CHAPTER VIII
SOLUTIONS OF SOLIDS IN LIQUIDS, ONLY ONE OF THE COMPONENTS BEING VOLATILE
B.—Hydrated Salt and Water.
In the preceding chapter we discussed the behaviour of systems formed of two components, only one of which was volatile, in those cases where the two components separated from solution in the pure state. In the present chapter we shall consider those systems in which combination between the components can occur with the formation of definite compounds; such as are found in the case of crystalline salt hydrates. Since a not inconsiderable amount of study has been devoted to the systems formed by hydrated salts and water, systems which are of great chemical interest and importance, the behaviour of these will first call for discussion in some detail, and it will be found later that the relationships which exist in such systems appear also in a large number of other two-component systems.
The systems belonging to this group may be divided into two classes according as the compounds formed possess a definite melting point, i.e. form a liquid phase of the same composition, or do not do so. We shall consider the latter first.
1. The Compounds formed do not have a Definite Melting Point.
Concentration-Temperature Diagram.—In the case of salts which can form crystalline hydrates, the temperature-concentration diagram, representing the equilibria of the
different possible systems, must necessarily be somewhat more complicated than where no such combination of the components occurs. For, as has already been pointed out, each substance has its own solubility curve; and there will therefore be as many solubility curves as there are solid phases possible, the curve for each particular solid phase being continuous so long as it remains unchanged in contact with the solution. As an example of the relationships met with in such cases, we shall first of all consider the systems formed of sodium sulphate and water.
Sodium Sulphate and Water.—At the ordinary temperatures, sodium sulphate crystallises from water with ten molecules of water of crystallisation, forming Glauber's salt. On determining the solubility of this salt in water, it is found that the solubility increases as the temperature rises, the values of the solubility, represented graphically by the curve AC (Fig. 33), being given in the following table.[[209]] The numbers denote grams of sodium sulphate, calculated as anhydrous salt, dissolved by 100 grams of water.
Solubility of Na2SO4,10H2O.
| Temperature. | Solubility. |
| 0° | 5.02 |
| 10° | 9.00 |
| 15° | 13.20 |
| 18° | 16.80 |
| 20° | 19.40 |
| 25° | 28.00 |
| 30° | 40.00 |
| 33° | 50.76 |
| 34° | 55.00 |
On continuing the investigation at higher temperatures, it was found that the solubility no longer increased, but decreased with rise of temperature. At the same time, it was observed that the solid phase was now different from that in contact with the solution at temperatures below 33°; for whereas in the latter case the solid phase was sodium sulphate decahydrate, at temperatures above 33° the solid phase was the anhydrous salt. The course of the solubility curve of anhydrous sodium sulphate is shown by BD, and the values of the solubility are given in the following table:—[[210]]
Solubility of Anhydrous Sodium Sulphate.
| Temperature. | Solubility. |
| 18° | 53.25 |
| 20° | 52.76 |
| 25° | 51.53 |
| 30° | 50.37 |
| 33° | 49.71 |
| 34° | 49.53 |
| 36° | 49.27 |
| 40.15° | 48.78 |
| 50.40° | 46.82 |
As is evident from the figure, the solubility curve which is obtained when anhydrous sodium sulphate is present as the solid phase, cuts the curve representing the solubility of the decahydrate, at a temperature of about 33°.
If a solution of sodium sulphate which has been saturated at a temperature of about 34° be cooled down to a temperature below 17°, while care is taken that the solution is protected against access of particles of Glauber's salt, crystals of a second hydrate of sodium sulphate, having the composition Na2SO4,7H2O, separate out. On determining the composition of the solutions in equilibrium with this hydrate at different temperatures, the following values were obtained, these values being represented by the curve FE (Fig. 33):—
Solubility of Na2SO4,7H2O.
| Temperature. | Solubility. |
| 0° | 19.62 |
| 10° | 30.49 |
| 15° | 37.43 |
| 18° | 41.63 |
| 20° | 44.73 |
| 25° | 52.94 |
| 26° | 54.97 |
Since, as has already been stated, each solid substance has its own solubility curve, there are three separate curves to be considered in the case of sodium sulphate and water. Where two curves cut, the solution must be saturated with respect to two solid phases; at the point B, therefore, the point of intersection of the solubility curve of anhydrous sodium sulphate with that of the decahydrate, the solution must be saturated with respect to these two solid substances. But a system of two components existing in four phases, anhydrous salt—hydrated salt—solution—vapour, is invariant; and this invariability will remain even if only three phases are present, provided that one of the factors, pressure, temperature, or concentration of components retains a constant value. This is the case when solubilities are determined in open vessels; the pressure is then equal to atmospheric pressure. Under these circumstances, then, the system, anhydrous sodium sulphate—decahydrate—solution, will possess no degree of freedom, and can exist, therefore, only at one definite temperature and when the solution has a certain definite composition. The temperature of this point is 32.482° on a mercury thermometer, or 32.379° on the hydrogen thermometer.[[211]]
Suspended Transformation.—Although it is possible for the anhydrous salt to make its appearance at the temperature of the quadruple point, it will not necessarily do so; and it is therefore possible to follow the solubility curve of sodium sulphate decahydrate to a higher temperature. Since, however, the solubility of the decahydrate at temperatures above the quadruple point is greater than that of the anhydrous salt, the solution which is saturated with respect to the former will be supersaturated with respect to the latter. On bringing a small quantity of the anhydrous salt in contact with the solution, therefore, anhydrous salt will be deposited; and all the hydrated salt present will ultimately undergo conversion into the anhydrous salt, through the medium of the solution. In this case, as in all cases, the solid phase, which is the most stable at the temperature of the experiment, has at that temperature the least solubility.
Similarly, the solubility curve of anhydrous sodium sulphate has been followed to temperatures below 32.5°. Below this temperature, however, the solubility of this salt is greater than that of the decahydrate, and the saturated solution of the anhydrous salt will therefore be supersaturated for the decahydrate, and will deposit this salt if a "nucleus" is added to the solution. From this we see that at temperatures above 32.5° the anhydrous salt is the stable form, while the decahydrate is unstable (or metastable); at temperatures below 32.5° the decahydrate is stable. This temperature, therefore, is the transition temperature for decahydrate and anhydrous salt.
From Fig. 33 we see further that the solubility curve of the anhydrous salt (which at all temperatures below 32.5° is metastable) is cut by the solubility curve of the heptahydrate; and this point of intersection (at a temperature of 24.2°) must be the transition point for heptahydrate and anhydrous salt. Since at all temperatures the solubility of the heptahydrate is greater than that of the decahydrate, the former hydrate must be metastable with respect to the latter; so that throughout its whole course the solubility curve of the heptahydrate
represents only metastable equilibria. Sodium sulphate, therefore, forms only one stable hydrate, the decahydrate.
The solubility relations of sodium sulphate illustrate very clearly the importance of the solid phase for the definition of saturation and supersaturation. Since the solubility curve of the anhydrous salt has been followed backwards to a temperature of about 18°, it is readily seen, from Fig. 33, that at a temperature of, say, 20° three different saturated solutions of sodium sulphate are possible, according as the anhydrous salt, the heptahydrate or the decahydrate, is present as the solid phase. Two of these solutions, however, would be metastable and supersaturated with respect to the decahydrate.
Further, the behaviour of sodium sulphate and water furnishes a very good example of the fact that a "break" in the solubility curve occurs when, and only when, the solid phase undergoes change. So long as the decahydrate, for example, remained unaltered in contact with the solution, the solubility curve was continuous; but when the anhydrous salt appeared in the solid phase, a distinct change in the direction of the solubility curve was observed.
Dehydration by Means of Anhydrous Sodium Sulphate.—The change in the relative stability of sodium sulphate decahydrate and anhydrous salt in presence of water at a temperature of 32.5° explains why the latter salt cannot be employed for dehydration purposes at temperatures above the transition point. The dehydrating action of the anhydrous salt depends on the formation of the decahydrate; but since at temperatures above 33° the latter is unstable, and cannot be formed in presence of the anhydrous salt, this salt cannot, of course, effect a dehydration above that temperature.
Pressure-Temperature Diagram.—The consideration of the pressure-temperature relations of the two components, sodium sulphate and water, must include not only the vapour pressure of the saturated solutions, but also that of the crystalline hydrates. The vapour pressures of salt hydrates have already been treated in a general manner (Chap. V.), so that it is only necessary here to point out the connection between the two classes of systems.
In most cases the vapour pressure of a salt hydrate, i.e. the vapour pressure of the system hydrate—anhydrous salt (or lower hydrate)—vapour, is at all temperatures lower than that of the system anhydrous salt (or lower hydrate)—solution—vapour. This, however, is not a necessity; and cases are known where the vapour pressure of the former system is, under certain circumstances, equal to or higher than that of the latter. An example of this is found in sodium sulphate decahydrate.
On heating Na2SO4,10H2O, a point is reached at which the dissociation pressure into anhydrous salt and water vapour becomes equal to the vapour pressure of the saturated solution of the anhydrous salt, as is apparent from the following measurements;[[212]] the differences in pressure being expressed in millimetres of a particular oil.
| Temperature: | 29.0° | 30.83° | 31.79° | 32.09° | 32.35° | 32.6° |
| Difference of pressure: | 23.8 | 10.8 | 5.6 | 3.6 | 1.6 | 0 |
At 32.6°, therefore, the vapour pressures of the two systems
Na2SO4,10H2O—Na2SO4—vapour
Na2SO4—solution—vapour
are equal; at this temperature the four phases, Na2SO4,10H2O; Na2SO4; solution; vapour, can coexist. From this it is evident that when sodium sulphate decahydrate is heated to 32.6°, the two new phases anhydrous salt and solution will be formed (suspended transformation being supposed excluded), and the hydrate will appear to undergo partial fusion; and during the process of "melting" the vapour pressure and temperature will remain constant.[[213]] This is, however, not a true but a so-called incongruent melting point; for the composition of the liquid phase is not the same as that of the solid. As has already been pointed out (p. [137]), we are dealing here with the transition point of the decahydrate and anhydrous salt, i.e. with the reaction Na2SO4,10H2O
Since at the point of partial fusion of the decahydrate four
phases can coexist, the point is a quadruple point in a two-component system, and the system at this point is therefore invariant. The temperature of this point is therefore perfectly definite, and on this account the proposal has been made to adopt this as a fixed point in thermometry.[[214]] The temperature is, of course, practically the same as that at which the two solubility curves intersect (p. [112]). If, however, the vapour phase disappears, the system becomes univariant, and the equilibrium temperature undergoes change with change of pressure. The transition curve has been determined by Tammann,[[215]] and shown to pass through a point of maximum temperature.
The vapour pressure of the different systems of sodium sulphate and water can best be studied with the help of the diagram in Fig. 34.[[216]] The curve ABCD represents the vapour-pressure curve of the saturated solution of anhydrous sodium sulphate. GC is the pressure curve of decahydrate + anhydrous salt, which, as we have seen, cuts the curve ABCD at the transition temperature, 32.6°. Since at this point the solution is saturated with respect to both the anhydrous salt and the decahydrate, the vapour-pressure curve of the saturated solution of the latter must also pass through the point C.[[217]] As at temperatures below this point the solubility of the decahydrate is less than that of the anhydrous salt, the vapour pressure of the solution will, in accordance with Babo's law (p. [126]), be higher than that of the solution of the anhydrous salt; which was also found experimentally to be the case (curve HC).
In connection with the vapour pressure of the saturated solutions of the anhydrous salt and the decahydrate, attention must be drawn to a conspicuous deviation from what was found to hold in the case of one-component systems in which a vapour phase was present (p. [31]). There, it was seen that the vapour pressure of the more stable system was always lower than that of the less stable; in the present case, however, we find that this is no longer so. We have already learned that at temperatures below 32.5° the system decahydrate—solution—vapour is more stable than the system anhydrous salt—solution—vapour; but the vapour pressure of the latter system is, as has just been stated, lower than that of the former. At temperatures above the transition point the vapour pressure of the saturated solution of the decahydrate will be lower than that of the saturated solution of the anhydrous salt.
This behaviour depends on the fact that the less stable form is the more soluble, and that the diminution of the vapour pressure increases with the amount of salt dissolved.
With regard to sodium sulphate heptahydrate the same considerations will hold as in the case of the decahydrate. Since at 24° the four phases heptahydrate, anhydrous salt, solution, vapour can coexist, the vapour-pressure curves of the systems hydrate—anhydrous salt—vapour (curve EB) and hydrate—solution—vapour (curve FB) must cut the pressure curve of the saturated solution of the anhydrous salt at the above temperature, as represented in Fig. 34 by the point B. This constitutes, therefore, a second quadruple point, which is, however, metastable.
From the diagram it is also evident that the dissociation pressure of the heptahydrate is higher than that of the decahydrate, although it contains less water of crystallization. The system heptahydrate—anhydrous salt—vapour must be metastable with respect to the system decahydrate—anhydrous salt—vapour, and will pass into the latter.[[218]] Whether or not there is a temperature at which the vapour-pressure curves of the two systems intersect, and below which the heptahydrate becomes the more stable form, is not known.
In the case of sodium sulphate there is only one stable hydrate. Other salts are known which exhibit a similar behaviour; and we shall therefore expect that the solubility relationships will be represented by a diagram similar to that for sodium sulphate. A considerable number of such cases have, indeed, been found,[[219]] and in some cases there is more than one metastable hydrate. This is found, for example, in the case of nickel iodate,[[220]] the solubility curves for which are given in Fig. 35. As can be seen from the figure, suspended transformation occurs, the solubility curves having in some cases been followed to a considerable distance beyond the transition point. One of the most brilliant examples, however, of suspended transformation in the case of salt hydrates, and the sluggish transition from the less stable to the more stable form, is found in the case of the hydrates of calcium chromate.[[221]]
In the preceding cases, the dissociation-pressure curve of the hydrated salt cuts the vapour-pressure curve of the saturated
solution of the anhydrous salt. It can, however, happen that the dissociation-pressure curve of one hydrate cuts the solubility curve, not of the anhydrous salt, but of a lower hydrate; in this case there will be more than one stable hydrate, each having a stable solubility curve; and these curves will intersect at the temperature of the transition point. Various examples of this behaviour are known, and we choose for illustration the solubility relationships of barium acetate and its hydrates[[222]] (Fig. 36).
At temperatures above 0°, barium acetate can form two stable hydrates, a trihydrate and a monohydrate. The solubility of the trihydrate increases very rapidly with rise of temperature, and has been determined up to 26.1°. At temperatures above 24.7°, however, the trihydrate is metastable with respect to the monohydrate; for at this temperature the solubility curve of the latter hydrate cuts that of the former. This is, therefore, the transition temperature for the trihydrate and monohydrate. The solubility curve of the monohydrate succeeds that of the trihydrate, and exhibits a conspicuous point of minimum solubility at about 30°. Below 24.7° the
monohydrate is the less stable hydrate, but its solubility has been determined to a temperature of 22°. At 41° the solubility curve of the monohydrate intersects that of the anhydrous salt, and this is therefore the transition temperature for the monohydrate and anhydrous salt. Above this temperature the anhydrous salt is the stable solid phase. Its solubility curve also passes through a minimum.
The diagram of solubilities of barium acetate not only illustrates the way in which the solubility curves of the different stable hydrates of a salt succeed one another, but it has also an interest and importance from another point of view. In Fig. 36 there is also shown a faintly drawn curve which is continuous throughout its whole course. This curve represents the solubility of barium acetate as determined by Krasnicki.[[223]] Since, however, three different solid phases can exist under the conditions of experiment, it is evident, from what has already been stated (p. [111]), that the different equilibria between barium acetate and water could not be represented by one continuous curve.
Another point which these experiments illustrate and which it is of the highest importance to bear in mind is, that in making determinations of the solubility of salts which are capable of forming hydrates, it is not only necessary to determine the composition of the solution, but it is of equal importance to determine the composition of the solid phase in contact with it. In view of the fact, also, that the solution equilibrium is in many cases established with comparative slowness, it is necessary to confirm the point of equilibrium, either by approaching it from higher as well as from lower temperatures, or by actually determining the rate with which the condition of equilibrium is attained. This can be accomplished by actual weighing of the dissolved salt or by determinations of the density of the solution, as well as by other methods.
2. The Compounds formed have a Definite Melting Point.
In the cases which have just been considered we saw that the salt hydrates on being heated did not undergo complete fusion, but that a solid was deposited consisting of a lower hydrate or of the anhydrous salt. It has, however, been long known that certain crystalline salt hydrates (e.g. sodium thiosulphate, Na2S2O3,5H2O, sodium acetate, NaC2H3O2,3H2O) melt completely in their water of crystallization, and yield a liquid of the same composition as the crystalline salt. In the case of sodium thiosulphate pentahydrate the temperature of liquefaction is 56°; in the case of sodium acetate trihydrate, 58°. These two salts, therefore, have a definite melting point. For the purpose of studying the behaviour of such salt hydrates, we shall choose not the cases which have just been mentioned, but two others which have been more fully studied, viz. the hydrates of calcium chloride and of ferric chloride.
Solubility Curve of Calcium Chloride Hexahydrate.[[224]]—Although calcium chloride forms several hydrates, each of which possesses its own solubility, it is nevertheless the solubility curve of the hexahydrate which will chiefly interest us at present, and we shall therefore first discuss that curve by itself.
The solubility of this salt has been determined from the cryohydric point, which lies at about -55°, up to the melting point of the salt.[[225]] The solubility increases with rise of temperature, as is shown by the figures in the following table, and by the (diagrammatic) curve AB in Fig. 37. In the table, the numbers under the heading "solubility" denote the number of grams of CaCl2 dissolved in 100 grams
of water; those under the heading "composition," the number of gram-molecules of water in the solution to one gram-molecule of CaCl2.
Solubility of Calcium Chloride Hexahydrate.
| Temperature. | Solubility. | Composition. |
| -55° | 42.5 | 14.5 |
| -25° | 50.0 | 12.3 |
| -10° | 55.0 | 11.2 |
| 0° | 59.5 | 10.37 |
| 10° | 65.0 | 9.49 |
| 20° | 74.5 | 8.28 |
| 25° | 82.0 | 7.52 |
| 28.5° | 90.5 | 6.81 |
| 29.5° | 95.5 | 6.46 |
| 30.2° | 102.7 | 6.00 |
| 29.6° | 109.0 | 5.70 |
| 29.2° | 112.8 | 5.41 |
So far as the first portion of the curve is concerned, it resembles the most general type of solubility curve. In the present case the solubility is so great and increases so rapidly with rise of temperature, that a point is reached at which the water of crystallization of the salt is sufficient for its complete solution. This temperature is 30.2°; and since the composition of the solution is the same as that of the solid salt, viz. 1 mol. of CaCl2 to 6 mols. of water, this temperature must be the melting point of the hexahydrate. At this point the hydrate will fuse or the solution will solidify without change of temperature and without change of composition. Such a melting point is called a congruent melting point.
But the solubility curve of calcium chloride hexahydrate differs markedly from the other solubility curves hitherto considered in that it possesses a retroflex portion, represented in the figure by BC. As is evident from the figure, therefore, calcium chloride hexahydrate exhibits the peculiar and, as it was at first thought, impossible behaviour that it can be in equilibrium at one and the same temperature with two different solutions, one of which contains more, the other less, water than the solid hydrate; for it must be remembered that
throughout the whole course of the curve ABC the solid phase present in equilibrium with the solution is the hexahydrate.
Such a behaviour, however, on the part of calcium chloride hexahydrate will appear less strange if one reflects that the melting point of the hydrate will, like the melting point of other substances, be lowered by the addition of a second substance. If, therefore, water is added to the hydrate at its melting point, the temperature at which the solid hydrate will be in equilibrium with the liquid phase (solution) will be lowered; or if, on the other hand, anhydrous calcium chloride is added to the hydrate at its melting point (or what is the same thing, if water is removed from the solution), the temperature at which the hydrate will be in equilibrium with the liquid will also be lowered; i.e. the hydrate will melt at a lower temperature. In the former case we have the hydrate in equilibrium with a solution containing more water, in the latter case with a solution containing less water than is contained in the hydrate itself.
It has already been stated (p. [109]) that the solubility curve (in general, the equilibrium curve) is continuous so long as the solid phase remains unchanged; and we shall therefore expect that the curve ABC will be continuous. Formerly, however, it was considered by some that the curve was not continuous, but that the melting point is the point of intersection of two curves, a solubility curve and a fusion curve. Although the earlier solubility determinations were insufficient to decide this point conclusively, more recent investigation has proved beyond doubt that the curve is continuous and exhibits no break.[[226]]
Although in taking up the discussion of the equilibria between calcium chloride and water, it was desired especially to call attention to the form of the solubility curve in the case of salt hydrates possessing a definite melting point, nevertheless, for the sake of completeness, brief mention may be made of the other systems which these two components can form.
Besides the hexahydrate, the solubility curve of which has already been described, calcium chloride can also crystallize in two different forms, each of which contains four molecules
of water of crystallization; these are distinguished as α-tetrahydrate, and β-tetrahydrate. Two other hydrates are also known, viz. a dihydrate and a monohydrate. The solubility curves of these different hydrates are given in Fig. 38.
On following the solubility curve of the hexahydrate from the ordinary temperature upwards, it is seen that at a temperature of 29.8° represented by the point H, it cuts the solubility curve of the α-tetrahydrate. This point is therefore a quadruple point at which the four phases hexahydrate, α-tetrahydrate, solution, and vapour can coexist. It is also the transition point for these two hydrates. Since, at temperatures above 29.8°, the α-tetrahydrate is the stable form, it is evident from the data given before (p. [146]), as also from Fig. 38, that the portion of the solubility curve of the hexahydrate lying above this temperature represents metastable equilibria. The realization of the metastable melting point of the hexahydrate is, therefore, due to suspended transformation. At the transition point, 29.8°, the solubility of the hexahydrate and α-tetrahydrate is 100.6 parts of CaCl2 in 100 parts of water.
The retroflex portion of the solubility curve of the hexahydrate extends to only 1° below the melting point of the hydrate. At 29.2° crystals of a new hydrate, β-tetrahydrate, separate out, and the solution, which now contains 112.8 parts of CaCl2 to 100 parts of water, is saturated with respect to the two hydrates. Throughout its whole extent the solubility curve EDF of the β-tetrahydrate represents metastable equilibria. The upper limit of the solubility curve of β-tetrahydrate is reached at 38.4° (F), the point of intersection with the curve for the dihydrate.
Above 29.8° the stable hydrate is the α-tetrahydrate; and its solubility curve extends to 45.3° (K), at which temperature it cuts the solubility curve of the dihydrate. The curve of the latter hydrate extends to 175.5° (L), and is then succeeded by the curve for the monohydrate. The solubility curve of the anhydrous salt does not begin until a temperature of about 260°. The whole diagram, therefore, shows a succession of stable hydrates, a metastable hydrate, a metastable melting point and retroflex solubility curve.
Pressure-Temperature Diagram.—The complete study of the equilibria between the two components calcium chloride and water would require the discussion of the vapour pressure of the different systems, and its variation with the temperature. For our present purpose, however, such a discussion would not be of great value, and will therefore be omitted here; in general, the same relationships would be found as in the case of sodium sulphate (p. [138]), except that the rounded portion of the solubility curve of the hexahydrate would be represented by a similar rounded portion in the pressure curve.[[227]] As in the case of sodium sulphate, the transition points of the different hydrates would be indicated by breaks in the curve of pressures. Finally, mention may again be made of the difference of the pressure of dissociation of the hexahydrate according as it becomes dehydrated to the α- or the β-tetrahydrate (p. [88]).
The Indifferent Point.—We have already seen that at 30.2° calcium chloride hexahydrate melts congruently, and that, provided the pressure is maintained constant, addition or withdrawal of heat will cause the complete liquefaction or solidification, without the temperature of the system undergoing change. This behaviour, therefore, is similar to, but is not quite the same as the fusion of a simple substance such as ice; and the difference is due to the fact that in the case of the hexahydrate the emission of vapour by the liquid phase causes an alteration in the composition of the latter, owing to the non-volatility of the calcium chloride; whereas in the case of ice this is, of course, not so.
Consider, however, for the present that the vapour phase is absent, and that we are dealing with the two-phase system solid—solution. Then, since there are two components, the system is bivariant. For any given value of the pressure, therefore, we should expect that the system could exist at different temperatures; which, indeed, is the case. It has, however, already been noted that when the composition of the liquid phase becomes the same as that of the solid, the system then behaves as a univariant system; for, at a given pressure, the system solid—solution can exist only at one temperature, change of temperature producing complete transformation in
one or other direction. The variability of the system has therefore been diminished.
This behaviour will perhaps be more clearly understood when one reflects that since the composition of the two phases is the same, the system may be regarded as being formed of one component, just as the system NH4Cl
A point such as has just been referred to, which represents the special behaviour of a system of two (or more) components, in which the composition of two phases becomes identical, is known as an indifferent point,[[229]] and it has been shown[[230]] that at a given pressure the temperature in the indifferent point is the maximum or minimum temperature possible at the particular pressure[[231]] (cf. critical solution temperature). At such a point a system loses one degree of freedom, or behaves like a system of the next lower order.
The Hydrates of Ferric Chloride.—A better illustration of the formation of compounds possessing a definite melting point, and of the existence of retroflex solubility curves, is afforded by the hydrates of ferric chloride, which not only possess definite points of fusion, but these melting points are stable. A very brief description of the relations met with will suffice.[[232]]
Ferric chloride can form no less than four stable hydrates, viz. Fe2Cl6,12H2O, Fe2Cl6,7H2O, Fe2Cl6,5H2O, and Fe2Cl6,4H2O, and each of these hydrates possesses a definite, stable melting point. On analogy with the behaviour of calcium chloride, therefore, we shall expect that the solubility curves of these different hydrates will exhibit a series of temperature maxima; the points of maximum temperature representing systems in which the composition of the solid and liquid phases is the same. A graphical representation of the solubility relations is given in Fig. 39, and the composition of the different saturated solutions which can be formed is given in the following tables, the composition being expressed in molecules of Fe2Cl6 to 100 molecules of water. The figures printed in thick type refer to transition and melting points.
Composition of the Saturated Solutions of Ferric Chloride and its Hydrates.
(The name placed at the head of each table is the solid phase.)
| Ice. | |
| Temperature. | Composition. |
| ±-55° | ±2.75 |
| -40° | 2.37 |
| -27.5° | 1.90 |
| -20.5° | 1.64 |
| -10° | 1.00 |
| 0° | 0 |
| Fe2Cl6,12H2O. | |
| Temperature. | Composition. |
| -55° | ±2.75 |
| -41° | 2.81 |
| -27° | 2.98 |
| 0° | 4.13 |
| 10° | 4.54 |
| 20° | 5.10 |
| 30° | 5.93 |
| 35° | 6.78 |
| 36.5° | 7.93 |
| 37° | 8.33 |
| 36° | 9.29 |
| 33° | 10.45 |
| 30° | 11.20 |
| 27·4° | 12.15 |
| 20° | 12.83 |
| 10° | 13.20 |
| 8° | 13.70 |
| Fe2Cl6,7H2O. | |
| Temperature. | Composition. |
| 20° | 11.35 |
| 27·4° | 12.15 |
| 32° | 13.55 |
| 32.5° | 14.29 |
| 30° | 15.12 |
| 25° | 15.54 |
| Fe2Cl6,5H2O. | |
| Temperature. | Composition. |
| 12° | 12.87 |
| 20° | 13.95 |
| 27° | 14.85 |
| 30° | 15.12 |
| 35° | 15.64 |
| 50° | 17.50 |
| 55° | 19.15 |
| 56° | 20.00 |
| 55° | 20.32 |
| Fe2Cl6,4H2O | |
| Temperature. | Composition. |
| 50° | 19.96 |
| 55° | 20.32 |
| 60° | 20.70 |
| 69° | 21.53 |
| 72.5° | 23.35 |
| 73.5° | 25.00 |
| 72.5° | 26.15 |
| 70° | 27.90 |
| 66° | 29.20 |
| Fe2Cl6 (ANHYDROUS). | |
| Temperature. | Composition. |
| 66° | 29.20 |
| 70° | 29.42 |
| 75° | 28.92 |
| 80° | 29.20 |
| 100° | 29.75 |
The lowest portion of the curve, AB, represents the equilibria between ice and solutions containing ferric chloride. It represents, in other words, the lowering of the fusion point of ice by addition of ferric chloride. At the point B (-55°), the cryohydric point (p. [117]) is reached, at which the solution is in equilibrium with ice and ferric chloride dodecahydrate. As
has already been shown, such a point represents an invariant system; and the liquid phase will, therefore, solidify to a mixture of ice and hydrate without change of temperature. If heat is added, ice will melt and the system will pass to the curve BCDN, which is the solubility curve of the dodecahydrate. At C (37°), the point of maximum temperature, the hydrate melts completely. The retroflex portion of this curve can be followed backwards to a temperature of 8°, but below 27.4° (D), the solutions are supersaturated with respect to the heptahydrate; point D is the eutectic point for dodecahydrate and heptahydrate. The curve DEF is the solubility curve of the heptahydrate, E being the melting point, 32.5°. On further increasing the quantity of ferric chloride, the temperature of equilibrium is lowered until at F (30°) another eutectic point is reached, at which the heptahydrate and pentahydrate can co-exist with solution. Then follow the solubility curves for the pentahydrate, the tetrahydrate, and the anhydrous salt; G (56°) is the melting point of the former hydrate, J (73.5°) the melting point of the latter. H and K, the points at which the curves intersect, represent eutectic points; the temperature of the former is 55°, that of the latter 66°. The dotted portions of the curves represent metastable equilibria.
As is seen from the diagram, a remarkable series of solubility curves is obtained, each passing through a point of maximum temperature, the whole series of curves forming an undulating "festoon." To the right of the series of curves the diagram represents unsaturated solutions; to the left, supersaturated.
If an unsaturated solution, the composition of which is represented by a point in the field to the right of the solubility curves, is cooled down, the result obtained will differ according as the composition of the solution is the same as that of a cryohydric point, or of a melting point, or has an intermediate value. Thus, if a solution represented by x1 is cooled down, the composition will remain unchanged as indicated by the horizontal dotted line, until the point D is reached. At this point, dodecahydrate and heptahydrate will separate out, and the liquid will ultimately solidify completely to a mixture or "conglomerate" of these two hydrates; the temperature of
the system remaining constant until complete solidification has taken place. If, on the other hand, a solution of the composition x3 is cooled down, ferric chloride dodecahydrate will be formed when the temperature has fallen to that represented by C, and the solution will completely solidify, without alteration of temperature, with formation of this hydrate. In both these cases, therefore, a point is reached at which complete solidification occurs without change of temperature.
Somewhat different, however, is the result when the solution has an intermediate composition, as represented by x2 or x4. In the former case the dodecahydrate will first of all separate out, but on further withdrawal of heat the temperature will fall, the solution will become relatively richer in ferric chloride, owing to separation of the hydrate, and ultimately the eutectic point D will be reached, at which complete solidification will occur. Similarly with the second solution. Ferric chloride dodecahydrate will first be formed, and the temperature will gradually fall, the composition of the solution following the curve CB until the cryohydric point B is reached, when the whole will solidify to a conglomerate of ice and dodecahydrate.
Suspended Transformation.—Not only can the upper branch of the solubility curve of the dodecahydrate be followed backwards to a temperature of 8°, or about 19° below the temperature of transition to the heptahydrate; but suspended transformation has also been observed in the case of the heptahydrate and the pentahydrate. To such an extent is this the case that the solubility curve of the latter hydrate has been followed downwards to its point of intersection with the curve for the dodecahydrate. This point of intersection, represented in Fig. 39 by M, lies at a temperature of about 15°; and at this temperature, therefore, it is possible for the two solid phases dodecahydrate and pentahydrate to coexist, so that M is a eutectic point for the dodecahydrate and the pentahydrate. It is, however, a metastable eutectic point, for it lies in the region of supersaturation with respect to the heptahydrate; and it can be realized only because of the fact that the latter hydrate is not readily formed.
Evaporation of Solutions at Constant Temperature.—On
evaporating dilute solutions of ferric chloride at constant temperature, a remarkable series of changes is observed, which, however, will be understood with the help of Fig. 40. Suppose an unsaturated solution, the composition of which is represented by the point x1, is evaporated at a temperature of about 17° - 18°. As water passes off, the composition of the solution will follow the dotted line of constant temperature, until at the point where it cuts the curve BC the solid hydrate Fe2Cl6,12H2O separates out. As water continues to be removed, the hydrate must be deposited (in order that the solution shall remain saturated), until finally the solution dries up to the hydrate. As dehydration proceeds, the heptahydrate can be formed, and the dodecahydrate will finally pass into the heptahydrate; and this, in turn, into the pentahydrate.
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 at a; 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 must pass into solution in 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 by b, 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 line x212345. 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 composition x2, 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, the quantity of 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 accompanied
by fusion of the ice, and the quantity of solution will remain constant. Such solutions are called inevaporable.[[235]]
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 solid
which separated from the solutions represented by BC was a bright yellow crystalline 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 a red crystalline 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 this yellow solid, 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,14SO2 can exist together in equilibrium with solution and vapour. The curve DE is the solubility curve of the red crystalline solid, and the
point 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,14SO2 and KI,4SO2 can 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, the transition point for KI,4SO2 and 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 on lowering the 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,14SO2 and 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:—
| Point. | Temperature. | Composition of the solution per cent. KI. |
| A (m.p. of SO2) | -72.7° | — |
| B (eutectic point) | — | 0.86 |
| C (m.p. of KI,14SO2) | -23.4° | 17.63 |
| E (m.p. of KI,4SO2) | +0.26° | 39.33 |
| G (KI + two liquid phases) | (about) 88° | 24.0 |
| H (critical solution point) | 77.3° | 12 |
| K (KI + two liquid phases) | (about) 88° | 2.7 |