The Solid-Liquid Phase Equilibria of Two Component Systems WALTER W. LUCASSE, ROBERT P. KOOB, and JOHN G. MILLER University of Pennsylvania. Philadelphia, Pennsylvania
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ROM the standpoint of the many applicatiolis of condensed phases, the solid-liquid region of phase diagrams of polycomponent systems is perhaps the most important portion of the complete or limited space models. It is the effect of the variables of condition on the equilibria of condensed phases which has fuithered the interpretations of geology, aided in the classificationsof mineralogy and been of value to metallurgy and to industry, in general, in the purification of materials and in the fabrication of products of chosen characteristics. TYPESOR SYSTEMS Even in two component systems, the equilibrium curves in the solid-liquid region show wide variety and the many types may be classified in a number of ways. Considering only cases in which the components are miscible in all proportions in the liquid state, a convenient grouping, which places emphasis upon the solid phases, is as follows: A . Solid solutions are formed.
1. The solids are completely misible. (a) The melting points of the solid solutions lie everywhere between those of the pure components. ( b ) The melting point curve shows a maximum. (c) The melting point curve shows a minimum. 2. The solids are partially miscible. (a) The melting ljoint curve shows a eutectic. ( b ) The melting paint curve shows a transition point. B. The equilibrium solid at each point is a single constituent. 1. Over the entire curve, the constituent is one of the pure components. 2. Along part of the curve, the constituent is a compound of the pure components. ( a The compound has a congruent melting point. ( h ) The compound has an incongruent melting point.
Generalized curves, together with examples of these various types of systems, may be found in several books dealing with the phase rule and illustrations, of a t least some, are given in most of the elementary texts of physical chemistry. Suitable laboratory experiments covering this important aspect of the phase rule are, however, less readily available. There is, perhaps, no need for experiments pertaining to systems falling in the first group, A . Curves entirely analogous to those in the first portion of this group, 1, are obtained with completely miscible liquid pairs in which the boiling points of the mixtures, a, lie everywhere between those of the pure components, b, show
a maximum, or c, a minimum. Information from these readily determined liquid-vapor curves is easily applied to the solid-liquid systems. Discussion of either the liquid-vapor or of the solid-liquid systems makes the other more clear and real. Such consideration usually involves the difference in composition of the two phases in equilibrium at the same temperature, the effect of change in temperature upon the composition and relative amounts of the two phases a t constant total composition, and the ultimate result of successive removals of one phase from the system-fractional distillation or fractional crystallization. Usually this operates to the clarification of solid-liquid systems and of the nature of the solid state. Indeed, following common experience with solutions of gases in gases, solids in liquids, and only slightly lesser familiarity with solutions of liquids in liquids, these phase diagrams offer a unique opportunity to make more tangible one of the types of true solutions least often encountered by undergraduates, namely, solutions of solids in solids. Extension of the general picture of solutions is likewise obtained from the second part, 2, of the first group, A , in which the solids are only partially miscible. The curves realized are entirely analogous to those for partially miscible liquids and can be obtained much more readily for the latter systems. The significance of the vaporization and condensation curvesparticularly after a thorough study of the familiar liquid-liquid system, phenol-water--can be extended to the melting point and freezing point curves of partially miscible solids. Experiments designed to illustrate the solid-liquid equilibria in the second group, B, are found in numerous laboratory outlines. The components used are either metals of relatively low melting point or organic compounds, American authors favoring the former. The use of metals offers the advantage of experience with a thermocouple, and possibly its construction and calibration, together with the experimentally desirable conditions of high heat conductance and absence of supercooling. The temperatures of the less oxidizable molten metals are, however, a hazard in crowded laboratories and with groups having less skillful technique; also, part of the apparatus is often of short life; and finally, perhaps educational institutions should set an example in the conservation of exhaustible resources. Combinations of organic compounds afford a wide range of temperature choice but often show a strong
tendency toward supercooling. This difficulty can be effectively circumvented by selection of the method of study. The variety of compounds available offers an opportunity for use of inexpensive materials which are of sufficient familiarity that interest in the study a t hand is not obscured by curiosity as to the nature and structure of the substances used. In the present paper, determination of the equilibrium curves with two pairs of organic chemicals, which have proven advantageous, is discussed. The one combination shows a simple entectic, that is, over the entire curve, the equilibrium solid is one of the original pure components--1 of group B. The second pair illustrates compound formation, that is, along part of the curve the equilibrium solid is a new constituent, a compound of the original components-2 a of group B. Having studied liquid-vapor, liquid-liquid, and the two types of solid-liquid equilibria just mentioned, there seems little need for the average undergraduate to acquire personal experience with the highly complicated, last type of solid-liquid system listed above-2b of group B.
pedagogical advantages of the other methods, direct determination of the melting point is perhaps the most obvious and convenient method for student experimentation. In such studies, whereas theoretically the temperature should be observed a t which the last crystal of solid disappears, in practice, due to the usually too rapid rate of temperature change and the lack of sufficient stimng, the melting point corresponds to a temperature a t which there is still a fairly large amount of solid present, the point a t which a sudden sharp rise in temperature takes place. THE BENZENE-ACETIC ACID SYSTEM
Discussion. The data for the solid-liquid equilibria of the system, benzene-acetic acid, given in the International Critical Tables of Numerical Data (3), are plotted as curve A B in Figure 1 and show that the system forms a simple eutectic a t 43 mole per cent acetic acid, with the corresponding temperature -8.8'C.
METHODS OF OBSERVATION
Basically, there are two methods for obtaining the curves for the systems being considered: determination of the composition of the liquid in equilibrium with the solid a t a series of constant temperatures; determination of the temperature of phase change a t a series of constant total compositions. The latter can be found either by cooling the system to the first incidence of solid, the freezing point, which in practice becomes the cooling curve method; or by heating to the disappearance of the last trace of solid, the melting point, which should not be confused with the appearance of the first trace of liquid, the thaw point. The distinction between these two points, incidentally, is of primary importance in the study of systems in the first group. The various lines of approach have particular advantages and disadvantages so that which is chosen depends frequently upon the system to be investigated. If one of the constituents is readily removed, as by evaporation, or can be determined by convenient analytical methods, evaluation of the composition of the liquid in equilibrium with the solid offers a convenient and direct method. Its primary difficulties, however, particularly as an undergraduate experiment, involve maintenance of constant temperature, establishment of true equilibrium, and the isothermal withdrawal of the solution to be determined. In general, systems with high thermal conductance and only slight tendency to supercool are readily studied by means of cooling curves. The point of abrupt change in slope of the temperature-time curve marks the temperature a t which solid first starts to form. Even where supercooling takes place, the correct value of the freezing point can frequently be obtained by repeated determination of the cooling curve a t a single total composition. thus permittha extrapolation to zero snpe&mlini ~ l t h o u ~lacking h some of the
,
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Mole Per Cent Acetic Acid Frcuns 1.-THE SYSTEM BENZENE-ACETIC ACID. CURVEAB-I.C.T. MOLEPERCENTBASED DATA, ON SINGLE FORMULA WEIGHT FOR ACID. CURVE FG-I.C.T. DATA. MOLE PER CENT BASED ON DOUBLE FORMULA WEIGHTPOR ACID. CURVECDIDEUCunvs, ASSUMINGSINGLE MOLECULES FOR ACID. CURVE E-IDEALCURVE,ASSUMINGDOUBLE MOLECULE^
POR
ACID.
Phase data may frequently be plotted in a number of ways in order to achieve a certain type or distribution of curve or to emphasize a basic significance in the relations involved.. -1n the figure, &e placement of the curveis satisfactory and its formconvenient for comparison; however, it is questionable whether its significance is as basic as might a t first be thought. I t has long
been known (6, 1, 2, 5) that acetic acid a t such low temperatures is highly associated into double molecules not only in the vapor and liquid states but also in nonpolar solvents. Assuming the acid to be made. up entirely of double molecules, the data have been replotted to give curve FG showing a eutectic a t 27.4 mole per cent acid, with, of course, the same value as in curve AB for the eutectic temperature. Emphasis in the discussion of solid-liquid curves of this type is usually centered upon their showing both the freezing points of solutions of various compositions and the solubilities of the constituents a t a series of temperatures. If ideal solutions were formed over the entire range, plots of the reciprocal of the absolute temperature against the logarithm of the mole fraction would be of greatest significance. On that basis, the curves would be straight lines of the form, log x =
L
A H "2D '. "l. \. -
1 7) 1
in which x is the solubility of the solid constituent in terms of mole fraction a t the temperature T, its freezing point and latent heat of fusion per mole being To and AH. Taking the freezing point of acetic acid to be 16.64"C. and that of benzene 5.51°C. with the heats of fusion per formula weight 2680 and 2370 calories, respectively, the equation simplifies to log x = 2.02
- 586/T
for acetic acid and log z
=
1.86
- 518/T
for benzene. These equations lead to the curves C and D in Figure 1 and show the ideal solubilities. Taking double the heat of fusion of acetic acid modifies the equation for the acid and gives the curve E. The intersection of curves C and D shows the ideal eutectic to be a t 43.3 mole per cent acid, which is practically the same as the value from the experimental curve on the same basis. At this composition, the indicated melting point, -27.3T., however, is much lower than the experimental. Assuming the acid to be dimeric gives the ideal eutectic a t 30.0 mole per cent acid with a melting point about 7.4OC. below the experimental value, presenting further indication of the molecular condition in the liquid state. The deviation of the real solubility curve from the ideal is, of course, due to a number of factors such as the variance of the heat of fusion with temperature and the interaction of solute and solvent. Thinking of the curves as freezing points of solutions of various compositions normally focuses attention upon the eutectic, and there are several aspects which often require particular emphasis. Since metallurgical and other work is usually carried out a t atmospheric pressure one of the variables has already been fixed and likewise one phase, the vapor, is virtually removed. Thus, the two component system has become fixed in the presence of the three phases, solid 1, solid 2, and liquid, only because the number of variables has been reduced from four to three by the arbitrary selection of
the pressure. If the pressure is retained as a variable, the eutectic temperature and composition will assume new values. Only in case the pressure is reduced to the +apor pressure of the coexisting solids and liquid, with the result that the fourth phase, the vapor, is in equilibrium with the others, will the system become truly invariant, pressure, temperature, and composition all being a t definite values. Perhaps, in analogy to normal boiling point and normal melting point, the term normal eutedic should be introduced, or possibly the fixed point might be called the true eutectic, to suggest that just as the boiling point and the melting point of one component systems are functions of the pressure, so the point of "easy-melting" of two component systems is variable. In all three cases, the generality of the phase rule is colored by our existence in a pressure bath of approximately constant value. In defense of the common usage, however, it must be noted that the eutectic temperature and composition change only slightly with theApressure. Closely related to this point is the manner of expressing the composition in the region of complete solidification. In cooling any melt except that of the eutectic. the solid phase which appears a t the freezing point is one of the pure components. Upon further cooling, in the main, accretion upon the initial solid takes place rather than formation of additional nuclei. Thus a t the eutectic temperature, when the entire mass solidifies isothermally, relatively large particles of the pure component become embedded in an apparently homogeneous solid of eutectic composition. This appearance of two contrasting solid portions, which is particularly evident in microphotographs of metallurgical systems, has fostered the tendency to express the composition of the solid in terms of the pure component and the eutectic mixture. Since the latter, however, is not of constant composition, throughout the entire solid region it is more appropriate and less misleading to express the composition in terms of the pure components. Experimental. In studying the system benzeneacetic acid, i t is not necessary to determine the cooling curves and is more rapid and convenient to obtain only the melting points. The inner tube of a Beckmann freezing point apparatus, or merely an &inch pyrex test tube, together with an ordinary thermometer serve for making the observations. It is advisable to use a glass stirrer which can easily be made from 3-mm. glass rod. Metal stirrers, such as brass, cause reaction in the system which leads to discoloration and, i t would seem, a greater tendency toward supercooling. Furthermore, to avoid contamination with stopcock grease, i t is well to use Mohr burets for the liquids. The low temperatures needed to freeze the various compositions are obtained by use of a salt-ice mixture held in a 400-ml. beaker and a minimum temperature of about - 10°C. will suffice. An experimental advantage of the present system, in addition to its convenient temperature range, is the freedom from time-consuming weighings. The masses
used may be determined with sufficient accuracy from the volume and density of the liquids a t room temperature. Ten ml. of the acid are 6rst introduced into the tube and cooled in the ice bath. As soon as crystals start to form, the tube is removed and the temperature observed, with continued stirring, as room temperature causes the crystals to melt. As indicated above, the best melting-point readings are obtained in the study of this system, while appreciable solid still exists, just before the temperature starts to rise rapidly, rather than a t the theoretically correct point where the last crystal disappears. In the same manner, the melting point of the mixture is determined when benzene bas been added to the contents of the tube in the following successive amounts: 1.5, 2, 3, 3, and 3.5 ml. To complete the composition range, the experiment is repeated, starting this time with 15 ml. of benzene and adding acetic acid to the contents of the tube in the following successive amounts: 1.5, 1.5, 2, and 3 ml. Here, as in the experiment below, the suggested amounts give a satisfactory distribution of points and should be used as nearly as possible. In Figure 2, the data which gave the curves of Figure 1 are replotted as a smooth curve in terms of weight per cent. It is doubtful whether there is any advantage in pointing out to the student that such a plot avoids the question of molecular aggregation. I t is sufficient that he see from the present and the following experiment that phase data may be plotted in more than one way, sometimes to advantage directly in terms of weight. To show the distribution of the points and to indicate the student accuracy, all of the points obtained by six undergraduate students, working in groups of two each, are superimposed upon the plot. p-TOLUIDINE-ACETIC ACID SYSTEM Discussion. The system p-toluidiue-acetic acid is of particular interest since compound formation is here encountered. The average student is aware of compounds between metals and nonmetals and those of organic nature almost to the exclusion of other types. He has rarely more than a vague knowledge of the existence of compounds between the various halogens and of such compounds as iodine oxide. Compounds between two of the more electropositive elements are still less familiar and possibly the cause can be found both in the physical nature of the reacting elements and in the limited importance of the compounds. If the metals were molten a t lower temperatures or more commonly soluble in nonmetallic, nonaqueous solvents, or if the resulting compounds were of more practical interest beyond such restricted fields as metallurgy, it is possible that the nature and properties of intermetallic compounds would be of more general knowledge. Obviously, i t is not implied that such compounds should be discussed in general chemistry with resulting danger to the unifying simplicity of the subject. Rather, it is indicated that here again physical chemistry offers a unique opportunity not only to present its restricted field but also to unfold a t an age of greater THE
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Acetic Acid
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FIGURE 2.-THE SYSTEM BENZBNPACETICACID. THE CIRCLS, 0 , 0-, -0, SHOWTHE RESETS OF THREE STUDENT GROUPS. intellectual maturity some of the more advanced facts and theories of branches of chemistry presented a t an earlier period of training. Studies of intermetallic compounds can be made by means of a number of physical properties such as specific resistance and the temperature coefficient of resistance, hardness, thermal conductivity, and thermoelectromotive force. Perhaps the most frequently used and simple method is that of thermal analysis. However, as has already been indicated, such phase studies with metallic systems are frequently difficult and similar experience and understanding can be obtained from organic systems. Having fully studied a phase diagram in which a simple eutectic is present, the interpretation of a system in which compound formation appears is facilitated by initial consideration of the diagram as made up of two parts, each showing the temperature-composition relations of a system made up of the compound and one of the pure components. It is immediately seen that in both parts, the curves represent the freezing points of mixtures of definite compositions and the solubilities of the components, together with those of the resulting compound, a t a series of temperatures. Again, the fact may be emphasized that the eutectic is not a compound, the composition being a function of the external pressure just as with the more readily comprehended constant boiling mixtures of two component liquid systems. Interest in such diagrams has to do primarily with the compound and involves both composition and temperature. As an introduction, i t is readily uuderstood that when gaseous hydrogen chloride is added to gaseous ammonia until the components are present in equimolecular amounts, the system suddenly ceases to be a solution of one in the other, becoming identical with the vapor of ammonium chloride and thus a one component system. This picture is easily carried over to the solid-liquid system a t the indierent mint and the contrast betwe& this point and the euteciic can be amplified by means of the phase rule. At the indifferent point, under normal conditions, the system is made
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6, 0-, -0,SHOW THE RESULTS OF THREE STUDENT GROUPS. 3.-THE SYSTEM 9-TOLUIDINE-ACETIC ACID. THECIRCLES,
up of one component in two phases, and hence there is but one degree of freedom. With changes in the external pressure, as with other pure compounds, the melting point only and not the composition is altered. Finally, when the external pressure is lowered to the vapor pressure of the condensed phases, the vapor is also present and the system becomes entirely fixed a t a definite temperature, pressure, and composition, the latter being the same for each phase and unaltered during the changes in pressure and temperature. The indifferent temperature may he further contrasted with the eutectic point. From experience with the lowering of the freezing point of a pure solvent by a solute, that is, the lowering of the freezing point of one pure component by the addition of a second, the observation that the temperature of the indifferent point is lowered by the addition of one of the components, whereas the eutectic temperature is raised, immediately relates the former with a chemical entity. The form of the curve in the neighborhood of the maximum can now be contrasted with the rectilinear lowering to be expected from the laws of dilute solutions. That the maximum is frequently flat is seen as evid a c e of the lowering of the freezing point of the compound by the products of its own dissociation and as a measure of the stability of the compound. This instability, together with difficulties of isolation and study by the usual methods, is in keeping with the general lack of information relative to such compounds. Ezperimentul. In Figure 3 the data from a recent study (4) of the system p-toluidine-acetic acid are
plotted as a smooth curve showing formation of the compound 9-toluidine.2 aceticacid. If themole fraction had been plotted in terms of double rather than single formula weights of acetic add, as study of the system benzene-acetic add would suggest, the maximum would have been a t 50 mole per cent and the indicated formula p-toluidine(acetic acid)^. The general uncertainty as to the molecular condition of substances in the liquid state, however, makes more appropriate the form of plot shown. Superimposed on the curve are unselected points from a group of undergraduate experiments from which it can be seen that the form of the curve can be duplicated with a reasonable degree of accuracy. In studying the system 9-toluidine-acetic acid, the apparatus and method are the same as indicated above. It is even more essential in this case than when working with the benzene-acetic acid system that a glass stirrer be used, as there seems to be a still greater tendency with a metal stirrer toward reaction and supercooling. With a brass stirrer the system quickly becomes dark hrown, practically black, and i t is almost impossible to observe the incidence and disappearance of crystals. In case of all mixtures, the system should first be heated until a homogeneous liquid results, then cooled to partial solidification, and finally warmed gradually to obtain the melting point. Upon cooling, some of the mixtures crystallize only with diiculty, a t first merely becoming increasingly viscous. In taking the melting points, the mixtures should be heated very slowly and only for those melting above 15'C. should a burner be used.
In order to minimize the number of weighings necessary, the system might be studied by adding acetic acid to a weighed amount of p-toluidine until well toward the eutectic on the acetic acid side. However, since classroom consideration of the phase rule does not always precede or accompany the laboratory work, it seems as well to emphasize the nature of the system by dividing its study into four parts, as follows: 1. Approximately 10 g. of p-toluidine is weighed into the test tube to the nearest centigram and the melting point determined. It is then partially solidified and the melting point checked. In the same manner the melting point is found of each mixture resulting from the following successive additions of glacial acetic acid: 0.5, 0.5, 0.5, 0.5, 1,2, and 2 ml. 2. A fresh start is made with about 3 g. (ca. 2.89 ml.) of acetic acid and 2.68 g. of p-toluidine. The mixture is melted, partially solidified, and the melting point observed. The melting point is then determined of each of the mixtures resulting from the following additions of p-toluidine: 0.8,0.8,0.8,1.5,2.5,and 3.5 g. 3. Ten grams of acetic acid are introduced into the
tube and the melting point determined. The melting point is then found after making each of the following additions of p-toluidine: 0.5, 0.5, 0.7, and 0.8 g. 4. A new start is made with 6 g. of acetic acid and 5.35 g. of p-toluidine. The mixture is melted, partially solidified,and the melting point determined. The melting point is then obtained after making each of the following successive additions of acetic acid: 0.5, 0.5, 0.5, 1, 2, 2, 3, 3, 3, and 5 ml. In any event, if fewer points are determined, more material introduced inadvertently, or the specified amounts not conveniently weighed out exactly-as would seldom be the case-the amounts actually used must be known in all cases to a t least 1 per cent. LITERATURE CITED
(1) B E C ~ N N 2.,physik. Chent.. 2, 715 (1888). Ber., 38, 1138 (1905). (2) HERZAND FISCHER, (3) "International Critical Tables of Numerical Data." McGrawHill Book Company, Inc., New York, 1928, 'Vol. IV, p. 108. , J . Phys. Chem.. 48, 85 (4) LWCASSB. KOOB, AND MILLEI (1944). AND SCARLETT, J . Am. Chem. Soc., 39 2275 (1917). (5) MORGAN (6) RAMSAV AND YOUNG, J . Chem. Soc., 49, 790 (1%).
