  vol. 1, “Physical Methods of Organic Chemistry,” 3d ed., pt. 1, chap. 3, Interseience Publishers,   Inc., New York, 1959.