BY T I L D E R D. B A S C R O F T
T h e first complete pressure-temperature diagram was given about a )-ear ago by van’t Hoff ; I but he did not put in the curves for the partial pressures. T h e object of this paper is to fili this g a p in our knowledge to a certain extent, qualitatively. T1-e will first consider systems in which there can be only one liquid phase and in which the only solid phases possible are tlie two pure components. Two classes are then to be distinguished. I n the first the vapor-pressure boundary curves for the less fusible component lie wholly below the corresponding set of ciirves for tlie more fusible substance; in the second, the yapor-pressure boundary curves for the less fusible substance lie wholly above the corresponding set of curves for the more fusible component. Intermediate systems with intersecting pressure curves are quite conceivable but do not need be considered i n detail. I n Fig. I OB is the sublimation curve, OA4is the vaporization ciirve and 0 the triple point for the more fusible component. OIB1and OIL-iIare the corresponding curves for the other coinponent, O1 being the triple point. If the eutectic temperature be that of the points H and HI, the partial pressure of the more fusible component, while it is solid phase, will be represented by O H provided we ignore any solvent action of the 1-apors. In the same way the partial pressure of the second component when present as solid phase will be OIHI. T h e partial pressures of the substance which is not present as solid phase are given by DIHl and DH, the curve DIHl belonging with OH while DH goes with OrHI. By adding OH and DIHi we get the curve OC, representing the boundary curve for solid, liquid and vapor Yorlesungen iiber theoretische Chemie, 3j.
when the more fusible component is solid phase. R y adding OTHland DH n-e get the curve OIC, the boundary curve for solid, liquid and vapor when the less fusible component is solid phase. BJ. adding H B and H I B I we get the curve CK) the boundary curve for the two solid components and vapor. T h e curve for two solids and solution is omitted, so as not to complicate the diagraiii unnecessarily. I t woiild, of course, run almost vertically from C. ,Although the pressure corresponding to the
t Fig.
I
point C is less than that of the point 0 in the diagram, it is to be noticed that this is not necessarily the case. If the curves O H and OTHlwere to coincide more closely than they do in Fig. I . the point C would lie above instead of below 0. T h e curves D H and DIHr have been drawn veq- nearly as though they were straight lines for the excellent reason that little is known about them. IVheii the \.apor-pressure of the less fusible component at the triple point is very much lower than the vapor-pressure of the point on 0-1for the same temperature, we shall have astate of things represented schematically in Fig. 2.
T h e letters ha\-e the same signification as before. T h e cur\-e DH lias a distinctly marked masiiiium and, in consequence, the curve OIC passes through a maximum. U'e kno\v that this must be the case with potassium nitrate aiid water because a
t
Fig. 2
solution saturated with respect to the salt boils under atmospheric pressure at about I 20' while tlie vapor-pressure of potassium nitrate at its melting-point is scarcely measurable. This is the case cited by van't Hoff: but tlie phenonienon is 1-ei-ygeneral. For instance, Stortenheker' found that \\-lien the freezing-point of iodin was lowered by the addition of chlorin, the vapor-pressure of the system first increased and then tlecreased. In Fig. 3 is given the general diagram for the case in which the vapor-pressure curves for the less fusible coinponelit lie whol1~-above the correspondiiig set of curves for the other substance. T h e letters have tlie same signification as before. In a system coming iiider this head, the pressure corresponding to the point C will usually be higher than that of the point 0 ; 1
Zeit. phys. Chem. 3, 19 (1SS9).
4
1ViZder D. 6’nrtcr-aft
but this is not necessarily the case. It is conceivable that if tlie temperature and pressure of 0 differed but little from that of OI and if the temperature of C were sufficiently lon-, the pressure corresponding to the point 0 might be higher than that of C. It seems probable that this will be the exceptional case, though it
Fig. 3
is the more probable state of things when there are intersecting vapor-pressure ciirves. very interesting case occiirs when the less frisible coinponent is more dense as solid than as liquid and when tlie other component is a gas at the teniperature of Ox. If we assilllie that the gas is practically insoluble in the liquid formed by melting the less fusible component, the pressure of the gas will be a more important factor than its solubility and we shall have a rise of freezing-point. T h i s brings iip the partial pressure of the solvent in the vapor phase. Ordiiizrily we say that the solid solvent is in equilibrium with solution and vapor nheii the partial pressure of the solvent i n the sjsteni, solution and vapor, is equal to the vapor-pressure of the sol\ eiit in the SJ stem, solid and xapor. If we exclude a possible sol\ent action of the gas, this definition seems to be a souiid one, and it follows therefore that the partial pressure of the solvent in the s~steiii,solid sol-
Pwsszr rc-fcnz$ern f ii Y P Dingrn iizs for Bizn ry Sj~stc~nls j l-ent, solution and vapor, will be eqiial, at temperatiires a1ioi.e the meltiiig-point, to the vapor-pressure of the system, superheated solid and vapor. T h e details of such a system are shown in Fig. 3, with a complete disregard of scale. T h e apparent mitiis not to be taken seriously. It owes its existence iintini in OIAAT to a desire riot to crowd the curve
t Fig. 3
O r A I I OIBl ) and OrEl are the boundary curves for piire liquid and vapor, solid and i-apor, solid and liqnid respectii,el!-, O,Oq is tlie prolongation of BIC)I) the system being instable n-it11 respect to the liquid phase. T h e partial pressure of the gas is gii-en by the curl-e DS. This, of course, continues to tlie n e s t quadruple point ; but we sliall only consider the curves in the iiiiriiediate neighborhood of the point Or so that it is quite iiuinaterial whether the new phase appearing at tlie nest qiiadruple point be pure solid, a compound or a second solution. T h e total 1-apor-pressareof tlie system is represented by OISC. If the gas Tvere absolntelj- insoliible in the melt, this curve n.ould coincide wit11 OIEr. this can nei-er be the case theoreticall!., tlie curve O r K C will a1waj.s lie ahoi-e O,E,. 111 the constriiction of Fig. 4 it has beer1 assumed that with increasing pressure
the gas becomes more and more soluble in the melt until, at length, the lowering of the freezing-point due to the solubility overbalances the rise of freezing-point due to the increase of pressure. I t has recently been pointed out by Taniiiianiir that systems of this sort h a \ e been studied by Danien,* the coinponents being air and iiaphthylainin, diplienylamiii, paratoluidin or tnononitronaplitlialene. In Fig. 4 the temperature and pressure of tlie maximum freezing-point are represented b j the point S. T h e point X I denotes the point on the curie 0102 at which the temperature is that of the tnasimum freezing-point. .Is the total pressure of the sjstem increases from 0 to S ,the partial pressure of the less fusible component increases from O1 to SI. Xs the total pressure of the system changes from S to C, the partial pressure of the solvent decreases from SIback to OTand is represented by the c i i n e OIHl as tlie system passes along the prolongation of O I S C . Sitice the field for solution and vapor is bounded by X,Ol and O I S C , it is obvious that if n e start at some point on OIAII having a temperature lower than that of the point S and add the gas continuously a t constant temperature keeping the volume of the system constant, the pressure will change until the solid phase appears a t the pressure represented b j the point on OrS for that temperature. During this process the partial pressure of the solvent has increased from that of a point on OI.I, to a pressure represented b, a point 011 OXOq. From this we see that if we compress a liquid by means of a gas practically insoluble in it, n-e shall increase the partial pressure of the liquid quite apart from any solvent action of the gas. This phenomenon has been observed by Scliilleri and has been discussed at some length b\- Ostwald.4 From the diagram n-e see that, if the gas exerts no solvent action, the curl-e 0102 represents tlie limiting partial pressures that can be reached in this n a y . i n the same way in-
' \ V i e d .Inn. 66, 177 (1S9S). ' Comptes renclus. 1x2, i S j (1S91). "\Vied.
Xtl11.
60, 7jj (rS9;).
' Lehrhuch, z , 11, 361.
crease of pressure at temperatures below that of O1 will cause an increase in the partial pressnre of the less fusible component, the limiting values given by the prolongation of A4101. Up to this point we have expressly excluded any solvent action in the vapor phase ; but it is now desirable to determine what will be the effect of dropping this limitation. In Fig. 5 is
P / /
/
1
Fig. j
given the diagram for a system in which such a solvent action takes place. T o avoid cumbering the diagram with unnecessarj. curves, the assumption has been made that the vapor of the less fusible component exercises no perceptible solvent action on the other substance. T h e effect of this limitation will be pointed out in the discussion. T h e essential feature of this system, in which it differs from that shown in Fig. 2, is the presence of the curve OIHTBZ. T h e partial pressure of the less fusible component when present as solid phase cannot be represented by the curve OIB, ; as heretofore because that is the state of things when the solvent action of the vapor is excluded. T h e curve OrHrB2represents the parial pressures of the less fusible component when it is present as
8
1Vilder D. Bnizcroft
solid phase in equilibrium with solution and vapor. It should be understood that no attempt has been made to draw any of these diagraiiis to scale. IVlien some actual system coining under this head is studied, it will probably be found that OIHIB2passes througli a maximum very near the point O1 and that, for the rest of its course, it will coincide \-cry nearly with OTBI. I n the same way it is more than probable that, in all cases in which the divergence of OIHrRzfrom OiBT is marked, the cume DH will pass through a inaximuin just as in Fig. 2. These, howeyer, are matters of cletail varying from one system to another and have no effect on the general relations. If we were to take into account a sol\-ent action due to the vapor of the less fusible component we shoulcl have a curve starting from 0 and lying just above OR. T h e point H would then be on this new curve and not oil OR. If there were a point of maximum temperature on the curve OICwe should also ha1-e to consider a curve starting froin Or and lying above the prolongation of BIOI. Froin the last diagram it was clear that, when one coniponent can dissoll-e in the vapor of the other, the partial pressures for the solvent i n the system, solid solvent, solution and vapor, are given by a ciirve starting from the triple point and lying above the boundary curve for solid and vapor. T h e reverse state of things mill be found i n case the solid phase has a perceptible solvent action ; in other words, in case a solid solution is formed. I n Fig. 6 is given the diagram for a system i n which two systems of solid solutions are possible. O A lis the vaporization curve and OB the sublimation curve for one of the pure components; OIAIIand OIBr the corresponding curves for the other piire component. O H L gives the partial pressures of the more fusible component in one set of saturated solid solutions at different temperatures, while OIHr gives the relation between the temperature and the partial pressme of the less fusible component when the solid phase is the other set of saturated solid solutions. If the temperature of the eutectic point be that of the points C, H and HI, the partial pressures of the solutes along the two boundary curves may be represented
by DIHl and D H respectivel!.. The boundary ciirves for the OTHI-~D H , arid CK = s!.:;tein are OC 1OH -~IIIHI,0 , C :_ HI, -~HILI. In cases where no solid solutions are possible the ciir1.e OC inust lie abol-e the ciirve O R because it is equal to the ciirvt: 013 pliis the curve for tlie partial pressures of the other coniponent. V71ien solid solntions occiir, this is no longer necessar!. and i n the present rather extreme case the ciirve OC lies conipletel!. below OR. /
I' A
P
,e'
/ I
t Fig. 6
If the two substances form one continuous series of solid solutions, the cnrves HL and H I L I disappear and we have two continuous curr-es O H D and OIH,DI. For the isomorplioiis mixtures studied by Kiister' O H D and OIHrDI become the straight lines OD and O,D,, and we have a state of things represented graphically in Fig. 7. OD gives the partial pressures for the more fusible conipoiieiit in the system, solid solution, liquid solution and vapor, while OIDIgives the corresponding values for tlie other. T h e siiiii of these two ciirves is 001, which represents the total vaporpressure along the boundary curve. Of course, it is very im'%eit. phys. Cliem. 8 , jj7 I rS91)
probable that the ciirves OD and OIDI are ever absolutely straight lines, but this diagram may be considered as the limiting case. There is one other point that calls for discussion. Xt temperatures below that of the quadruple point, 11)-drated sodium
F1g. j
sulfate can exist in stable equilibriuni with solution and vapor, while the system, anhydrous sodium sulfate, solution and vapor, though realizable experimentally, is instable with respect to the hydrated salt. T h e metastable solution contains more sodium sulfate than the other and has a lower vapor-pressure. In oneconiponent systems the phase that is in equilibrium with vapor at a higher pressure is instable with respect to the phase that is in equilibrium with vapor at a lower pressure. At first sight it would appear as though the solution saturated with respect to the anhydrous salt should be the more stable or,at any rate, that the difference of vapor-pressures would tend to change the equilibrium in one direction and that the difference of concentrations would tend to displace the equilibrium in the opposite direction, the latter tendency being the decisive one. a matter of fact there is no such conflict of forces. Let the solution saturated with respect to the lirdrated salt be called X and the solution satnrated with respect to the anhydrous salt be called B. If these two solutions are brought in contact, salt willdiffuse
from the place of higher concentration to that of lon-er concentration, in other words from R to Ai. T h e solution A being saturated, by definition, the salt that has diffused in will crystallize as decahydrate ; in tlie meanwhile salt nil1 dissolve in R to restore the original concentration and will then diffuse into -4. Tlie final result will be the disappearance of the anhydrous salt and of the difference between the solutions. T h e actual result, apart from tlie question of transference, will be that anhydrous salt goes into solution and that hydrated salt crl-stallizes. Suppose, now, that the solutions be so arranged that they have a coninion vapor phase, diffusion however being impossible. T h i s may be done by placing the solutions in two beaker, under a bell-glass. IYater will then distil from the place of higher pressure to the place of lower pressure, in other words from to B. T h e solution in \vi11 tend to become more concentrated and hydrated salt \vi11 therefore separate. T h e soluticin i n B will tend to become more dilute and equilibrium will continually he restored by the anhydrous salt going into solution. T h e final equilibrium will depend on the relative masseof the phases. If the ma5s of solution in -4 be relatively small with reference to the mass of solution or to the mass of anhj-drous salt in €3, the final equilibrium will be hydrated crjstal-, in -1, solution and anhydrous salt i n R. If the mass of solution be not relativelj- small n-ith reference to either of the phases in R,the final equilibrium will be hj-drated crystals and solution i n -4 and a solution of the same composition in B. TThatever be the final combination of phases, the change taking place has been that anhydrous salt goes into solution and hydrated salt cr:\-stallizes. IYe see, therefore, that the anhydrous salt is tlie metastable form whether we consider the matter from the point of view of tlie x-apor-pressures or of the concentrations. COYIIEZL L-niz,eYsify
