CHAPTER VII
SOLUTIONS OF SOLIDS IN LIQUIDS, ONLY ONE OF THE COMPONENTS BEING VOLATILE
General.—When a solid is brought into contact with a liquid in which it can dissolve, a certain amount of it passes into solution; and the process continues until the concentration reaches a definite value independent of the amount of solid present. A condition of equilibrium is established between the solid and the solution; the solution becomes saturated. Since the number of components is two, and the number of phases three, viz. solid, liquid solution, vapour, the system is univariant. If, therefore, one of the factors, pressure, temperature, or concentration of the components (in the solution[[180]]), is arbitrarily fixed, the state of the system becomes perfectly defined. Thus, at any given temperature, the vapour pressure of the system and the concentration of the components have a definite value. If the temperature is altered, the vapour pressure and also, in general, the concentration will undergo change. Likewise, if the pressure varies, while the system is isolated so that no heat can pass between it and its surroundings, the concentration and the temperature must also undergo variation until they attain values corresponding to the particular pressure.
That the temperature has an influence, sometimes a very considerable influence, on the amount of substance passing into solution, is sufficiently well known; the effect of pressure, although less apparent, is no less certain. If at any given temperature the volume of the vapour phase is diminished,
vapour will condense to liquid, in order that the pressure may remain constant, and so much of the solid will pass into solution that the concentration may remain unchanged; for, so long as the three phases are present, the state of the system cannot alter. If, however, one of the phases, e.g. the vapour phase, disappears, the system becomes bivariant; at any given temperature, therefore, there may be different values of concentration and pressure.
The direction in which change of concentration will occur with change of pressure can be predicted by means of the theorem of Le Chatelier, if it is known whether solution is accompanied by increase or diminution of the total volume. If diminution of the total volume of the system occurs on solution, increase of pressure will increase the solubility; in the reverse case, increase of pressure will diminish the solubility.
This conclusion has also been verified by experiment, as is shown by the following figures.[[181]]
| Salt. | Change of volume by dissolving 1 gm. of salt in the saturated solution. | Solubility (at 18°) (grams salt in 1 gram of solution). | |
| Pressure = 1 atm. | Pressure = 500 atm. | ||
| Sodium chloride | -0.07 | 0.264 | 0.270 |
| Ammonium chloride | +0.10 | 0.272 | 0.258 |
| Alum | -0.067 | 0.115 | 0.142 |
| (p = 400 atm.) | |||
As can be seen, a large increase of the pressure brings about a no more than appreciable alteration of the solubility; a result which is due, as in the case of the alteration of the fusion point with the pressure, to the small change in volume accompanying solution or increase of pressure. For all practical purposes, therefore, the solubility as determined under atmospheric pressure may be taken as equal to the true
solubility, that is, the solubility when the system is under the pressure of its own vapour.
The Saturated Solution.—From what has been said above, it will be seen that the condition of saturation of a solution can be defined only with respect to a certain solid phase; if no solid is present, the system is undefined, for it then consists of only two phases, and is therefore bivariant. Under such circumstances not only can there be at one given temperature solutions of different concentration, all containing less of one of the components than when that component is present in the solid form, but there can also exist solutions containing more of that component than corresponds to the equilibrium when the solid is present. In the former case the solutions are unsaturated, in the latter case they are supersaturated with respect to a certain solid phase; in themselves, the solutions are stable, and are neither unsaturated nor supersaturated. Further, if the solid substance can exist in different allotropic modifications, the particular form of the substance which is in equilibrium with the solution must be known, in order that the statement of the solubility may be definite; for each form has its own solubility, and, as we shall see presently, the less stable form has the greater solubility (cf. p. [47]). In all determinations of the solubility, therefore, not only must the concentration of the components in the solution be determined, but equal importance should be attached to the characterisation of the solid phase present.
In this connection, also, one other point may be emphasised. For the production of the equilibrium between a solid and a liquid, time is necessary, and this time not only varies with the state of division of the solid and the efficiency of the stirring, but is also dependent on the nature of the substance.[[182]] Considerable care must therefore be taken that sufficient time is allowed for equilibrium to be established. Such care is more especially needful when changes may occur in the solid phase, and neglect of it has greatly diminished the value of many of the older determinations of solubility.
Form of the Solubility Curve.—The solubility curve—that
is, the curve representing the change of concentration of the components in the solution with the temperature—differs markedly from the curve of vapour pressure (p. [63]), in that it possesses no general form, but may vary in the most diverse manner. Not only may the curve have an almost straight and horizontal course, or slope or curve upwards at varying angles; but it may even slope downwards, corresponding to a decrease in the solubility with rise of temperature; may exhibit maxima or minima of solubility, or may, as in the case of some hydrated salts, pass through a point of maximum temperature. In the latter case the salt may possess two values of solubility at the same temperature. We shall consider these cases in the following chapter.
The great variety of form shown by solubility curves is at once apparent from Fig. 26, in which the solubility curves of various substances (not, however, drawn to scale) are reproduced.[[183]]
Varied as is the form of the solubility curve, its direction, nevertheless, can be predicted by means of the theorem of van't Hoff and Le Chatelier; for in accordance with that theorem (p. [57]) increase of solubility with the temperature must occur in those cases where the process of solution is accompanied by an absorption of heat; and a decrease in the solubility with rise of temperature will be found in cases where solution occurs with evolution of heat. Where there is no heat effect accompanying solution,
change of temperature will be without influence on the solubility; and if the sign of the heat of solution changes, the direction of the solubility curve must also change, i.e. must show a maximum or minimum point. This has in all cases been verified by experiment.[[184]]
In applying the theorem of Le Chatelier to the course of the solubility curve, it should be noted that by heat of solution there is meant, not the heat effect produced on dissolving the salt in a large amount of solvent (which is the usual signification of the expression), but the heat which is absorbed or evolved when the salt is dissolved in the almost saturated solution (the so-called last heat of solution). Not only does the heat effect in the two cases have a different value, but it may even have a different sign. A striking example of this is afforded by cupric chloride, as the following figures show:[[185]]—
| Number of gram-molecules of CuCl2, 2H2O dissolved in 198 gram-molecules of water. | Heat effect. |
| 1 | +37 K |
| 2.02 | +66 ,, |
| 4.15 | +105 ,, |
| 7.07 | +117 ,, |
| 9.95 | +117 ,, |
| 11 | +91 ,, |
| 18.8 | -10 ,, |
| 19.6 | -31 ,, |
| 24.75 | -198 ,, |
In the above table the positive sign indicates evolution of heat, the negative sign, absorption of heat; and the values of the heat effect are expressed in centuple calories. Judging from the heat effect produced on dissolving cupric chloride in a large bulk of water, we should predict that the solubility of that salt would diminish with rise of temperature; as a matter of fact, it increases. This is in accordance with the fact that
the last heat of solution is negative (as expressed above), i.e. solution of the salt in the almost saturated solution is accompanied by absorption of heat. We are led to expect this from the fact that the heat of solution changes sign from positive to negative as the concentration increases; experiment also showed it to be the case.
Despite its many forms, it should be particularly noted that the solubility curve of any substance is continuous, so long as the solid phase, or solid substance in contact with the solution, remains unchanged. If any "break" or discontinuous change in the direction of the curve occurs, it is a sign that the solid phase has undergone alteration. Conversely, if it is known that a change takes place in the solid phase, a break in the solubility curve can be predicted. We shall presently meet with examples of this.[[186]]
A.—Anhydrous Salt and Water.
The Solubility Curve.—In studying the equilibria in those systems of two components in which the liquid phase is a solution or phase of varying composition, we shall in the present chapter limit the discussion to those cases where no compounds are formed, but where the components crystallise out in the pure state. Since some of the best-known examples of such systems are yielded by the solutions of anhydrous salts in water, we shall first of all briefly consider some of the results which have been obtained with them.
For the most part the solubility curves have been studied only at temperatures lying between 0° and 100°, the solid phase in contact with the solution being the anhydrous salt. For the representation of these equilibria, the concentration-temperature
diagram is employed, the concentration being expressed as the number of grams of the salt dissolved in 100 grams of water, or as the number of gram-molecules of salt in 100 gram-molecules of water. The curves thus obtained exhibit the different forms to which reference has already been made. So long as the salt remains unchanged the curve will be continuous, but if the salt alters its form, then the solubility curve will show a break.
Now, we have already seen in Chapter III. that certain substances are capable of existing in various crystalline forms, and these forms are so related to one another that at a given temperature the relative stability of each pair of polymorphic forms undergoes change. Since each crystalline variety of a substance must have its own solubility, there must be a break in the solubility curve at the temperature of transition of the two enantiotropic forms. At this point the two solubility curves must cut, for since the two forms are in equilibrium with respect to their vapour, they must also be in equilibrium with respect to their solutions. From the table on p. [63] it is seen that potassium nitrate, ammonium nitrate, silver nitrate, thallium nitrate, thallium picrate, are capable of existing in two or more different enantiotropic crystalline forms, the range of stability of these forms being limited by definite temperatures (transition temperature). Since the transition point is not altered by a solvent (provided the latter is not absorbed by the solid phase), we should find on studying the solubility of these substances in water that the solubility curve would exhibit a change in direction at the temperature of transition. As a matter of fact this has been verified, more especially in the case of ammonium nitrate[[187]]
and thallium picrate.[[188]] The following table contains the values of the solubility of ammonium nitrate obtained by Müller and Kaufmann, the solubility being expressed in gram-molecules NH4NO3 in 100 gram-molecules of water. In Fig. 27 these results are represented graphically. The equilibrium point was approached both from the side of unsaturation and of supersaturation, and the condition of equilibrium was controlled by determinations of the density of the solution.
Solubility of Ammonium Nitrate.
| Temperature. | Solubility. | Temperature. | Solubility. |
| 12.2° | 34.50 | 32.7° | 57.90 |
| 20.2° | 43.30 | 34.0° | 58.89 |
| 25.05° | 48.19 | 35.0° | 59.80 |
| 28.0° | 51.86 | 36.0° | 61.00 |
| 30.0° | 54.40 | 37.5° | 62.90 |
| 30.2° | 54.61 | 38.0° | 63.60 |
| 31.9° | 57.20 | 39.0° | 65.09 |
| 32.1° | 57.60 | 40.0° | 66.80 |
From the graphic representation of the solubility given in Fig. 27, there is seen to be a distinct change in the direction of the curve at a temperature of 32°; and this break in the curve corresponds to the transition of the β-rhombic into the α-rhombic form of ammonium nitrate (p. [63]).
Suspended Transformation and Supersaturation.—As has already been learned, the transformation of the one crystalline form into the other does not necessarily take place immediately the transition point has been passed; and it has therefore been found possible in a number of cases to follow the solubility curve of a given crystalline form beyond the point at which it ceases to be the most stable modification. Now, it will be readily seen from Fig. 27 that if the two solubility curves be prolonged beyond the point of intersection, the solubility of the less stable form is greater than that of the more stable. A solution, therefore, which is saturated with respect to the less stable form, i.e. which is in equilibrium with that form, is supersaturated with respect to the more stable modification. If,
therefore, a small quantity of the more stable form is introduced into the solution, the latter must deposit such an amount of the more stable form that the concentration of the solution corresponds to the solubility of the stable form at the particular temperature. Since, however, the solution is now unsaturated with respect to the less stable variety, the latter, if present, must pass into solution; and the two processes, deposition of the stable and solution of the metastable form, must go on until the latter form has entirely disappeared and a saturated solution of the stable form is obtained. There will thus be a conversion, through the medium of the solvent, of the less stable into the more stable modification. This behaviour is of practical importance in the determination of transition points (v. Appendix).
From the above discussion it will be seen how important is the statement of the solid phase for the definition of saturation and supersaturation.[[189]]
Solubility Curve at Higher Temperatures.—On passing to the consideration of the solubility curves at higher temperatures, two chief cases must be distinguished.
(1) The two components in the fused state can mix in all proportions.
(2) The two components in the fused state cannot mix in all proportions.
1. Complete Miscibility of the Fused Components.
The best example of this which has been studied, so far as anhydrous salts and water are concerned, is that of silver nitrate and water. The solubility of this salt at temperatures
above 100° has been studied chiefly by Etard[[190]] and by Tilden and Shenstone.[[191]] The values obtained by Etard are given in the following table, and represented graphically in Fig. 28.
Solubility of Silver Nitrate.
| Temperature. | Parts of dry salt in 100 parts of solution. |
| -7° | 46.2 |
| -1° | 52.1 |
| +5° | 56.3 |
| 10° | 61.2 |
| 20° | 67.8 |
| 40.5° | 76.8 |
| 73° | 84.0 |
| 135° | 92.8 |
| 182° | 96.9 |
In this figure the composition of the solution is expressed in parts of silver nitrate in 100 parts by weight of the solution, so that 100 per cent. represents pure silver nitrate. As can be seen, the solubility increases with the temperature. At a temperature of about 160° there should be a break in the curve due to change of crystalline form (p. [63]). Such a change in the direction of the solubility curve, however, does not in any way alter the essential nature of the relationships discussed here, and may for the present be left out of account. On following the solubility curve of silver nitrate to higher temperatures, therefore, the concentration of silver nitrate in the solution gradually increases, until at last, at a temperature of 208°,[[192]] the melting point of pure silver nitrate is reached, and the concentration of the water has become zero. The curve throughout its whole extent represents the equilibrium between silver nitrate, solution, and vapour. Conversely, starting with pure silver nitrate in contact with the fused salt, addition of water will lower the melting point, i.e. will lower the temperature at which the solid salt can exist in contact with the liquid;
and the depression will be all the greater the larger the amount of water added. As the concentration of the water in the liquid phase is increased, therefore, the system will pass back along the curve from higher to lower temperatures, and from greater to smaller concentrations of silver nitrate in the liquid phase. The curve in Fig. 28 may, therefore, be regarded either as the solubility curve of silver nitrate in water, or as the freezing point curve for silver nitrate in contact with a solution consisting of that salt and water.
As the temperature of the saturated solution falls, silver nitrate is deposited, and on lowering the temperature sufficiently a point will at last be reached at which ice also begins to separate out. Since there are now four phases co-existing, viz. silver nitrate, ice, solution, vapour, the system is invariant, and the point is a quadruple point. This quadruple point, therefore, forms the lower limit of the solubility curve of silver nitrate. Below this point the solution becomes metastable.
Ice as Solid Phase.—Ice melts or is in equilibrium with water at a temperature of 0°. The melting point, will, however, be lowered by the solution of silver nitrate in the water; and the greater the concentration of the salt in the solution the greater will be the depression of the temperature of equilibrium. On continuing the addition of silver nitrate, a point will at length be reached at which the salt is no longer dissolved, but remains in the solid form along with the ice. We again obtain, therefore, the invariant system ice—salt—solution—vapour. The temperature at which this invariant system can exist has been found by Middelberg[[193]] to be -7.3°, the solution at this point containing 47.1 per cent. of silver nitrate.
The same general behaviour will be found in the case of all other systems of two components belonging to this class; that is, in the case of systems from which the components crystallise out in the pure state, and in which the fused components are miscible in all proportions. In all such cases, therefore, the solubility curves (curves of equilibrium) can be represented diagrammatically as in Fig. 29. In this figure OA represents the solubility curve of the salt, and OB the freezing
point curve of ice. O is the quadruple point at which the invariant system exists, and may be regarded as the point of intersection of the solubility curve with the freezing-point curve. Since this point is fixed, the condition of the system as regards temperature, vapour pressure, and concentration of the components (or composition of the solution), is perfectly definite. From the way, also, in which the condition is attained, it is evident that the quadruple point is the lowest temperature that can be obtained with mixtures of the two components in presence of vapour. It is known as the cryohydric point, or, generally, the eutectic point.[[194]]
Cryohydrates.[[195]]—On cooling a solution of common salt in water to a temperature of -3°, Guthrie observed that the hydrate NaCl,2H2O separated out. This salt continued to be deposited until at a temperature of -22° opaque crystals made their appearance, and the liquid passed into the solid state without change of temperature. A similar behaviour was found by Guthrie in the case of a large number of other salts, a temperature below that of the melting point of ice being reached at which on continued withdrawal of heat, the solution solidified at a constant temperature. When the system had attained this minimum temperature, it was found that the composition of the solid and the liquid phases was the same, and remained unchanged throughout the period of solidification. This is shown by the following figures, which give the composition of different samples of the solid phase deposited from the solution at constant temperature.[[196]]
| No. | Temperature of solidification. | NaCl. Per cent. |
| 1 | -21° to -22° | 23.72 |
| 2 | -22° | 23.66 |
| 3 | -22° | 23.73 |
| 4 | -23° | 23.82 |
| 5 | -23° | 23.34 |
| 6 | -23° | 23.35 |
| Mean | 23.6 | |
Conversely, a mixture of ice and salt containing 23.6 per cent. of sodium chloride will melt at a definite and constant temperature, and exhibit, therefore, a behaviour supposed to be characteristic of a pure chemical compound. This, then, combined with the fact that the solid which was deposited was crystalline, and that the same constant temperature was attained, no matter with what proportions of water and salt one started, led Guthrie to the belief that the solids which thus separated at constant temperature were definite chemical compounds, to which he gave the general name cryohydrate. A large number of such cryohydrates were prepared and analysed by Guthrie, and a few of these are given in the following table, together with the temperature of the cryohydric point:[[197]]—
Cryohydrates.
| Salt. | Cryohydric point. | Percentage of anhydrous salt in the cryohydrate. |
| Sodium bromide | -24° | 41.33 |
| Sodium chloride | -22° | 23.60 |
| Potassium iodide | -22° | 52.07 |
| Sodium nitrate | -17.5° | 40.80 |
| Ammonium sulphate | -17° | 41.70 |
| Ammonium chloride | -15° | 19.27 |
| Sodium iodide | -15° | 59.45 |
| Potassium bromide | -13° | 32.15 |
| Potassium chloride | -11.4° | 20.03 |
| Magnesium sulphate | - 5° | 21.86 |
| Potassium nitrate | -2.6° | 11.20 |
| Sodium sulphate | -0.7° | 4.55 |
The chemical individuality of these cryohydrates was, however, called in question by Pfaundler,[[198]] and disproved by Offer,[[199]] who showed that in spite of the constancy of the melting point, the cryohydrates had the properties, not of definite chemical compounds, but of mixtures; the arguments given being that the heat of solution and the specific volume are the same for the cryohydrate as for a mixture of ice and salt of the same composition; and it was further shown that the cryohydrate had not a definite crystalline form, but separated out as an opaque mass containing the two components in close juxtaposition. The heterogeneous nature of cryohydrates can also be shown by a microscopical examination.
At the cryohydric point, therefore, we are not dealing with a single solid phase, but with two solid phases, ice and salt; the cryohydric point, therefore, as already stated, is a quadruple point and represents an invariant system.
Although on cooling a solution to the cryohydric point, separation of ice may occur, it will not necessarily take place; the system may become metastable. Similarly, separation of salt may not take place immediately the cryohydric point is reached. It will, therefore, be possible to follow the curves BO and AO beyond the quadruple point,[[200]] which is thereby clearly seen to be the point of intersection of the solubility curve of the salt and the freezing-point curve of ice. At this point, also, the curves of the univariant systems ice—salt—vapour and ice—salt—solution intersect.
Changes at the Quadruple Point.—Since the invariant system ice—salt—solution—vapour can exist only at a definite temperature, addition or withdrawal of heat must cause the disappearance of one of the phases, whereby the system will become univariant. So long as all four phases are present the temperature, pressure, and concentration of the components in the solution must remain constant. When, therefore, heat is added to or withdrawn from the system, mutually compensatory changes will take place within the system whereby the
condition of the latter is preserved. These changes can in all cases be foreseen with the help of the theorem of van't Hoff and Le Chatelier; and, after what was said in Chap. IV., need only be briefly referred to here. In the first place, addition of heat will cause ice to melt, and the concentration of the solution will be thereby altered; salt must therefore dissolve until the original concentration is reached, and the heat of fusion of ice will be counteracted by the heat of solution of the salt. Changes of volume of the solid and liquid phases must also be taken into account; an alteration in the volume of these phases being compensated by condensation or evaporation. All four phases will therefore be involved in the change, and the final state of the system will be dependent on the amounts of the different phases present; the ultimate result of addition or withdrawal of heat or of change of pressure at the quadruple point will be one of the four univariant systems: ice—solution—vapour; salt—solution—vapour; ice—salt—vapour; ice—salt—solution. If the vapour phase disappear, there will be left the univariant system ice—salt—solution, and the temperature at which this system can exist will alter with the pressure. Since in this case the influence of pressure is comparatively slight, the temperature of the quadruple point will differ only slightly from that of the cryohydric point as determined under atmospheric pressure.
Freezing Mixtures.—Not only will the composition of a univariant system undergo change when the temperature is varied, but, conversely, if the composition of the system is caused to change, corresponding changes of temperature must ensue. Thus, if ice is added to the univariant system salt—solution—vapour, the ice must melt and the temperature fall; and if sufficient ice is added, the temperature of the cryohydric point must be at length reached, for it is only at this temperature that the four phases ice—salt—solution—vapour can coexist. Or, on the other hand, if salt is added to the system ice—solution—vapour, the concentration of the solution will increase, ice must melt, and the temperature must thereby fall; and this process also will go on until the cryohydric point is reached. In both cases ice melts and there is a change in the
composition of the solution; in the former case, salt will be deposited[[201]] because the solubility diminishes as the temperature falls; in the latter, salt will pass into solution. This process may be accompanied either by an evolution or, more generally, by absorption of heat; in the former case the effect of the addition of ice will be partially counteracted; in the latter case it will be augmented.
These principles are made use of in the preparation of freezing mixtures. The lowest temperature which can be reached by means of these (under atmospheric pressure) is the cryohydric point. This temperature-minimum is, however, not always attained in the preparation of a freezing mixture, and that for various reasons. The chief of these are radiation and the heat absorbed in cooling the solution produced. The lower the temperature falls, the more rapid does the radiation become; and the rate at which the temperature sinks decreases as the amount of solution increases. Both these factors counteract the effect of the latent heat of fusion and the heat of solution, so that a point is reached (which may lie considerably above the cryohydric point) at which the two opposing influences balance. The absorption of heat by the solution can be diminished by allowing the solution to drain off as fast as it is produced; and the effect of radiation can be partially annulled by increasing the rate of cooling. This can be done by the more intimate mixing of the components. Since, under atmospheric pressure, the temperature of the cryohydric point is constant, the cryohydrates are very valuable for the production of baths of constant low temperature.
2. Partial Miscibility of the Fused Components.
On passing to the study of the second class of systems of two components belonging to this group, namely, those in which the fused components are not miscible in all proportions, we find that the relationships are not quite so simple as
in the case of silver nitrate and water. In the latter case, only one liquid phase was possible; in the cases now to be studied, two liquid phases can be formed, and there is a marked discontinuity in the solubility curve on passing from the cryohydric point to the melting point of the second (non-volatile) component.
Paratoluidine dissolves in water, and the solubility increases as the temperature rises.[[202]] At 44.2°, however, paratoluidine in contact with water melts, and two liquid phases are formed, viz. a solution of water in fused paratoluidine and a solution of fused paratoluidine in water. We have, therefore, the phenomenon of melting under the solvent. This melting point will, of course, be lower than the melting point of the pure substance, because the solid is now in contact with a solution, and, as we have already seen, addition of a foreign substance lowers the melting point. Such cases of melting under the solvent are by no means rare, and a review of the relationships met with may, therefore, be undertaken here. As an example, there may be chosen the equilibrium between succinic nitrile, C2H4(CN)2 and water, which has been fully studied by Schreinemakers.[[203]]
If to the system ice—water at 0° succinic nitrile is added, the temperature will fall; and continued addition of the nitrile will lead at last to the cryohydric point b (Fig. 30), at which solid nitrile, ice, solution, and vapour can coexist. The temperature of the cryohydric point is -1.2°, and the composition of the solution is 1.29 mol. of nitrile in 100 mol. of solution. From a to b the solid phase in contact with the solution is ice.
If the temperature be now raised so as to cause the disappearance of the ice, and the addition of nitrile be continued, the concentration of the nitrile in the solution will increase as represented by the curve bc. At the point c (18.5°), when the concentration of the nitrile in the solution has increased to 2.5 molecules per cent., the nitrile melts and two liquid phases are formed; the concentration of the nitrile in these two phases is given by the points c and c′. As there are now four phases present, viz. solid nitrile, solution of fused nitrile in water, solution of water in fused nitrile, and vapour, the system is invariant. Since at this point the concentration, temperature, and pressure are completely defined, addition or withdrawal of heat can only cause a change in the relative amounts of the phases, but no variation of the concentrations of the respective phases. As a matter of fact, continued addition of nitrile and addition of heat will cause an increase in the amount of the liquid phase containing excess of nitrile (i.e. the solution of water in fused nitrile), whereas the other liquid phase, the solution of fused nitrile in water, will gradually disappear. When it has completely disappeared, the system will be represented by the point c′, where the molecular concentration of nitrile is now 75 per cent., and again becomes univariant, the three phases being solid nitrile, liquid phase containing excess of nitrile, and vapour; and as the amount of the water is diminished the temperature of equilibrium rises, until at 54° the melting point of the pure nitrile is reached.
Return now to the point c. At this point there exists the invariant system solid nitrile, two liquid phases, vapour. If heat be added, the solid nitrile will disappear, and there will be left the univariant system, consisting of two liquid phases and vapour.[[204]] Such a system will exhibit relationships similar to those already studied in the previous chapter. As the temperature rises, the mutual solubility of the two fused components becomes greater, until at d (55.5°) the critical solution temperature is reached, and the fused components become miscible in all proportions.
At all temperatures and concentrations lying to the right
of the curve abcdc′e there can be only one liquid phase; in the field cdc′ there are two liquid phases.
From the figure it will be easy to see what will be the result of bringing together succinic nitrile and water at different temperatures and in different amounts. Since b is the lowest temperature at which liquid can exist in stable equilibrium with solid, ice and succinic nitrile can be mixed in any proportions at temperatures below b without undergoing change. Between b and c succinic nitrile will be dissolved until the concentration reaches the value on the curve bc, corresponding to the given temperature. On adding the nitrile to water at temperatures between c and d, it will dissolve until a concentration lying on the curve cd is attained; at this point two liquid phases will be formed, and further addition of nitrile will cause the one liquid phase (that containing excess of nitrile) to increase, while the other liquid phase will decrease, until it finally disappears and there is only one liquid phase left, that containing excess of nitrile. This can dissolve further quantities of the nitrile, and the concentration will increase until the curve c′e is reached, when the concentration will remain unchanged, and addition of solid will merely increase the amount of the solid phase.
If a solution represented by any point in the field lying below the curve bcd is heated to a temperature above d, the critical solution temperature, then the concentration of the nitrile can be increased to any desired amount without at any time two liquid phases making their appearance; the system can then be cooled down to a temperature represented by any point between the curves dc′e. In this way it is possible to pass continuously from a solution containing excess of one component to solutions containing excess of the other, as represented by the dotted line xxxx (v. p. [100]). At no point is there formation of two liquid phases.
Supersaturation.—Just as suspended transformation is rarely met with in the passage from the solid to the liquid state, so also it is found in the case of the melting of substances under the solvent that suspended fusion does not occur; but that when the temperature of the invariant point is reached at which, therefore, the formation of two liquid layers is possible,
these two liquid layers, as a matter of fact, make their appearance. Suspended transformation can, however, take place from the side of the liquid phase, just as water or other liquid can be cooled below the normal freezing point without solidification occurring. The question, therefore, arises as to the relative solubilities of the solid and the supercooled liquid at the same temperature.
The answer to this question can at once be given from what we have already learned (p. [113]), if we recollect that at temperatures below the point of fusion under the solvent, the solid form, at temperatures above that point, the liquid form, is the more stable; at this temperature, therefore, the relative stability of the solid and liquid forms changes. Since, as we have already seen, the less stable form has the greater solubility, it follows that the supercooled liquid, being the less stable form, must have the greater solubility. This was first proved experimentally by Alexejeff[[205]] in the case of benzoic acid and water, the solubility curves for which are given in Fig. 31. As can be seen from the figure, the prolongation of the curve for liquid—liquid, which represents the solubility of the supercooled liquid benzoic acid, lies above that for the solubility of the
solid benzoic acid in water; the solution saturated with respect to the supercooled liquid is therefore supersaturated with respect to the solid form. A similar behaviour has been found in the case of other substances.[[206]]
Pressure-Temperature Diagram.—Having considered the changes which occur in the concentration of the components in a solution with the temperature, we may conclude the discussion of the equilibrium between a salt and water by studying the variation of the vapour pressure.
Since in systems of two components the two phases, solution and vapour, constitute a bivariant system, the vapour pressure is undefined, and may have different values at the same temperature, depending on the concentration. In order that there may be for each temperature a definite corresponding pressure of the vapour, a third phase must be present. This condition is satisfied by the system solid—liquid (solution)—vapour; that is, by the saturated solution (p. [108]). In the case of a saturated solution, therefore, the pressure of the vapour at any given temperature is constant.
Vapour Pressure of Solid—Solution—Vapour.—It has long been known that the addition of a non-volatile solid to a liquid in which it is soluble lowers the vapour pressure of the solvent; and the diminution of the pressure is approximately proportional to the amount of substance dissolved (Law of Babo). The vapour-pressure curve, therefore, of a solution of a salt in water must lie below that for pure water. Further, in the case of a pure liquid, the vaporization curve is a function only of the temperature (p. [63]), whereas, in the case of a solution, the pressure varies both with the temperature and the concentration. These two factors, however, act in opposite directions; for although the vapour pressure in all cases increases as the temperature rises, increase of concentration, as we have seen, lowers the vapour pressure. Again, since the concentration itself varies with the temperature, two cases have to be considered, viz. where the concentration increases with rise of
temperature, and where the concentration diminishes with rise of temperature.
The relations which are found here will be best understood with the help of Fig. 32.[[207]] In this figure, OB represents the sublimation curve of ice, and BC the vaporization curve of water; the curve for the solution must lie below this, and must cut the sublimation curve of ice at some temperature below the melting point. The point of intersection A is the cryohydric point. If the solubility increases with rise of temperature, the increase of the vapour pressure due to the latter will be partially annulled. Since at first the effect of increase of temperature more than counteracts the depressing action of increase of concentration, the vapour pressure will increase on raising the temperature above the cryohydric point. If the elevation of temperature is continued, however, to the melting point of the salt, the effect of increasing concentration makes itself more and more felt, so that the vapour-pressure curve of the solution falls more and more below that of the pure liquid, and the pressure will ultimately become equal to that of the pure salt; that is to say, practically equal to zero. The curve will therefore be of the general form AMF shown in Fig. 32. If the solubility should diminish with rise of temperature, the two factors, temperature and concentration, will act in the same direction, and the vapour-pressure curve will rise relatively more rapid than that of the pure liquid; since, however, the pure salt is ultimately obtained, the vapour-pressure curve must in this case also finally approach the value zero.
Other Univariant Systems.—Besides the univariant system
salt—solution—vapour already considered, three others are possible, viz. ice—solution—vapour, ice—salt—solution, and ice—salt—vapour.
The fusion point of a substance is lowered, as we have seen, by the addition of a foreign substance, and the depression is all the greater the larger the quantity of substance added. The vapour pressure of the water, also, is lowered by the solution in it of other substances, so that the vapour pressure of the system ice—solution—vapour must decrease as the temperature falls from the fusion point of ice to the cryohydric point. This curve is represented by BA (Fig. 32), and is coincident with the sublimation curve of ice.
This, at first sight, strange fact will be readily understood when we consider that since ice and solution are together in equilibrium with the same vapour, they must have the same vapour pressure. For suppose at any given temperature equilibrium to have been established in the system ice—solution—vapour, removal of the ice will not alter this equilibrium. Suppose, now, the ice and the solution placed under a bell-jar so that they have a common vapour, but are not themselves in contact; then, if they do not have the same vapour pressure, distillation must take place and the solution will become more dilute or more concentrated. Since, at the completion of this process, the ice and solution are now in equilibrium when they are not in contact, they must also be in equilibrium when they are in contact (p. [32]). But if distillation has taken place the concentration of the solution must have altered, so that the ice will now be in equilibrium with a solution of a different concentration from before. But according to the Phase Rule ice cannot at one and the same temperature be in equilibrium with two solutions of different concentration, for the system ice—solution—vapour is univariant, and at any given temperature, therefore, not only the pressure but also the concentration of the components in the solution must be constant. Distillation could not, therefore, take place from the ice to the solution or vice versâ; that is to say, the solution and the ice must have the same vapour pressure—the sublimation pressure of ice. The reason of the coincidence is the non-volatility of the salt: had
the salt a measurable vapour pressure itself, the sublimation curve of ice and the curve for ice—solution—vapour would no longer fall together.
The curve AO represents the pressures of the system ice—salt—vapour. This curve will also be coincident with the sublimation curve of ice, on account of the non-volatility of the salt.
The equilibria of the fourth univariant system ice—salt—solution are represented by AE. Since this is a condensed system, the effect of a small change of temperature will be to cause a large change of pressure, as in the case of the fusion point of a pure substance. The direction of this curve will depend on whether there is an increase or diminution of volume on solidification; but the effect in any given case can be predicted with the help of the theorem of Le Chatelier.
Since the cryohydric point is a quadruple point in a two-component system, it represents an invariant system. The condition of the system is, therefore, completely defined; the four phases, ice, salt, solution, vapour, can co-exist only when the temperature, pressure, and concentration of the solution have constant and definite values. Addition or withdrawal of heat, therefore, can cause no alteration of the condition of the system except a variation of the relative amounts of the phases. Addition of heat at constant volume will ultimately lead to the system salt—solution—vapour or the system ice—solution—vapour, according as ice or salt disappears first. This is readily apparent from the diagram (Fig. 32), for the systems ice—salt—solution and ice—salt—vapour can exist only at temperatures below the cryohydric point (provided the curve for ice—salt—solution slopes towards the pressure axis).
Bivariant Systems.—Besides the univariant systems already discussed, various bivariant systems are possible, the conditions for the existence of which are represented by the different areas of Fig. 32. They are as follows:—
| Area. | System. |
| OAMF | Salt—vapour. |
| CBAMF | Solution—vapour; salt—solution. |
| EABD | Salt—solution; ice—solution. |
| EAO | Ice—salt. |
Deliquescence.—As is evident from Fig. 32, salt can exist in contact with water vapour at pressures under those represented by OAMF. If, however, the pressure of the vapour is increased until it reaches a value lying on this curve at temperatures above the cryohydric point, solution will be formed; for the curve AMF represents the equilibria between salt—solution—vapour. From this, therefore, it is clear that if the pressure of the aqueous vapour in the atmosphere is greater than that of the saturated solution of a salt, that salt will, on being placed in the air, form a solution; it will deliquesce.
Separation of Salt on Evaporation.—With the help of Fig. 32 it is possible to state in a general manner whether or not salt will be deposited when a solution is evaporated under a constant pressure.[[208]]
The curve AMF (Fig. 32) is the vapour-pressure curve of the saturated solutions of the salt, i.e. it represents, as we have seen, the maximum vapour pressure at which salt can exist in contact with solution and vapour. The dotted line aa represents atmospheric pressure. If, now, an unsaturated solution, the composition of which is represented by the point x, is heated in an open vessel, the temperature will rise, and the vapour pressure of the solution will increase. The system will, therefore, pass along a line represented diagrammatically by xx′. At the point x′ the vapour pressure of the system becomes equal to 1 atm.; and as the vessel is open to the air, the pressure cannot further rise; the solution boils. If the heating is continued, water passes off, the concentration increases, and the boiling point rises. The system will therefore pass along the line x′m, until at the point m solid salt separates out (provided supersaturation is excluded). The system is now univariant, and continued heating will no longer cause an alteration of the concentration; as water passes off, solid salt will be deposited, and the solution will evaporate to dryness.
If, however, the atmospheric pressure is represented not by aa but by bb, then, as Fig. 32 shows, the maximum vapour
pressure of the system salt—solution—vapour never reaches the pressure of 1 atm. Further, since the curve bb lies in the area of the bivariant system solution—vapour there can at no point be a separation of the solid form; for the system solid—solution—vapour can exist only along the curve AMF.
On evaporating the solution of a salt in an open vessel, therefore, salt can be deposited only if at some temperature the pressure of the saturated solution is equal to the atmospheric pressure. This is found to be the case with most salts. In the case of aqueous solutions of sodium and potassium hydroxide, however, the vapour pressure of the saturated solution never reaches the value of 1 atm., and on evaporating these solutions, therefore, in an open vessel, there is no separation of the solid. Only a homogeneous fused mass is obtained. If, however, the evaporation be carried out under a pressure which is lower than the maximum pressure of the saturated solution, separation of the solid substance will be possible.
General Summary.—The systems which have been discussed in the present chapter contained water as one of their components, and an anhydrous salt as the other. It will, however, be clear that the relationships which were found in the case of these will be found also in other cases where it is a question of the equilibria between two components, which crystallize out in the pure state, and only one of which possesses a measurable vapour pressure. A similar behaviour will, for example, be found in the case of many pairs of organic substances; and in all cases the equilibria will be represented by a diagram of the general appearance of Fig. 29 or Fig. 30. That is to say: Starting from the fusion point of component I., the system will pass, by progressive addition of component II., to regions of lower temperature, until at last the cryohydric or eutectic point is reached. On further addition of component II., the system will pass to regions of higher temperature, the solid phase now being component II. If the fused components are miscible with one another in all proportions a continuous curve will be obtained leading up to the point of fusion of component II. Slight changes of direction, it is true, due to changes in the crystalline form, may be found along this curve,
but throughout its whole course there will be but one liquid phase. If, on the other hand, the fused components are not miscible in all proportions, then the second curve will exhibit a marked discontinuity, and two liquid phases will make their appearance.