TWO LIQUID PHASES FIRST PAPER
BY WILDER D. BANCROFT
Roozebooml has already pointed out the different types of equilibrium to be expected in three-component systems with only one liquid phase ; but he has not discussed the possibilities when two liquid phases can coexist. T h e object of this paper is to go over qualitatively some of the ground not yet covered by Roozeboom. Let us suppose that we start. with three substances, A, B and C, which form no compounds ; that the melting point of A is higher than that of B ; and that A and B can form the binary nonvariant system, solid A, two solutions and vapor. This system has no degrees of freedom ; but on adding the third component C, there is added a degree of freedom and the four phases, solid A, two solutions and vapor can exist over a range of temperatures, terminated only by the appearance of a new phase or the disappearance of an old one. I n all the two-component systems, which have yet been studied, the inversion temperature for the quadruple point, solid, two solutions and vapor lies between the temperatures at which the pure components melt. It will, nevertheless, be convenient to distinguish three types which may be represented by phenol and water, naphthalene and water benzene and water. I n the first, the inversion temperature is only about two degreesa above the freezing point of water while it is a good deal below the melting point of phenol. I n the second the inversion temperature is but little lower than the melting point of naphthalene and, relatively speaking, far above that of ice3. With benzene and water the melting points are only a Zeit. phys. Chem. 12,367 (1893). =Alexejew Wied. Ann. 28, 332 (1886). 3On determining this point myself, I found that water lowers the freezing point of naphthalene less than a degree instead of six degrees as I had been told was the case.
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few degrees apart and the inversion temperature is therefore not very far from either, though very much nearer the temperature for benzene than for water. There is no fundamental difference between these three types but certain equilibria are easier to realize in one case than in another. For instance with phenol and water it is very difficult to find a third component which will give a quintuple point at temperatures near the melting point of phenol while with naphthalene and water, it is very difficult to have ice in equilibrium with two solution phases and vapor when the third component is not a liquid at the temperature of the experiment. Whether the temperature of the three-component nonvariant system, two solids, two solutions and vapor, be higher or lower than the inversion temperature for the two-component nonvariant system, solid, two solutions and vapor, depends primarily upon the relative solubility of the third component in the other two. If we call phenol A, water B and the third component C, we can make the following classification : I. T h e component C is a solid a t all temperatures included in the experiment. a. C is soluble in B, practically insoluble in A. b. C is soluble in A, practically insoluble in B. c. C is soluble in A and B. 11. T h e component C is a liquid at all temperatures included in the experiment. a. C is consolute with liquid B, practically nonmiscible with liquid A. b. C is consolute with liquid A, practically nonmiscible with liquid B. c. C is consolute with both liquid A and liquid B. 111. T h e component C is a gas at all temperatures included in the experiment. a. C is much more soluble in B than in A. b. C is much more soluble in A than in B. c. C is readily soluble both in A and in B. Ia. T h e component is a solid, soluble in water, insoluble in phenol., Potassium nitrate and sugar satisfy these conditions. T h e effect of adding C is to decrease the mutual solubilities of the two
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substances A and B. Since the solution in which A is solvent becomes more and more dilute with addition of C, the monovariant system, solid phenol, two solutions and vapor, can exist at higher and higher temperature the more of C is added. The final nonvariant system will have A and C as solid phases. Since potassium nitrate is not very soluble in cold water, it will precipitate before the temperature has risen very much, while with sugar the tetnperature difference between the inversion point for the ternary system and that for the binary system shall be much greater. This is the case experimentally. The temperature at which solid phenol separates from a mixture of phenol and water forming two liquid layers was found to be 0.8' when using ordinary phenol. On adding potassium nitrate in excess, the temperature was raised to over 2' while with sugar a temperature of ten degrees was reached without difficulty and the solution was not yet saturated with sugar. With the increasing nonmiscibility of phenol and water caused by adding potassium nitrate, sugar or any substance coming under the heading I a , one of the solutions can be made to approach pure liquid phenol in composition to within almost any degree of accuracy depending on the solubility of the component C. Since the temperature at which this solution phase can be in equilibrium with solid phenol can not be forced above the melting point for pure phenol, solid solutions being excluded, it follows that no matter how soluble in water the third component may be, a quintuple point with two solution phases is always possible, that the temperature at which this point occurs can never be higher than the melting point of pure phenol and that the solid phases are necessarily phenol and the third component. Since the maxinium rise of temperature which is possible with phenol and water is nearly forty degrees and with naphthalene and water less than one degree, it is clear that the absolute rise of temperature on adding a given quantity of potassium nitrate will be much less for the monovariant system with naphthalene as component A than for the one with phenol. Ib. T h e component C is a solid, soluble in phenol, insoluble in water. Naphthalene will serve as an instance. T h e effect of adding the component C will be to make the two liquids A and B less miscible than they are ordinarily. T h e difference between
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the behavior of sugar and the behavior of naphthalene is that with the former we approach a saturated solution of sugar in water and a phase composed of pure liquid phenol as limits while with the latter we approach a saturated solution of naphthalene in pure phenol and a phase composed of pure water as limits. In the first case the solution in which phenol is solvent becomes dilute and the solution in which water is solvent becomes more concentrated with increased addition of sugar' while in the second case the solution in which water is solvent becomes more dilute and the solution in which phenol is solvent more concentrated with increased addition of naphthalene. T h e temperature at which solid phenol can exist in equilibrium with two solutions and vapor will be raised by addition of sugar and lowered by addition of naphthalene. If the component C is only sparingly soluble in phenol, it will precipitate as solid phase before the temperature reaches the freezing point of water and we shall have the nonvariant system, phenol, solid C, two solutions and vapor. This system can not be formed with naphthalene but it could probably be realized if sulfur were taken as the third component. If naphthalene be added continuously to a mixture of phenol and water the temperature at which solid phenol can coexist with the two solutions and vapor will soon fall below zero. Since the phase in which water is solvent is continually becoming more dilute, it is clear that at some temperature not far below zero degrees we shall have ice separating and the formation of the nonvariant system, phenol, ice, two solutions and vapor. If we continue to add naphthalene keeping the system at constant temperature the phenol will melt and finally disappear, the concentrations remaining unchanged. With increasing concentration of naphthalene in the solution in which phenol is solvent, the solution in which water is solvent will disappear. When this has vanished, leaving the divariant system, ice, solution of water and naphthalene-principally the latter-in phenol and vapor, a further addition of naphthalene will cause the formation of the monovariant system, ice, naphthalene, solution and vapor. On raising the temperature there will come a point at which the ice begins to nielt with formation of a second liquid layer and we have the nonvariant system, ice, naphthalene, two solutions and vapor. The temperature of this quintuple point is necessarily higher than
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that of the one in which phenol replaces naphthalene as solid phase because there is more naphthalene i n solution and therefore the phase in which water is solvent is more dilute and can coexist with ice at a higher temperature. Using crude phenol the temperature for the quintuple point with naphthalene as solid phase was found to be about - 0.8' while with phenol as solid phase the temperature was several tenths of a degree lower. These measurements are only approximate and will be repeated using pure phenol. Changing from the particular to the general, we may make the following statement : If the component C is sparingly soluble in A , the solid phases in equilibrium with two solutions and vapor will be A and C. If C is sufficiently soluble in A, two quintuple points of the type under consideration will be possible, the solid phases being A and B in the one case, B and C in the other. T h e temperature of the quintuple point with A and B as solid phases is lower than that of the one with B and C as solid phases. I t is to be noticed that the difference between these two temperatures will be greater the more soluble A and B are and the greater the difference in the concentrations of the solutions in which A is solvent for the two cases that A and that C is the solid phase. IC. T h e component C is a solid, soluble both in phenol and in water. Pyrogallol would undoubtedly come under this head though I know of no experiments with it. The effect of adding the component C is to increase the mutual solubilities of the components, A and B. This solvent effect is not very large in most cases and is usually neglected in applications of Nernst's Distribution Law. Since both solutions become more concentrated the temperatures are lowered at which solid phenol and ice can appear. If the concentration in the solution in which water is solvent increases faster than the concentration in which phenol is solvent, the only solid phases which can exist in equilibriiim with two solutions and vapor are phenol and the third component. If the concentration in the solu.tion in which phenol is solvent increases faster than the concentration in the other solution we shall have much the same behavior as with substances classified under Ib. There will either be one quintuple point with phenol and the third component as solid phases or there will be two quintuple points with phenol and ice in the one
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case and ice and the third component in the other. There is one important difference however. I n case there are two inversion points, the one with A and B as solid phases will exist at a higher temperature than the one with B and C as solid phases whereas the reverse was the case when C was insoluble in B. I t may also happen that the solubility of the third component in the other two and its solvent action may be so great that the two solutions will become consolute before a second solid phase appears. This will be realized if we take glycerol as the third component. I n classifying these three cases, Ia, I b and IC,it has seemed easiest to consider the third component as insoluble in one or the other of the two components A and B or as soluble in both ; but this can not be defended as exact since all solids are somewhat soluble in all liquids according to the view generally adopted. This discussion has brought out the sense in which the classsification is to be taken. We group under I a all solids which precipitate A from the solution in which B is solvent, under I b all solids which precipitate B from the solution in which A is solvent and under IC all solids which increase the mutual solubilities of A and B. I I a . T h e component C is a liquid, miscible in all proportions with water and practically nonmiscible with melted phenol. I am not able to name such a substance ; but its effect will be similar to that of the component C in Ia and the temperature, at which phenol can exist in equilibrium with two solutions and vapor, will rise with increasing addition of the component C. Since this third component can not form a solid phase by definition, no quintuple point is possible. IIb. T h e component C is a liquid, miscible in all proportions with liquid phenol and practically nonmiscible with water. Chloroform would come in this category, The addition of chloroform will lower the freezing point of phenol and the nonvariant system will have phenol and ice as solid phases. IIc. The component C is a liquid consolute both with liquid A and liquid B. Alcohol or acetone niay be taken as typical instances. Addition of alcohol or acetone will bring the two solutions nearer in composition and will also lower the temperature at which phenol can exist as solid phase. There are two possibilities. T h e freezing point
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of the phenol may be lowered so much more rapidly than that of the water that the ice may appear as solid phase before the two solutions become identical in composition, forming the nonvariant system, phenol, ice, two solutions and vapor. If that is not the case, one of the solution phases will disappear leaving the divariant system, phenol, solution and vapor. The condition for the first state of things is that the concentration of the third component shall be much larger in the phase in which phenol is solvent than in the phase in which water is solvent while the condition for the second case is the keverse of this. IIIa. T h e component C is a gas, much more soluble in water than in phenol. Hydrochloric acid answers this description. T h e effect of adding the component C will be the same as in Ia and IIa, namely that the miscibility of A and B decreases and solid A will be stable a t higher and higher temperatures. It was found experimentally that, using the ordinary hydrochloric acid of the laboratory, solid phenol appeared at twenty-five degrees above zero. Since hydrochloric acid can not separate as a solid phase there is no nonvariant system possible with two solution phases. IIIb. T h e component C is a gas, much moresoluble in phenol than in water. This could undoubtedly be realized with some organic compound though there are no data upon the subject. T h e freezing point of the phenol will be lowered by the addition of the component C and the solid phases at the quintuple point will be phenol and ice. IIIc. T h e component C is a gas, readily soluble both in A and in B. T h e effect will be the same as in IIc, a lowering of the freezing point of phenol and either no inversion point with two solution phases in equilibrium or one with phenol and ice as solid phases. T h e system, phenol, water and a third Component, is typical of all systems in which the components A and B form the nonvariant system, solid A, two solutions and vapor ; but, as has already been said, the relative positions of the quadruple point and the melting points of the components A and B determine the ease with which theoretically possible quintuple points can be realized experimentally and affect the stoichiometric relations very markedly. If we add sugar to naphthalene and water we shall get the nonvariant system,
Two Liquid Phases naphthalene, sugar, two solutions and ' vapor, existing at a higher temperature than the binary nonvariant system for naphthalene and water; but the rise of temperature will be only a fraction of a degree. T h e maximum rise of temperature theoretically possible with a solid, soluble in water and insoluble in naphthalene is less than one degree while, with the corresponding case for water and phenol, a rise of nearly forty degrees may occur-at any rate on paper. With water and benzene the rise would be practically imperceptible. T h e niolecular raising of the freezing point is thus a function of this temperature difference as has been pointed out by Nernst.' On the other hand adding a solid, soluble in melted naphthalene and insoluble in water will lead practically invariably to the quintuple point with naphthalene and the third component whereas with phenol and water the corresponding inversion point can be realized only in case the third component is very sparingly soluble in phenol. Benzene and water occupy an intermediate position since it is not difficult to find organic substances which will lower the freezing point of benzene less than six degrees nor to find others which will lower it more than that amount. Whether it is possible to lower the freezing point of naphthalene enough to give the two quintuple points with ice and naphthalene, ice and the third component as solid phases when the third component melts above go0, is difficult to say. With sulfur one can not get below 70' and with phenanthrene2the temperature of the quintuple point would be about 48'. When the third coniponent is a liquid at all temperatures covered by the experiment it is possible to have naphthalene and ice as solid phases. This could be realized with chloroform for instance ; but it is very doubtful whether we should be justified in classifying the quintuple point, naphthalene, ice, two solutions and vapor under IIb. That would be calling naphthalene A, water B and chloroform C whereas it is much inore probable that it should be classified under I a , calling water A , chloroform B and naphthalene C. T h e point upon which the matter turns is whether naphthalene or chloroform is solvent at this temperature. If a mixture of naphthalene and 'Zeit. phys. Chem. 6, 27 (1890). lMiolati Zeit. phys. Chem. 9, 649 (1892)
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chloroform at zero degrees, saturated with respect to naphthalene, lies on the fusion curve for naphthalene, the three-component system falls under I I b ; if it is a portion of the solubility curve we must classify under Ia. With phenol, water and glycerol it is probable that the two liquid layers would become consolute before ice appeared as solid phase ; with benzene, water and glycerol this would certainly be the case ; with naphthalene and water it would probably be impossible to find a solid which would not precipitate before the two liquid layers became of the same composition.' With liquids miscible in all proportions with water and with liquid naphthalene, the result will always be disappearance of the second liquid phase and formation of the divariant system, naphthalene, solution and vapor. With benzene and water, this is no longer the necessary result and with phenol and water, it is more likely to be the exception than the rule. Benzene, water and alcohol furnish the quintuple point, benzene, ice, two solutioiis and vapor. I have not tried other liquids. It will be noticed that the direction in which the equilibrium is displaced on adding the third component is the same whether that component is a solid or liquid or a gas at the temperature of the experiment. This is a necessary consequence of the discovery by Raoult that, in a binary system, the change of the partial pressure is not a function of the physical state of the pure solute at that teiiiperature and of the conclusion ofvan ' t Hoff that for many purposes the solute may be considered as if it were present in the gaseous state in the volume occupied by the solution. This view does not involve the further assumption that the components in a solution necessarily behave in all ways like gases though this is often overlooked. I n certain ways a solute may be expected to behave like a liquid and to show a solvent or a precipitating action, depending on its nature and on that of the other components. This is seen to be the case in the systems which have been discussed in this paper. Since the solvent action of a liquid mass is a function of its chemical nature, it is to be expected that in the cases where the solute is to be treated as a liquid we should get a specific effect for each solute and the con'It might be worth while to try pyrogallol.
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centration would not be the only factor in the problem. This is an experimental fact since it has been shown that benzene precipitates water to different extents, varying with the nature of the consolute liquid' or, putting it the other way round, ethyl alcohol does not change the mutual solubilities of benzene and water in the same way that methyl alcohol or acetone does. Nernst' has called attention to the fact that a mixture of ether, water and a third substance, soluble in ether and insoluble in water, gives a more constant freezing point than is the case with binary monovariant systems. The explanation which he offers for this apparent anomaly is a very simple one. The concentrations of the ether and of the third component in the aqueous phase and consequently the temperature at which ice is formed, depend upon the concentration of the third component in the ethereal phase. Since the amount of ether and of the third component in the aqueous phase is very small, the change in the concentration of the ethereal phase, with increasing separation of ice, will be negligible in most cases and the temperature will remain practically constant until this aqueous phase disappears. I t is clear from this that the monovariant system, solid A, two solutions and vapor will behave in one way on withdrawal of heat if the the third component is soluble in the component A, insoluble in B and in a very different way if the third component is soluble in B and insoluble in A. To take a concrete case, we may suppose a mixture of naphthalene and water to which a little phenanthrene has been added. Solid As naphthalene naphthalene begins to appear, let us say, at 78'. separates, the concentration of the solution in which naphthalene is solvent increases and the freezing point falls. Before the phase in which naphthalene is solvent disappears, the temperature will fall in the neighborhood of thirty degrees. An analogous case to the one described by Nernst would be found with phenol, water and hydrochloric acid. Here, as the phehol separates the amount of water which passes into the other solution phase will not be sufficient to change the concentration to any extent and the ~~
TBancroft.Phys. Rev 3, ZI (1895). "Zeit. phys. Chem. 6, 30 (1890).
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freezing point will remain practically constant. This will not be the case if the mass of the phase in which phenol is solvent is very large relatively to that of the phase in which water is solvent. Under these circumstances the freezing point would change as the phenol separated in solid form, the amount of the change being determined by the difference between the initial and final concentrations of the phase in which water is solvent. It seems as though phenol might be a good substance to use in standardizing hydrochloric acid. . It would merely be necessary to make a table once for all showing the relation between the concentration of hydrochloric acid and the freezing point of phenol and the actual determination of any particular acid would not take five minutes. If one read the thermometer to hundredths of a degree there should be no difficulty in determining the concentration of hydrchloric acid to within three hundredths of a gram per liter. Using the Beckmann apparatus still greater accuracy could be obtained ; but there is little advantage in that. This would do away with all weighings and the difficulties accompanying the preparation of standard solutions and it is therefore to be hoped that some one directly interested in analytical chemistry will make the preliminary measurements necessary to drawing up a standard table. Before we can get an accurate understanding of the behavior of ternary systems where two liquid phases are possible, it will be necessary to consider the relation between temperature and concentration for the divariant systems, two solutions and vapor, and solid, solution and vapor ; the graphical representation of the various equilibria and the form of the isotherms. I n addition there are the systems illustrated by potassium chlorid, acetone and water in which there can be two liquid phases at temperatures at which no two of the components form two liquid phases. T h e time at my disposal does not permit of niy treating these points now and I shall have to postpone a consideration of them and take them up in a subsequent paper. I n this paper I have coiisidered the general case of quintuple points with two solid phases, two liquid phases and vapor formed by adding a component C to two components A and B such that there can be formed the quadruple point, solid A, two solutions and vapor. T h e general results are :
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I . T h e component C dissolves in B with precipitation of A. T h e freezing point rises. The solid phases at the quintuple point are A and C or else no nonvariant system with two liquid phases is possible. 2 . T h e component C dissolves in A with precipitation of B. The freezing point falls. There is one quintuple point with A and C as solid phases or two with A and B, I3 and C as solid phases or one with A and B as solid phases. 3. T h e component C increases the miscibility of A and B. T h e freezing point falls. There is one quintuple point with A and C as solid phases or one with A and B as solid phases or there is formed the divariant system, solid A, solution and vapor. 4. If the component C dissolves in A with precipitation of B and there are two quintuple points, the one with B and C as solid phases will exist at a higher temperature than the one with A and B as solid phases. $5. If the component C increases the miscibility of A and B and there are two quintuple points, the one with B and C as solid phases exists at a lower temperature than the one with A and B as solid phases. 6. A convenient method has been suggested for standardizing hydrochloric acid.
Cornell Universify.
