...
SOLUTION A N D FUSION BY WILDER D. BANCROFT
If phenanthrene be added to naphthalene' the freezing point of the latter is lowered and the depression increases with further addition of phenanthrene until the solution has the composition of the eutectic alloy' when naphthalene and phenanthrene crystallize side by side and the solution solidifies without change of temperature. If naphthalene be added in ever increasing quantities to phenanthrene the freezing point of the phenanthrene is lowered until the temperature is again reached at which the eutectic alloy freezes, This is shown qualitatively in Fig. I . T h e ordinates represent temperature and the abscissae the percentage composition of the solutions ; at the left beingnaphthalene, at theright phenanthrenee8 Along the curve AB the solutions are in equilibrium with solid naphthalene, along BC with solid phenanthrene while the point C, at the intersection of the two curves, shows the temperature and the composition of the solution at the quadruple point where the four phases co-exist, naphthalene, phenanthrene, solution and vapor. These I FIG. I. two curves are fusion curves and naphthalene is the solvent, phenanthrene the solute in the solutions. which are in equilibrium with solid naphthalene, while these terms are reversed for the solutions in equilibrium with solid phenanthrene.' 'Miolati. Zeit. phys. Chem. 9,649 (1892). Guthrie. Phil. Mag. (5) 17,462 (1884). 3Cf. Konowalow. W e d . Ann. 14, 40 (1881). 4Bancroft. Phys. Rev. 3, 20 (189.5).
i
W. D. Bancroft Suppose that instead of these two substances we take potassium chlorid and water as the two components. We find a series of solutions in equilibrium with solid potassium chlorid and a series of solutions in equilibrium with ice ; these, if plotted as before, will give two curves intersecting at the temperature of the cryohydrate in the quadruple point. This is represented in Fig. I by the lines DE and DF, potassium chlorid being at the left and water at the right. At first sight it seems as if these were both fusion curves and that in one set of solutions water is dissolved in potassium chlorid, in the other potassium chlorid in water. This view is adopted by most people'; but a very slight consideration will show that it is incorrect. I n the case first considered the two components are miscible in all proportions at any temperature at which both are liquid, a condition the importance and significance of which is often overloqked.' We cannot tell whether this is so in the case of potassium chlorid and water because the salt melts at too high a temperature. It will therefore be better to take two substances with melting-points lying within the range of experiment, such as naphthalene or phenol and water. I t is possible to make a series of solutions in equilibrium with solid naphthalene and another set in equilibrium with ice. There is no dispute about the second set of solutions. T h e curve representing them is a fusion curve .and water is the solvent. The accepted doctrine in regard to the other set is that, in so far as one niakes a distinction between solvent and solute at all, the naphthalene is the solvent and the curve representing the solutions is a fusion curve.' My own view is that the curve is a solubility curve and that naphthalene is the solute. T h e point at issue is whether solubility and fusion curves are always or even ever identical. T h e first part of the question can be answered off-hand in the negative. With partially miscible liquids, such as ether and water, one of the liquid phases is a solution of ether in water, the other of water in ether and the compositions of the phases at different temperatures give two solubility ciirves when represented graphically.
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'Le Chatelier. Equilibres chimiques, 130 ; Nernst. Theor. Chem. 394. 2Ostwald. Lehrbuch I, 1037 ; Riecke. Zeit. phys. Chem. 7, 422 (1891); Schroder. Ibid. 11, 452 (1893). 3Ostwald. Lehrbuch I, 1024; also Zeit. phys. Chem. 12, 394 (1893).
Sohitiox aizd Fusion
I39
These cannot be called fusion curves because the temperature of the experiment is above the fusion temperature of either of the components. T h e other part of the question is best answered by a study of the diagram for naphthalene and water (Fig. 2 ) . At the left is one hundred per cent naphthalene, at the right one hundred per cent water, while the ordinates represent temperature. T h e diagram is not to scale because all the the solubilities are unknown. I n the figure, A represents the fusion temperature of pure naphthalene A and AB the depression of the freezing-point by continued addition of water. AB is therefore the fusion curve for naphthalene in presence of water, naphthalene being solvent. Between 74' and Soo, there can exist also the jF system composed of two liquid phases and vapor. T h e hypoFIG. 2.
-[ - -- - - - ---
thetical compositions of the two solutions are shown by the curves BC and DE. These two are entirely analogous to the curves representing the two liquid layers formed by mixing ether and water ; they are therefore solubility curves, D E being the curve for the saturated solution of naphtbalene in water, BC for the saturated solution of water in naphthalene. T h e curves AB and CB cannot be identical because in that case we should have solid naphthalene in equilibrium with two liquid phases and vapor over a range of temperatures, which is impossible. A t B the fusion and the solubility curves become identical and at the temperature of about 74' there is equilibrium between the four phases, solid naphthalene, water in naphthalene, naphthalene in water and vapor. T h e curves BC and DE meet at some unknown temperature without much doubt.' At any temperature below that of the quadruple point, we have only solid naphthalene, naphthalene in water and vapor until the cryohydric temperature is reached at F. This equilibrium is shown by 'Alexejew. W e d . Ann. 28, 305 (1886);Masson. Zeit. phys. Chem. 7,500
t 1891).
1 40
w.D.Banc~oft
the curve D F which is neither a continuation of AB nor of CB, but of ED. It has a slightly different inclination from E D because the naphthalene now separates in the solid form and the heat of solution is much greater.' T h e last curve in the diagram, HF, is the fusion curve for ice in the presence of naphthalene. I t can not be identical with D F for the same reason that AB can not be CB, that it would involve a breach of. the Phase Rule. We see from this that a fusion curve is never a solubility curve and vice-versa. Also that the soiubility and fusion curves cease to be stable after their intersection. Below the inversion temperature neither of the two curves can exist except as a labile modification. I have illustrated this point by a reference to the equilibrium between naphthalene and water to show that the question can be settled by an application of the Phase Rule to the facts without any quantitative data being known. This does not imply that there are no quantitative data. Alexejew has made a study o'f benzoic acid and water which is quite sufficient for our purpose. T h e main features of his diagram are reproduced in Fig. 3, benzoic acid being at the left and water at the right. AB is the fusion curve when water is added to benzoic acid, LBM the solubility curve for water in benzoic acid, of which the labile part BM has actually been realized. LDN is the solubility curve for \ benzoic acid in water, the part DN being a supersaturated solution. From these solutions t h e FIG. 3. benzoic acid precipitates in liquid form. T h e two curves MBL and N D L meet at L, the two substances being miscible in all proportions at higher temperatures. D F is th'e solubility curve for benzoic acid in water, the solute separating as crystals, while the curve FH is the fusion curve for ice in the presence of benzoic acid. Owing to the sparing solubility of the latter 'Walker. Zeit. phys. Chem. 5, rgz (18go).
Sohition and Fusiox
141
in cold water this curve is very short and was not determined by Alexejew. It is thus clear that in all saturated solutions to the left of the point L the solvent is benzoic acid whereas to the right of this point water plays that part. I n the case of benzoic acid and water, only a short portion of t h e curves MI, and NI, corresponded to labile modifications ; but with salicylic acid and water the two liquid layers can exist only as labile forms. This will be clear from the diagram (Fig. 4) illustratthis case. Water is as before at the right. T h e curves MLN can only be obtained by working under pressure in sealed tubes. AB is certainly the fusion curve of salicylic acid in the presence of water and F D equally certainly the solubility curve of salicylic acid in water ; but where the one changes into the other or what BD actually represents is very uncertain. It is much to be deFIG.4. sired that someone should make a careful and exhaustive study of the3vapor pressures of this system. A curious point occurs in the behavior of sulfur dioxid and water, investigated by Bakhuis Roozeboom.' I t is possible at the same temperature to have the solid hydrate SO,7H,O in equilibrium with vapor and a solution of sulfur dioxid in water or with vapor and a solution of water in sulfur dioxid. These cannnot be fusfon curves because Stortenbeke? has shown that it is not permissible to apply the Theorem of Raoult-van ' t Hoff when the solute would be a component of the solvent. W e must interpret the phenomena something as follows : T h e first solution is saturated in respect to sulfur dioxid and tends, if more be added, to form two liquid layers ; the new phase is instable and changes into the solid hydrate. I n the second instance the solution is saturated in respect to water and 'Recueil Trav. Pays-Bas 3, 29 (1884) ; 4,65 ( 1885) ; also Zeit. phys. Chem. 2,
450 (1888). 21bid. IO, 194(1892).
W. D. Banoroft
,
*
an excess precipitates as a solution instable in presence of the other phases and therefore changing into the solid hydrate. I n other words the hydrate results from the precipitation of sulfur dioxid in one case and of water in the other. This explanation is not so farfetched as it may seem. Frankenheim' and others have shown that when salts are precipitated by alcohol there is formed first an instable liquid phase from which the salt then separates. This can be seen without the microscope if alcohol be added to a strong solution of sodium carbonate. T h e second liquid phase, although instable, does not disappear for quite a while. It is well known that when melted sulfur is poured into water it solidifies in a labile modification. I have noticed that the addition of water to a solution of mercuric iodid in methyl alcohol precipitates the yellow modification although it is instable at room temperatures. It will do this even when the red crystals are present. I t seems as if one might make the generalization that the less stable form is the first to appear in the case of sudden precipitation. ' While water is solvent in one of the solutions in equilibrium with the hydrate, SO27H,O,and solute in the other, it is solvent in both of the solutions in equilibrium with the hydrates of calcium or ferric chlorid.' T h e difference here is that there are never two liquid layers in equilibrium and there is no reason for assuming that in any of the cases is the water dissolved in the salt. I prefer to look upon the solutions containing more of the solid than the hydrate as stable, supersaturated solutions although this may seem a contradiction in terms. For a given temperature the vapor pressure of a hydrated salt can not fall below a certain value without the salt efflorescing. T h e saturated solution under discussion has that vapor pressure and as the solution would become more concentrated if the hydrate cryslallized out, its vapor pressure would fall below the lowest value at which the hydrate could exist. Therefore the hydrated salt can not crystallize out although the solution is supersaturated in respect to it. I t is thus possible, in certain well-defined cases, for a solution to be stable in the presence of the solid phase in respect to which it is supersaturated. 'Ostwald. Lehrbuch I , 1040-1043 ; zBakhuis Roozeboom. Zeit. phys., Chem 4931 (1889) ; 1 0 9 477 (1892).
Solution and Fusion
I43
T h e distinction between a fusion and a solubility curve has been recognized for a long time although no one hascalled attention to it. T h e approximation formulas for the change of concentration with the temperature have the same form for both curves, except that the heat of fusion enters into one' and the heat of solution into the other'. Since these two quantities are not identical] it follows that there is a radical distinction between the two curves.' There remains still a point to be considered. I n the first case taken up in this paper, that of naphthalene and phenanthrene] it was found that, instead of four curves as with naphthalene and water, there were only the two fusion curves because the two nielted components were consolute i. e. miscible in all proportions. It does not follow because two liquids are consolute that each has not a defini : solubility in the other. This can be seen from Fig. 5 . T h e ordinates represent temperature and the abscissae the percentage compositions of the solutions. There are two definite solubilities below the temperature 'I' and there can co-exist two liquid phases if the substances be. taken in proper proportions. At 'I' each liquid has a definite solubility in the other ; but the two saturated FIG. 5. solutions are identical in composition. For this reason there cannot be two liquid phases co-ekisting and we have at this temperature two liquids miscible in all proportions, each having a definite and known solubility in the other. A t higher temperature there are two possibilities. T h e solubilities may both become infinite as represented by the dotted line T A and T B Ivan ' t Hoff. Lois de l'kquilibres chimiques, 46 ; also Ostwald. Lehrbuch I, 760. *van 't Hoff. 1.c. 36 ; also Nernst. Theor. Chem. 515. Wnebarger, Am. Jour. Sci. 49, 48, (1895), has attempted to apply t h e Schroder-Le Chatelier Theorem for fusion curves to solubility curves-naturally without Success.
or they may not, as illustrated by the dotted lines T C and TD. There is a third possibility that one of the solubilities may become infinite and the other not ; but that is rather a combination of the other two cases than a new one. T h e first case is tacitly assumed to be the type of all pairs of consolute liquids and needs no discussion. I t will .be profitable to consider the second case. Above what may be called the consolute temperature’ the liquids have each a solubility in the other ; but two liquid phases can not co-exist because the two solubilities overlap, so that a mixture which is supersaturated in respect to one component as solute is unsaturated in respect to the other. (Two liquid phases are formed only when the mixture is supersaturated in respect to both components). There is thus no theoretical reason to prevent the assumption of definite but overlapping solubilities2 in the case of two consolute liquids and the only question is whether instances of this actually occur. If the two solubility curves cut each other at an angle at the consolute temperature, the solubilities can not become infinite immediately after passing that point. This is the case for the solubility curves in the diagram (Fig. 5 ) which represents the experimental data for sulfur and t o l ~ e n esulfur ,~ being at the left. Of course this effect is influenced very largely by the scale used and it is open to anyone to change the abscissae and to say that there is no angle and that the curve is continuous through the consolute temperature. A more extended series of very careful measurements would help matters somewhat ; but it is probable that the question can FIG. 5. only be settled by a study of the behavior of the liquids above the consolute temperature. I t now 1 ‘ ‘Mischziszgstewiperatur’ ’ of Alexejew . *Since writing this I have been surprised and pleased to find the same idea stated clearly by Horstmann. Graham-Otto’s Lehrbuch I , 32 (1885). 3Alexejew. Wied. Ann. 28, 310 (1886).
Solution and Fzisiou
I45
becomes probable in view of this one instance that it is the exception rather than the rule that the solubilities become infinite at the consolute temperature. There is indirect experimental evidence in favor of this view. W e know that in a homologous series of organic compounds the miscibility with water increases with decreasing amount of carbon' and there is no reason to assume that this ceases to be true after the liquids become consolute. I n Fig. 6 are rough reproductions of the general form of pressure curves found by Konowalow' for isobutyl, propyl, ethyl and methyl alcohols with water, numbered I, 11, 111 and IV respectively. T h e ordinates are pressures but are not measured from the same zero. The abscissae are percentage compositions, water being at the left. Isobutyl alcohol is only partially miscible with watrr, the others miscible in all proportions. Instead of having the same type of curve in the last three cases, it is evident that, as one passes from propyl to methyl alcohol, there is a regular change in the form of the vapor pressure curve as the mutual solubilities increase. We may therefore conclude that each of these three alcohols, propyl, ethyl and methyl, has a definite solubility in water and that the same is true for water in the three alcohols. A natural corollary would be that the first of any series of homologous compounds to be completely miscible with a given liquid might be expected to behave like propyl alcohol and water, giving a mixture with a constant boiling point lower than that of either pure component ; but this needs to be made more definite. If, just below the consolute temperature, the vapor pressure of the system, two liquid layers and vapor, is higher than that of either component at that temperature, the vapor pressure curve for these two substances will have a maximum a t temperatures just above the consolute temperature. If, just below the consolute temperature, the system, two liquid layers and vapor, has a vapor pressure lying between those of the two components at that temperature the vapor pressure curves for these two substances will not have a maximum j u s t above the consolute temperature. T h e first type will present a 'Ostwald. Lehrbuch I, 1065. 'Wied. Ann. 1 4 , 34 (1881)also Ostwald. Lehrbuch I, 647.
.
minimum boiling point if made to boil in the neighborhood of the consolute temperature ; the second type will not. A t temperatures well above the consolute temperatures a maximum vapor pressure for some concentration is no longer necessary. Phenol becomes miscible with water in all proportions at about 70' ; but no mixture of these two substances boil below 100'. It is not known whether, under diminished pressure, a maximum would appear or whether the vapor pressure of phenol and water at 65' is lower than that of water at the same temperature. I n connection with this I may say that a mixture of sulfur and toluene gives two liquid layers with a boiling point between those of the two pure components. So far as I know this is the first authentic instance of such a phenomenon occurring in an open vessel at atmospheric pressure, since sulfur dioxid and water show this only at a pressure of over two atmospheres' while the case of amylvalerate and water cited by OstwaldA seems a very doubtful one. Sulfur and xylene show the same thing in a more marked fashion and it would not be difficult now to multiply instances indefinitely. That in a solution one substance is solvent and the other solute has been recognized by Nernst in his treatment of the case when both components have an appreciable vapor pressure3. While he allows the vapor pressure of the solvent to vary according to the Theorem of r a n ' t Hoff, he assumes that the partial pressure of the solute follows the Theorem of Henry. This is, by the way, an assumption which he does not prove ; but the point of interest here is that he is forced to treat the two components differently. This does not seem to have been clearly understood by Beckmand if I 'have read his very obscure sentence correctly. While accepting without reserve Nernst's dictum that the Theorem of Henry holds for all solutes, he is surprised that the partial pressures of iodin vapor are not the same in solutions of the same strength with different solvents.' There is nothing in Henry's Theorem to the effect that 'Roozeboom. Recueil Trav. Pays-Bas. 3, 3s (1884) ; Zeit. phys. Chem. 8,. 526 (1891).
'Lehrbuch I , 643. 8Theor. Chem. 385.
4Zeit. phys. Chem. 5Ibid. 132.
I,
131 (~895).
Solzitioii and Fusion.
I47
the absorption coefficient of a gas is the same for all solvents'. Nernst has not carried this differentiation further ; but he has made another statement on the subject of partial pressures which is worthy of our attention. H e says :' ( ( T h e partial pressure of each component of a mixture is always less thaTi its vapor pressure in the pure state (solid or liquid) at that temperature.)) This is not accurate. Nernst himself has stated' that, at the freezing point of a solution, the vapor pressure of the solvent is the same for solution and for pure solid solvent. H e would admit this for the solute in the case of a saturated solution. His principle is thus seen to be wrong in the form in which he has stated it. I t is open also to a theoretical objection which has been entirely overlooked. From the Theorem of LeChatelier' it follows that when one substance is dissolved in another, some of the vapor of the solvent will condense in order to reduce the concentration of the solute. T h e partial pressure of the solvent is therefore always less than its vapor pressure as a pure liquid at the same temperature. This prqof applies only to the solvent. T h e same result would be obtained if the solute became more volatile. It is therefore possible for the vapor pressure of the solute to be greater or less than its vapor pressure in the pure state, depending on conditions with which we are not yet familiar. I t seems certain that the partial pressure of the solute can not be raised above the vapor pressure which it would have were it present as a liquid a t that temperature and that the effect can occur only with solutes which are normally solid at the temperature of the experiment. That the presence of a second substance may increase the partial pressure of the first would seem to follow from Hannay's' experiments on the solubility of solids in gases and from those of Villard' on the solubility of iodin in carbonic acid. I t seems very difficult to account for the results of Gooch' unless the vapor pressure of the boric acid is increased by the presence of the solvent. This possibility has not been taken into account by Ostwald' in his 'Ostwald. Lehrbuch I , 617. Theor. Chem. 97. JIbid. 97, 128. 4Ibid. 526.
SProc. Roy. S O ~30, . 178 ( 1880). Tomptes rendus, 120, 183 (1895). 7Proc. Am. Acad. 22,167 (18S6). 8Anal. Chemie, 33.
.
W. D. Bancyoft
148
treatment of distillation with a vapor current although he has explicitly admitted the solubility of solids in vapors’. I t may be urged that the effect would be infinitely small at ordinary temperatures and pressures ; but this has nothing to do with the theoretical side of the question. If the effect takes place at any temperature and pressure we have no right at present to assume that it does not also occur at any other temperature and pressure. A s for its being infinitely small at ordinary temperatures, no one has ever tried to see whether there might not be cases where the influence of the second component was really measurable. I t is very unsafe to base a general statement on the fact that you have not found a thing you never looked for. Ostwald’s view is that if one works with a saturated solution it is immaterial what vapor one uses as an aid in distilling solid substances having a low vapor pressure at the temperature of the experiment. Whether this is so cannot be answered definitely as there is no quantitative evidence either way ; but there is good reason to suppose that this position is untenable. T h e results of this paper may be summed up as follows :I. Solubility and fusion curves are never identical. 2. A solubility curve may seem to be a continuation of a fusion curve. . 3. Two consolute liquids may have definite solubilities, one in , t h e other. 4. T h e partial pressure of a solid solute may be greater t h a n its vapor pressure in the pure state.
Cornell Universib ;January, 1896 ILehrbuch I, 612.
