Fig. 40Fig.40.
But the heptahydrate is not always formed by the dehydration of the dodecahydrate, and the behaviour on evaporation is therefore somewhat perplexing at first sight. After the solution has dried to the dodecahydrate, as explained above, further removal of water causes liquefaction, and the system is now represented by the point of intersection ata; at this point the solid hydrate is in equilibrium with a solution containing relatively more ferric chloride. If, therefore, evaporation is continued, the solid hydrate mustpass into solutionin order that the composition of the latter may remain unchanged, so that ultimately a liquid will again be obtained. A very slight further dehydration will bring the solution into the state represented byb, at which the pentahydrate is formed, and the solution will at last disappear and leave this hydrate alone.
Without the information to be obtained from the curves in Figs. 39 and 40, the phenomena which would be observed on carrying out the evaporation at a temperature of about 31 - 32°would be still more bewildering. The composition of the different solutions formed will be represented by the perpendicular linex212345. Evaporation will first cause the separation of the dodecahydrate, and then total disappearance of the liquid phase. Then liquefaction will occur, and the system will now be represented by the point 2, in which condition it will remain until the solid hydrate has disappeared. Following this there will be deposition of the heptahydrate (point 3), with subsequent disappearance of the liquid phase. Further dehydration will again cause liquefaction, when the concentration of the solution will be represented by the point 4; the heptahydrate will ultimately disappear, and then will ensue the deposition of the pentahydrate, and complete solidification will result. On evaporating a solution, therefore, of the compositionx2, the following series of phenomena will be observed: solidification to dodecahydrate; liquefaction; solidification to heptahydrate; liquefaction; solidification to pentahydrate.[233]
Although ferric chloride and water form the largest and best-studied series of hydrates possessing definite melting points, examples of similar hydrates are not few in number; and more careful investigation is constantly adding to the list.[234]In all these cases the solubility curve will show a point of maximum temperature, at which the hydrate melts, and will end, above and below, in a cryohydric point. Conversely, if such a curve is found in a system of two components, we can argue that a definite compound of the components possessing a definite melting point is formed.
Inevaporable Solutions.—If a saturated solution in contact with two hydrates, or with a hydrate and anhydrous salt is heated, the temperature and composition of the solution will, of course, remain unchanged so long as the two solid phases are present, for such a system is invariant. In addition to this, however, thequantityof the solution will also remain unchanged, the water which evaporates being supplied by the higher hydrate. The same phenomenon is also observed in the case of cryohydric points when ice is a solid phase; so long as the latter is present, evaporation will be accompaniedby fusion of the ice, and the quantity of solution will remain constant. Such solutions are calledinevaporable.[235]
Fig. 41Fig.41.
Illustration.—In order to illustrate the application of the principles of the Phase Rule to the study of systems formed by a volatile and a non-volatile component, a brief description may be given of the behaviour of sulphur dioxide and potassium iodide, which has formed the subject of a recent investigation. After it had been found[236]that liquid sulphur dioxide has the property of dissolving potassium iodide, and that the solutions thus obtained present certain peculiarities of behaviour, the question arose as to whether or not compounds are formed between the sulphur dioxide and the potassium iodide, and if so, what these compounds are. To find an answer to this question, Walden and Centnerszwer[237]made a complete investigation of the solubility curves (equilibrium curves) of these two components, the investigation extending from the freezing point to the critical point of sulphur dioxide. For convenience of reference, the results which they obtained are represented diagrammatically in Fig. 41. The freezing point (A) of pure sulphur dioxide was found to be -72.7°. Addition of potassium iodide lowered the freezing point, but the maximum depression obtained was very small, and was reached when the concentration of the potassium iodide in the solution was only 0.336 mols. per cent. Beyond this point, an increase in the concentration of the iodide was accompanied by an elevation of the freezing point, the change of the freezing point with the concentration being represented by the curve BC. The solidwhich separated from the solutions represented by BC was a brightyellowcrystalline substance. At the point C (-23.4°) a temperature-maximum was reached; and as the concentration of the potassium iodide was continuously increased, the temperature of equilibrium first fell and then slowly rose, until at +0.26° (E) a second temperature-maximum was registered. On passing the point D, the solid which was deposited from the solution was aredcrystalline substance. On withdrawing sulphur dioxide from the system, the solution became turbid, and the temperature remained constant. The investigation was not pursued farther at this point, the attention being then directed to the equilibria at higher temperatures.
When a solution of potassium iodide in liquid sulphur dioxide containing 1.49 per cent. of potassium iodide was heated, solid (potassium iodide) was deposited at a temperature of 96.4°. Solutions containing more than about 3 per cent. of the iodide separated, on being heated, into two layers, and the temperature at which the liquid became heterogeneous fell as the concentration was increased; a temperature-minimum being obtained with solutions containing 12 per cent. of potassium iodide. On the other hand, solutions containing 30.9 per cent. of the iodide, on being heated, deposited potassium iodide; while a solution containing 24.5 per cent. of the salt first separated into two layers at 89.3°, and then, on cooling, solid was deposited and one of the liquid layers disappeared.
Such are, in brief, the results of experiment; their interpretation in the light of the Phase Rule is the following:—
The curve AB is the freezing-point curve of solid sulphur dioxide in contact with solutions of potassium iodide. BCD is the solubility curve of the yellow crystalline solid which is deposited from the solutions. C, the temperature-maximum, is the melting point of thisyellowsolid, and the composition of the latter must be the same as that of the solution at this point (p.145), which was found to be that represented by the formula KI,14SO2. B is therefore the eutectic point, at which solid sulphur dioxide and the compound KI,14SO2can exist together in equilibrium with solution and vapour. The curve DE is the solubility curve of theredcrystalline solid, and thepoint E, at which the composition of solution and solid is the same, is the melting point of the solid. The composition of this substance was found to be KI,4SO2.[238]D is, therefore, the eutectic point at which the compounds KI,14SO2and KI,4SO2can coexist in equilibrium with solution and vapour. The curve DE does not exhibit a retroflex portion; on the contrary, on attempting to obtain more concentrated solutions in equilibrium with the compound KI,4SO2, a new solid phase (probably potassium iodide) was formed. Since at this point there are four phases in equilibrium, viz. the compound KI,4SO2, potassium iodide, solution, and vapour, the system is invariant. E is, therefore, thetransition pointfor KI,4SO2and KI.
Passing to higher temperatures, FG is the solubility curve of potassium iodide in sulphur dioxide; at G two liquid phases are formed, and the system therefore becomes invariant (cf. p.121). The curve GHK is the solubility curve for two partially miscible liquids; and since complete miscibility occurs onloweringthe temperature, the curve is similar to that obtained with triethylamine and water (p.101). K is also an invariant point at which potassium iodide is in equilibrium with two liquid phases and vapour.
The complete investigation of the equilibria between sulphur dioxide and potassium iodide, therefore, shows that these two components form the compounds KI,14SO2and KI,4SO2; and that when solutions having a concentration between those represented by the points G and K are heated, separation into two layers occurs. The temperatures and concentrations of the different characteristic points are as follows:—
EQUILIBRIA BETWEEN TWO VOLATILE COMPONENTS
General.—In the two preceding chapters certain restrictions were imposed on the discussion of the equilibria between two components; but in the present chapter the restriction that only one of the components is volatile will be allowed to fall, and the general behaviour of two volatile[239]components, each of which is capable of forming a liquid solution with the other, will be studied. As we shall see, however, the removal of the previous restriction produces no alteration in the general aspect of the equilibrium curves for concentration and temperature, but changes to some extent the appearance of the pressure-temperature diagram. The latter would become still more complicated if account were taken not only of the total pressure but also of the partial pressures of the two components in the vapour phase; this complication, however, will not be introduced in the present discussion.[240]In this chapter we shall consider the systems formed by the two components iodine and chlorine, and sulphur dioxide and water.
Iodine and Chlorine.—The different systems furnished by iodine and chlorine, rendered classical by the studies of Stortenbeker,[241]form a very complete example of equilibria in a two-component system. We shall first of all consider therelations between concentration and temperature, with the help of the accompanying diagram, Fig. 42.
Fig. 42Fig. 42.
Concentration-Temperature Diagram.—In this diagram the temperatures are taken as the abscissæ, and the composition of the solution, expressed in atoms of chlorine to one atom of iodine,[242]is represented by the ordinates. In the diagram, A represents the melting point of pure iodine, 114°. If chlorine is added to the system, a solution of chlorine in liquid iodine is obtained, and the temperature at which solid iodine is in equilibrium with the liquid solution will be all the lower the greater the concentration of the chlorine. We therefore obtain the curve ABF, which represents the composition of the solutionwith which solid iodine is in equilibrium at different temperatures. This curve can be followed down to 0°, but at temperatures below 7.9° (B) it represents metastable equilibria. At B iodine monochloride can be formed, and if present the system becomes invariant; B is therefore a quadruple point at which the four phases, iodine, iodine monochloride, solution, and vapour, can coexist. Continued withdrawal of heat at this point will therefore lead to the complete solidification of the solution to a mixture or conglomerate of iodine and iodine monochloride, while the temperature remains constant during the process. B is the eutectic point for iodine and iodine monochloride.
Just as we found in the case of aqueous salt solutions that at temperatures above the cryohydric or eutectic point, two different solutions could exist, one in equilibrium with ice, the other in equilibrium with the salt (or salt hydrate), so in the case of iodine and chlorine there can be two solutions above the eutectic point B, one containing a lower proportion of chlorine in equilibrium with iodine, the other containing a higher proportion of chlorine in equilibrium with iodine monochloride. The composition of the latter solution is represented by the curve BCD. As the concentration of chlorine is increased, the temperature at which there is equilibrium between iodine monochloride and solution rises until a point is reached at which the composition of the solution is the same as that of the solid. At this point (C), iodine monochloride melts. Addition of one of the components will lower the temperature of fusion, and a continuous curve,[243]exhibiting a retroflex portion as in the case of CaCl2,6H2O, will be obtained. At temperatures below its melting point, therefore, iodine monochloride can be in equilibrium with two different solutions.
The upper portion of this curve, CD, can be followed downwards to a temperature of 22.7°. At this temperature iodine trichloride can separate out, and a second quadruplepoint (D) is obtained. This is the eutectic point for iodine monochloride and iodine trichloride.
By addition of heat and increase in the amount of chlorine, the iodine monochloride disappears, and the system passes along the curve DE, which represents the composition of the solutions in equilibrium with solid iodine trichloride. The concentration of chlorine in the solution increases as the temperature is raised, until at the point E, where the solution has the same composition as the solid, the maximum temperature is reached; the iodine trichloride melts. On increasing still further the concentration of chlorine in the solution, the temperature of equilibrium falls, and a continuous curve, similar to that for the monochloride, is obtained. The upper branch of this curve has been followed down to a temperature of 30°, the solution at this point containing 99.6 per cent. of chlorine.[244]The very rounded form of the curve is due to the trichloride being largely dissociated in the liquid state.
One curve still remains to be considered. As has already been mentioned, iodine monochloride can exist in two crystalline forms, only one of which, however, is stable at temperatures below the melting point; the two forms aremonotropic(p.44). The stable form which melts at 27.2°, is called theα-form, while the less stable variety, melting at 13.9°, is known as theβ-form. If, now, the presence ofα-ICl is excluded, it is possible to obtain theβ-form, and to study the conditions of equilibrium between it and solutions of iodine and chlorine, from the eutectic point F to the melting point G. As theβ-ICl becomes less stable in presence of excess of chlorine, it has not been possible to study the retroflex portion of the curve represented by the dotted continuation of FG.
The following table gives some of the numerical data from which Fig. 42 was constructed.[245]
Iodine and Chlorine.
I.Invariant systems.
II.Melting points.A. Iodine,[246]114.15° (pressure 89.8 mm.).C.α-Iodine monochloride, 27.2° (pressure 37 mm.).E. Iodine trichloride, 101° (pressure 16 atm.).G.β-Iodine monochloride, 13.9°.
II.Melting points.
II.Melting points.
A. Iodine,[246]114.15° (pressure 89.8 mm.).C.α-Iodine monochloride, 27.2° (pressure 37 mm.).E. Iodine trichloride, 101° (pressure 16 atm.).G.β-Iodine monochloride, 13.9°.
A. Iodine,[246]114.15° (pressure 89.8 mm.).
C.α-Iodine monochloride, 27.2° (pressure 37 mm.).
E. Iodine trichloride, 101° (pressure 16 atm.).
G.β-Iodine monochloride, 13.9°.
Since the vapour pressure at the melting point of iodine trichloride amounts to 16 atm., the experiments must of course be carried out in closed vessels. At 63.7° the vapour pressure of the system trichloride—solution—vapour is equal to 1 atm.
Pressure-Temperature Diagram.—In this diagram there are represented the values of the vapour pressure of the saturated solutions of chlorine and iodine. To give a complete picture of the relations between pressure, temperature, and concentration, a solid model would be required, with three axes at right angles to one another along which could be measured the values of pressure, temperature, and concentration of the components in the solution. Instead of this, however, there may be employed the accompanying projection figure[247](Fig. 43), the lower portion of which shows the projection of the equilibrium curve on the surface containing the concentration and temperature axes, while the upper portion is the projection on the plane containing the pressure and temperature axes. The lower portion is therefore a concentration-temperature diagram;the upper portion, a pressure-temperature diagram. The corresponding points of the two diagrams are joined by dotted lines.
Fig. 43Fig. 43.
Corresponding to the point C, the melting point of pure iodine, there is the pointC1, which represents the vapour pressure of iodine at its melting point. At this point three curves cut: 1, the sublimation curve of iodine; 2, the vaporization curve of fused iodine; 3, C1B1, the vapour-pressure curve of the saturated solutions in equilibrium with solid iodine. Starting, therefore, with the system solid iodine—liquid iodine, addition of chlorine will cause the temperature of equilibrium to fall continuously, while the vapour pressure will first increase, pass through a maximum and then fall continuouslyuntil the eutectic point, B (B1), is reached.[248]At this point the system is invariant, and the pressure will therefore remain constant until all the iodine has disappeared. As the concentration of the chlorine increases in the manner represented by the curve BfH, the pressure of the vapour also increases as represented by the curve B1f1H1. At H1, the eutectic point for iodine monochloride and iodine trichloride, the pressure again remains constant until all the monochloride has disappeared. As the concentration of the solution passes along the curve HF, the pressure of the vapour increases as represented by the curve H1F1; F1represents the pressure of the vapour at the melting point of iodine trichloride. If the concentration of the chlorine in the solution is continuously increased from this point, the vapour pressure first increases and then decreases, until the eutectic point for iodine trichloride and solid chlorine is reached (D1). Curves Cl2solid and Cl2liquid represent the sublimation and vaporization curves of chlorine, the melting point of chlorine being -102°.
Although complete measurements of the vapour pressure of the different systems of pure iodine to pure chlorine have not been made, the experimental data are nevertheless sufficient to allow of the general form of the curves being indicated with certainty.
Bivariant Systems.—To these, only a brief reference need be made. Since there are two components, two phases will form a bivariant system. The fields in which these systems can exist are shown in Fig. 43 and Fig. 44, which is a more diagrammatic representation of a portion of Fig. 43.
I. Iodine—vapour.II. Solution—vapour.III. Iodine trichloride—vapour.IV. Iodine monochloride—vapour.
I. Iodine—vapour.II. Solution—vapour.III. Iodine trichloride—vapour.IV. Iodine monochloride—vapour.
I. Iodine—vapour.
II. Solution—vapour.
III. Iodine trichloride—vapour.
IV. Iodine monochloride—vapour.
Fig. 44Fig. 44.
The conditions for the existence of these systems will probably be best understood from Fig. 44. Since the curve B′A′represents the pressures under which the system iodine—solution—vapour can exist, increase of volume (diminution of pressure) will cause the volatilization of the solution, and the system iodine—vapour will remain. If, therefore, we start with a system represented bya, diminution of pressure at constant temperature will lead to the condition represented byx. On the other hand, increase of pressure atawill lead to the condensation of a portion of the vapour phase. Since, now, the concentration of chlorine in the vapour is greater than in the solution, condensation of vapour would increase the concentration of chlorine in the solution; a certain amount of iodine must therefore pass into solution in order that the composition of the latter shall remain unchanged.[249]If, therefore, the volume of vapour be sufficiently great, continued diminution of volume will ultimately lead to the disappearance of all the iodine, and there will remain only solution and vapour (field II.). As the diminution of volume is continued, the vapour pressure and the concentration of the chlorine in the solution will increase, until when the pressure has reached the valueb, iodine monochloride can separate out. The system, therefore, again becomes univariant, and at constant temperature the pressure and composition of the phases must remain unchanged. Diminution of volume will therefore not effect an increase of pressure, but a condensation of the vapour; and since this is richer in chlorine than thesolution, solid iodine monochloride must separate out in order that the concentration of the solution remain unchanged.[250]As the result, therefore, we obtain the bivariant system iodine monochloride—vapour.
A detailed discussion of the effect of a continued increase of pressure will not be necessary. From what has already been said and with the help of Fig. 44, it will readily be understood that this will lead successively to the univariant system (c), iodine monochloride—solution—vapour; the bivariant system solution—vapour (field II.); the univariant system (d), iodine trichloride—solution—vapour; and the bivariant systemx′, iodine trichloride—vapour. If the temperature of the experiment is above the melting point of the monochloride, then the systems in which this compound occurs will not be formed.
Sulphur Dioxide and Water.—In the case just studied we have seen that the components can combine to form definite compounds possessing stable melting points. The curves of equilibrium, therefore, resemble in their general aspect those of calcium chloride and water, or of ferric chloride and water. In the case of sulphur dioxide and water, however, the melting point of the compound formed cannot be realized, because transition to another system occurs; retroflex concentration-temperature curves are therefore not found here, but the curves exhibit breaks or sudden changes in direction at the transition points, as in the case of the systems formed by sodium sulphate and water. The case of sulphur dioxide and water is also of interest from the fact that two liquid phases can be formed.
The phases which occur are—Solid: ice, sulphur dioxide hydrate, SO2,7H2O. Liquid: two solutions, the one containing excess of sulphur dioxide, the other excess of water, and represented by the symbols SO2wavyxH2O (solution I.), and H2OwavyySO2(solution II.). Vapour: a mixture of sulphur dioxide and water vapour in varying proportions. Since there are two components, sulphur dioxide and water, the number ofpossible systems is considerable. Only the following, however, have been studied:—
I.Invariant Systems: Four co-existing phases.(a) Ice, hydrate, solution, vapour.(b) Hydrate, solution I., solution II., vapour.II.Univariant Systems: Three co-existing phases.(a) Hydrate, solution I., vapour.(b) Hydrate, solution II., vapour.(c) Solution I., solution II., vapour.(d) Hydrate, solution I., solution II.(e) Hydrate, ice, vapour.(f) Ice, solution II., vapour.(g) Ice, hydrate, solution II.III.Bivariant Systems: Two co-existing phases.(a) Hydrate, solution I.(b) Hydrate, solution II.(c) Hydrate, vapour.(d) Hydrate, ice.(e) Solution I., solution II.(f) Solution I., vapour.(g) Solution I., ice.(h) Solution II., vapour.(i) Solution II., ice.(j) Ice, vapour.
I.Invariant Systems: Four co-existing phases.(a) Ice, hydrate, solution, vapour.(b) Hydrate, solution I., solution II., vapour.
I.Invariant Systems: Four co-existing phases.
(a) Ice, hydrate, solution, vapour.
(b) Hydrate, solution I., solution II., vapour.
II.Univariant Systems: Three co-existing phases.(a) Hydrate, solution I., vapour.(b) Hydrate, solution II., vapour.(c) Solution I., solution II., vapour.(d) Hydrate, solution I., solution II.(e) Hydrate, ice, vapour.(f) Ice, solution II., vapour.(g) Ice, hydrate, solution II.
II.Univariant Systems: Three co-existing phases.
(a) Hydrate, solution I., vapour.
(b) Hydrate, solution II., vapour.
(c) Solution I., solution II., vapour.
(d) Hydrate, solution I., solution II.
(e) Hydrate, ice, vapour.
(f) Ice, solution II., vapour.
(g) Ice, hydrate, solution II.
III.Bivariant Systems: Two co-existing phases.(a) Hydrate, solution I.(b) Hydrate, solution II.(c) Hydrate, vapour.(d) Hydrate, ice.(e) Solution I., solution II.(f) Solution I., vapour.(g) Solution I., ice.(h) Solution II., vapour.(i) Solution II., ice.(j) Ice, vapour.
III.Bivariant Systems: Two co-existing phases.
(a) Hydrate, solution I.
(b) Hydrate, solution II.
(c) Hydrate, vapour.
(d) Hydrate, ice.
(e) Solution I., solution II.
(f) Solution I., vapour.
(g) Solution I., ice.
(h) Solution II., vapour.
(i) Solution II., ice.
(j) Ice, vapour.
Fig. 45Fig.45.
Pressure-Temperature Diagram.[251]—If sulphur dioxide is passed into water at 0°, a solution will be formed and the temperature at which ice can exist in equilibrium with this solution will fall more and more as the concentration of the sulphur dioxide increases. At -2.6°, however, a cryohydric point is reached at which solid hydrate separates out, and the system becomes invariant. The curve AB (Fig. 45) therefore represents the pressure of the system ice—solution II.—vapour, and B represents the temperature and pressure at which the invariant system ice—hydrate—solution II.—vapour can exist. At this point the temperature is -2.6°, and the pressure 21.1 cm. If heat is withdrawn from this system, the solution will ultimatelysolidify to a mixture of ice and hydrate, and there will be obtained the univariant system ice—hydrate—vapour. The vapour pressure of this system has been determined down to a temperature of -9.5°, at which temperature the pressure amounts to 15 cm. The pressures for this system are represented by the curve BC. If at the point B the volume is diminished, the pressure must remain constant, but the relative amounts of the different phases will undergo change. If suitable quantities of these are present, diminution of volume will ultimately lead to the total condensation of the vapour phase, and there will remain the univariant system ice—hydrate—solution. The temperature of equilibrium of this system will alter with the pressure, but, as in the case of the melting point of a simple substance, great differences of pressure will cause only comparatively small changes in the temperature of equilibrium. The change of the cryohydric point with the pressure is represented by the line BE; the actual values have not been determined, but the curve must slope towards the pressure axis because fusion is accompanied by diminution of volume, as in the case of pure ice.
A fourth univariant system can be formed at B. This is the system hydrate—solution II.—vapour. The conditions for the existence of this system are represented by the curve BF, which may therefore be regarded as the vapour-pressure curve of the saturated solution of sulphur dioxide heptahydrate in water. Unlike the curve for iodine trichloride—solution—vapour, this curve cannot be followed to the melting point of the hydrate. Before this point is reached, a second liquid phase appears, and an invariant system consisting of hydrate—solution I.—solution II.—vapour is formed. We have here, therefore, the phenomenon of melting under the solution as in the case of succinic nitrile and water (p.122). This point is represented in the diagram by F; the temperature at this point is 12.1°, and the pressure 177.3 cm. The range of stable existence of the hydrate is therefore from -2.6° to 12.1°; nevertheless, the curve FB has been followed down to a temperature of -6°, at which point ice formed spontaneously.
So long as the four phases hydrate, two liquid phases, and vapour are present, the condition of the system is perfectly defined. By altering the conditions, however, one of the phases can be made to disappear, and a univariant system will then be obtained. Thus, if the vapour phase is made to disappear, the univariant system solution I.—solution II.—hydrate, will be left, and the temperature at which this system is in equilibrium will vary with the pressure. This is represented by the curve FI; under a pressure of 225 atm. the temperature of equilibrium is 17.1°. Increase of pressure, therefore, raises the temperature at which the three phases can coexist.
Again, addition of heat to the invariant system at F will cause the disappearance of the solid phase, and there will be formed the univariant system solution I.—solution II.—vapour. In the case of this system the vapour pressure increases as the temperature rises, as represented by the curve FG. Such a system is analogous to the case of ether and water, or other two partially miscible liquids (p.103). As the temperature changes, the composition of the two liquid phases will undergo change; but this system has not been studied fully.
The fourth curve, which ends at the quadruple point F, isthat representing the vapour pressure of the system hydrate—solution I.—vapour (FH). This curve has been followed to a temperature of 0°, the pressure at this point being 113 cm. The metastable prolongation of GF has also been determined. Although, theoretically, this curve must lie below FH, it was found that the difference in the pressure for the two curves was within the error of experiment.
Bivariant Systems.—The different bivariant systems, consisting of two phases, which can exist within the range of temperature and pressure included in Fig. 45, were given on p.170. The conditions under which these systems can exist are represented by the areas in the diagram, and the fields of the different bivariant systems are indicated by letters, corresponding to the letters on p.170. Just as in the case of one-component systems (p.29), we found that the field lying between any two curves gave the conditions of existence of that phase which was common to the two curves, so also in the case of two-component systems, a bivariant two-phase system occurs in the field enclosed[252]by the two curves to which the two phases are common. As can be seen, the same bivariant system can occur in more than one field.
As is evident from Fig. 45, three different bivariant systems are capable of existing in the area HFI; which of these will be obtained will depend on the relative masses of the different phases in the univariant or invariant system. Thus, starting with a system represented by a point on the curve HF, diminution of volume at constant temperature will cause the condensation of a portion of the vapour, which is rich in sulphur dioxide; since this would increase the concentration of sulphur dioxide in the solution, it must be counteracted by the passage of a portion of the hydrate (which is relatively poor in sulphur dioxide) into the solution. If, therefore, the amount of hydrate present is relatively very small, the final result of the compression will be the production of the systemf, solution I.—vapour. On the other hand, if the vapour is present in relatively small amount, it will be the first phase to disappear,and the bivariant systema, hydrate—solution I., will be obtained. Finally, if we start with the invariant system at F, compression will cause the condensation of vapour, while the composition of the two solutions will remain unchanged. When all the vapour has disappeared, the univariant system hydrate—solution I.—solution II. will be left. If, now, the pressure is still further increased, while the temperature is kept below 12°, more and more hydrate must be formed at the expense of the two liquid phases (because 12° is the lower limit for the coexistence of the two liquid phases), and if the amount of the solution I. (containing excess of sulphur dioxide) is relatively small, it will disappear before solution II., and there will be obtained the bivariant system hydrate—solution II. (bivariant systemb).
In a similar manner, account can be taken of the formation of the other bivariant systems.
A behaviour similar to that of sulphur dioxide and water is shown by chlorine and water and by bromine and water, although these have not been so fully studied.[253]In the case of hydrogen bromide and water, and of hydrogen chloride and water, a hydrate, viz. HBr,2H2O and HCl,2H2O, is formed which possesses a definite melting point, as in the case of iodine trichloride. In these cases, therefore, a retroflex curve is obtained. Further, just as in the case of the chlorides of iodine the upper branch of the retroflex curve ended in a eutectic point, so also in the case of the hydrate HBr,2H2O the upper branch of the curve ends in a eutectic point at which the system dihydrate—monohydrate—solution—vapour can exist. Before the melting point of the monohydrate is reached, two liquid phases are formed, as in the case of sulphur dioxide and water.
SOLID SOLUTIONS. MIXED CRYSTALS
General.—With the conception of gaseous and liquid solutions, every one is familiar. Gases can mix in all proportions to form homogeneous solutions. Gases can dissolve in or be "absorbed" by liquids; and solids, also, when brought in contact with liquids, "pass into solution" and yield a homogeneous liquid phase. On the other hand, the conception of asolid solutionis one which in many cases is found more difficult to appreciate; and the existence and behaviour of solid solutions, in spite of their not uncommon occurrence and importance, are in general comparatively little known.
The reason of this is to be found, to some extent, no doubt, in the fact that the term "solid solution" was introduced at a comparatively recent date,[254]but it is probably also due in some measure to a somewhat hazy comprehension of the definition of the term "solution" itself. As has already been said (p.92), a solution is a homogeneous phase, the composition of which can vary continuously within certain limits; the definition involves, therefore, no condition as to the physical state of the substances. Accordingly, solid solutions are homogeneous solid phases, the composition of which can undergo continuous variation within certain limits. Just as we saw that the range of variation of composition is more limited in the case of liquids than in the case of gases, so also we find that the limits of miscibility are in general still more restricted in the case of solids. Examples of complete miscibility are, however, not unknown even in the case of solid substances.
Solid solutions have long been known, although, of course,they were not defined as such. Thus, the phenomena of "occlusion" of gases by metals and other substances (occlusion of hydrogen by palladium; occlusion of hydrogen by iron) are due to the formation of solid solutions. The same is probably also true of the phenomena of "adsorption," as in the removal of organic colouring matter by charcoal, although, in this case, surface tension no doubt plays a considerable part.[255]
As examples of the solution of gases in solids there may be cited (in addition to the phenomena of occlusion already mentioned), the hydrated silicates and the zeolites. During dehydration these crystalline substances remain clear and transparent, and the pressure of the water vapour which they emit varies with the degree of hydration or the concentration of water in the mineral.[256]As examples of the solution of solids in solids we have the cementation of iron by charcoal, the formation of glass, and the crystallization together of isomorphous substances.
Although we have here spoken of the glasses as "solid solutions," it should be mentioned that the term "solid" is used in its popular sense. Strictly speaking, the glasses are to be regarded as supercooled liquids (see also p. 53,footnote).
In discussing the equilibria in systems containing a solid solution, it is of essential importance to remember that a solid solution constitutes onlyonephase, a phase of varying composition, as in the case of liquid solutions.
Solution of Gases in Solids.—Comparatively little work has been done in this connection, the investigations being limited chiefly to the phenomena of occlusion or adsorption of gases by charcoal.[257]We shall, therefore, indicate only brieflyand in a general manner, the behaviour which the Phase Rule enables us to foresee.[258]
In dealing with the systems formed by the two phases gas—solid, three chief cases call for mention:—
I.The gas is not absorbed by the solid, but when the pressure reaches a certain value, combination of the two components can result.