CHAPTER XV

PRESENCE OF SOLID PHASES

A. The Ternary Eutectic Point.—In passing to the consideration of those ternary systems in which one or more solid phases can exist together with one liquid phase, we shall first discuss not the solubility curves, as in the case of two-component systems, but the simpler relationships met with at the freezing point. That is, we shall first of all examine the freezing point curves of ternary systems.

Since it is necessary to take into account not only the changing composition of the liquid phase, but also the variation of the temperature, we shall employ the right prism for the graphic representation of the systems, as shown in Fig. 95. A, B, and C in this figure, therefore, denote the melting points of the pure components. If we start with the component A at its melting point, and add B, which is capable of dissolving in liquid A, the freezing point of A will be lowered; and, similarly, the freezing point of B by addition of A. In this way we get the freezing point curve Ak₁B for the binary system; k₁; being an eutectic point. This curve will of course lie in the plane formed by one face of the prism. In a similar manner we obtain the freezing point curves Ak₂C and Bk₃C. These curves give the composition of the binary liquid phases in equilibrium

with one of the pure components, or at the eutectic points, with a mixture of two solid components. If, now, to the system represented say by the point k₁, a small quantity of the third component, C, is added, the temperature at which the two solid phases A and B can exist in equilibrium with the liquid phase is lowered; and this depression of the eutectic point is all the greater the larger the addition of C. In this way we obtain the curve k₁K, which slopes inwards and downwards, and indicates the varying composition of the ternary liquid phase with which a mixture of solid A and B are in equilibrium. Similarly, the curves k₂K and k₃K are the corresponding eutectic curves for A and C, and B and C in equilibrium with ternary solutions. At the point K, the three solid components are in equilibrium with the liquid phase; and this point, therefore, represents the lowest temperature attainable with the three components given. Each of the ternary eutectic curves, as they may be called, is produced by the intersection of two surfaces, while at the ternary eutectic point, three surfaces, viz. Ak₁Kk₂, Bk₁Kk₃, and Ck₁Kk₃ intersect. Any point on one of these surfaces represents a ternary solution in equilibrium with only one component in the solid state; the lines or curves of intersection of these represent equilibria with two solid phases, while at the point K, the ternary eutectic point, there are three solid phases in equilibrium with a liquid and a vapour phase. The surfaces just mentioned represent bivariant systems. One component in the solid state can exist in equilibrium with a ternary liquid phase under varying conditions of temperature and concentration of the components in the solution; and before the state of the system is defined, these two variables, temperature and composition of the liquid phase, must be fixed. On the other hand, the curves formed by the intersection of these planes represent univariant systems; at a given temperature two solid phases can exist in equilibrium with a ternary solution, only when the latter has a definite composition. Lastly, the ternary eutectic point, K, represents an invariant system; three solid phases can exist in equilibrium with a ternary solution, only when the latter has one fixed composition and when the temperature has a definite value. This eutectic point, therefore,

has a perfectly definite position, depending only on the nature of the three components.

Instead of employing the prism, the change in the composition of the ternary solutions can also be indicated by means of the projections of the curves k₁K, k₂K, and k₃K on the base of the prism, the particular temperature being written beside the different eutectic points and curves. This is shown in Fig. 96.

The numbers which are given in this diagram refer to the eutectic points for the system bismuth—lead—tin, the data for which are as follows:—[^[331]]

Melting point of pure metal.	Percentage composition of binary eutectic mixture.			Temperature of binary eutectic point.
	Bi	Pb	Sn
Bismuth, 268°	55	45	—	Bi—Pb, 127°
Lead, 325°	58	—	42	Bi—Sn, 133°
Tin, 232°	—	37	63	Pb—Sn, 182°

Percentage composition of ternary eutectic mixture.			Temperature of ternary eutectic point.
Bi	Pb	Sn
52	32	16	96°

Formation of Compounds.—In the case just discussed, the components crystallized out from solution in the pure state. If, however, combination can take place between two of the components, the relationships will be somewhat different; the curves which are obtained in such a case being represented in Fig. 97. From the figure, we see that the two components B

and C form a compound, and the freezing point curve of the binary system has therefore the form shown in Fig. 64 (p. [209]). Further, there are two ternary eutectic points, K₁ and K₂, the solid phases present being A, B, and compound, and A, C, and compound respectively.

The particular point, now, to which it is desired to draw attention is this. Suppose the ternary eutectic curves projected on a plane parallel to the face of the prism containing B and C, i.e. suppose the concentrations of the two components B and C, between which interaction can occur, expressed in terms of a constant amount of the third component A,[^[332]] curves will then be obtained which are in every respect analogous to the freezing point curves of binary systems. Thus, suppose the eutectic curves k₁K and k₂K in Fig. 95 projected on the face BC of the prism, then evidently a curve will be obtained consisting of two branches meeting in an eutectic point. On the other hand, the projection of the ternary eutectic curves in Fig. 97 on the face BC of the prism, will give a curve consisting of three portions, as shown by the outline k₁K₁K₂k₂ in Fig. 97.

Various examples of this have been studied, and the following table contains some of the data for the system ethylene bromide (A), picric acid (B), and β-naphthol (C), obtained by Bruni.[^[333]]

	Temperature.	Solid phases present.
Point k₁	9.41°	Ethylene bromide, picric acid.
Curve k₁K₁	—	,, ,,
Point K₁	9.32°	Ethylene bromide, picric acid, and β-naphthol picrate.
Curve K₁D′K₂	—	Ethylene bromide, β-naphthol picrate.
Point D′	9.75°	,, ,, ,, ,,
Point K₂	8.89°	,, ,, β-naphthol, and picrate.
Curve K₂k₂	—	,, ,, β-naphthol.
Point k₂	9.04°	,, ,, ,,

From what has been said, it will be apparent that if the ternary eutectic curve of a three-component system (in which one of the components is present in constant amount) is determined, it will be possible to state, from the form of curve obtained, whether or not the two components present in varying amount crystallize out pure or combine with one another to form a compound. It may be left to the reader to work out the curves for the other possible systems; but it will be apparent, that the projections of the ternary eutectic curves in the manner given will yield a series of curves alike in all points to the binary curves given in Figs. 63-65, pp. [208]-210.

Since, from the method of investigation, the temperatures of the eutectic curves will depend on the melting point of the third component (A), it is possible, by employing substances with widely differing melting points, to investigate the interaction of the two components (e.g. two optical antipodes) B and C over a range of temperature; and thus determine the range of stability of the compound, if one is formed. Since, in some cases, two substances which at one temperature form mixed crystals combine at another temperature to form a definite compound, the relationships which have just been described can be employed, and indeed, have been employed, to determine the temperature at which this change occurs.[^[334]] By means of this method, Adriani found that below 103° i-camphoroxime exists as a racemic compound, while above

that temperature it occurs as a racemic mixed crystal[^[335]] (cf. p. [219]).

B. Equilibria at Higher Temperatures. Formation of Double Salts.—After having studied the relationships which are found in the neighbourhood of the freezing points of the components, we now pass to the discussion of the equilibria which are met with at higher temperatures. In this connection we shall confine the discussion entirely to the systems formed of two salts and water, dealing more particularly with those cases in which the water is present in relatively large amount and acts as solvent. Further, in studying these systems, one restriction must be made, viz. that the single salts are salts either of the same base or of the same acid; or are, in other words, capable of yielding a common ion in solution. Such a restriction is necessary, because otherwise the system would be one not of three but of four components.[^[336]]

Transition Point.—As is very well known, there exist a number of hydrated salts which, on being heated, undergo apparent partial fusion; and in Chapter V. the behaviour of such hydrates was more fully studied in the light of the Phase Rule. Glauber's salt, or sodium sulphate decahydrate, for example, on being heated to a temperature of about 32.5°, partially liquefies, owing to the fact that the water of crystallization is split off and anhydrous sodium sulphate formed, as shown by the equation—

Na₂SO₄,10H₂O = Na₂SO₄ + 10H₂O

The temperature of 32.5°, it was learned, constituted a transition point for the decahydrate and anhydrous salt plus water; decomposition of the hydrated salt occurring above this temperature, combination of the anhydrous salt and water below it.

Analogous phenomena are met with in systems constituted of two salts and water in which the formation of double salts can take place. Thus, for example, if d-sodium potassium

tartrate is heated to above 55°, apparent partial fusion occurs, and the two single salts, d-sodium tartrate and d-potassium tartrate, are deposited, the change which occurs being represented by the equation—

4NaKC₄O₆H₄,4H₂O = 2Na₂C₄O₆H₄,2H₂O + 2K₂C₄O₆H₄,½H₂O + 11H₂O

On the other hand, if sodium and potassium tartrates are mixed with water in the proportions shown on the right side of the equation, the system will remain partially liquid so long as the temperature is maintained above 55° (in a closed vessel to prevent loss of water), but on allowing the temperature to fall below this point, complete solidification will ensue, owing to the formation of the hydrated double salt. Below 55°, therefore, the hydrated double salt is the stable system, while above this temperature the two single salts plus saturated solution are stable.[^[337]]

A similar behaviour is found in the case of the double salt copper dipotassium chloride (CuCl₂,2KCl,2H₂O or CuK₂Cl₄,2H₂O).[^[338]] When this salt is heated to 92°, partial liquefaction occurs, and the original blue plate-shaped crystals give place to brown crystalline needles and white cubes; while on allowing the temperature to fall, re-formation of the blue double salt ensues. The temperature 92° is, therefore, a transition point at which the reversible reaction—

CuK₂Cl₄,2H₂O

takes place.

The decomposition of sodium potassium tartrate, or of copper dipotassium chloride, differs in so far from that of Glauber's salt that two new solid phases are formed; and in the case of copper dipotassium chloride, one of the decomposition products is itself a double salt.

In the two examples of double salt decomposition which have just been mentioned, sufficient water was yielded to cause a partial liquefaction; but other cases are known where this is not so. Thus, when copper calcium acetate is heated to a

temperature of 75°, although decomposition of the double salt into the two single salts occurs as represented by the equation[^[339]]—

CuCa(C₂H₃O₂)₄,8H₂O = Cu(C₂H₃O₂)₂,H₂O + Ca(C₂H₃O₂)₂,H₂O + 6H₂O

the amount of water split off is insufficient to give the appearance of partial fusion, and, therefore, only a change in the crystals is observed.

The preceding examples, in which decomposition of the double salt was effected by a rise of temperature, were chosen for first consideration as being more analogous to the case of Glauber's salt; but not a few examples are known where the reverse change takes place, formation of the double salt occurring above the transition point, and decomposition into the constituent salts below it. Instances of this behaviour are found in the case of the formation of astracanite from sodium and magnesium sulphates, and of sodium ammonium racemate from the two sodium ammonium tartrates, to which reference will be made later. Between these various systems, however, there is no essential difference; and whether decomposition or formation of the double salt occurs at temperatures above the transition point, will of course depend on the heat of change at that point. For, in accordance with van't Hoff's law of movable equilibrium (p. [58]), that change will take place at the higher temperature which is accompanied by an absorption of heat. If, therefore, the formation of the double salt from the single salts is accompanied by an absorption of heat, the double salt will be formed from the single salts on raising the temperature; but if the reverse is the case, then the double salt on being heated will decompose into the constituent salts.[^[340]]

In those cases, now, which have so far been studied, the change at the transition point is accompanied by a taking up or a splitting off of water; and in such cases the general rule can be given, that if the water of crystallization of the two constituent

salts together is greater than that of the double salt, the latter will be produced from the former on raising the temperature (e.g. astracanite from sodium and magnesium sulphates); but if the double salt contains more water of crystallization than the two single salts, increase of temperature will effect the decomposition of the double salt. When we seek for the connection between this rule and the law of van't Hoff, it is found in the fact that the heat effect involved in the hydration or dehydration of the salts is much greater than that of the other changes which occur, and determines, therefore, the sign of the total heat effect.[^[341]]

Vapour Pressure. Quintuple Point.—In the case of Glauber's salt, we saw that at a certain temperature the vapour pressure curve of the hydrated salt cut that of the saturated solution of anhydrous sodium sulphate. That point, it will be remembered, was a quadruple point at which the four phases sodium sulphate decahydrate, anhydrous sodium sulphate, solution, and vapour, could co-exist; and was also the point of intersection of the curves for four univariant systems. In the case of the formation of double salts, similar relationships are met with; and also certain differences, due to the fact that we are now dealing with systems of three components. Two cases will be chosen here for brief description, one in which formation, the other in which decomposition of the double salt occurs with rise of temperature.

On heating a mixture of sodium sulphate decahydrate and magnesium sulphate heptahydrate, it is found that at 22° partial liquefaction occurs with formation of astracanite. At this temperature, therefore, there can coexist the five phases—

Na₂SO₄,10H₂O; MgSO₄,7H₂O; Na₂Mg(SO₄)₂,4H₂O; solution; vapour.

This constitutes, therefore, a quintuple point; and since there are three components present in five phases, the system is invariant. This point, also, will be the point of intersection of curves for five univariant systems, which, in this case, must each be composed of four phases. These systems are—

I. Na₂SO₄,10H₂O; MgSO₄,7H₂O; Na₂Mg(SO₄)₂,4H₂O; vapour.

II. Na₂SO₄,10H₂O; MgSO₄,7H₂O; solution; vapour.

III. MgSO₄,7H₂O; Na₂Mg(SO₄)₂,4H₂O; solution; vapour.

IV. Na₂SO₄,10H₂O; Na₂Mg(SO₄)₂,4H₂O; solution; vapour.

V. Na₂SO₄,10H₂O; MgSO₄,7H₂O; Na₂Mg(SO₄)₂,4H₂O; solution.

On representing the vapour pressures of these different systems graphically, a diagram is obtained such as is shown in Fig. 98,[^[342]] the curves being numbered in accordance with the above list. When the system I. is heated, the vapour pressure increases until at the quintuple point the liquid phase (solution) is formed, and it will then depend on the relative amounts of the different phases whether on further heating there is formed system III., IV., or V. If either of the first two is produced, we shall obtain the vapour pressure of the solutions saturated with respect to both double salt and one of the single salts; while if the vapour phase disappears, there will be obtained the pressure of the condensed systems formed of double salt, two single salts and solution. This curve, therefore, indicates the change of the transition point with pressure; and since in the ordinary determinations of the transition point in open vessels, we are in reality dealing with condensed systems under the pressure of 1 atm., it will be evident that the transition point does not accurately coincide with the quintuple point (at which the system is under the pressure of its own vapour). As in the case of other condensed systems, however, pressure has only a slight influence on the temperature of the transition point. Whether or not pressure raises or lowers the transition point will depend on whether transformation is accompanied by an increase or

diminution of volume (theorem of Le Chatelier, p. [58]). In the case of the formation of astracanite, expansion occurs, and the transition point will therefore be raised by increase of pressure. Although measurements have not been made in the case of this system, the existence of such a curve has been experimentally verified in the case of copper and calcium acetates and water (v. infra).[^[343]]

The vapour pressure diagram in the case of copper calcium acetate and water (Fig. 99), is almost the reverse of that already discussed. In this case, the double salt decomposes on heating, and the decomposition is accompanied by a contraction. Curve I. is the vapour pressure curve for double salt, two single salts (p. [260]), and vapour; curves II. and III. give the vapour pressures of solutions saturated with respect to double salt and one of the single salts; curve IV. is the curve of pressures for the solutions saturated with respect to the two single salts; while curve V. again represents the change of the transition point with pressure. On examining this diagram, it is seen that whereas

astracanite could exist both above and below the quintuple point, copper calcium acetate can exist only below the quintuple point. This behaviour is found only in those cases in which the double salt is decomposed by rise of temperature, and where the decomposition is accompanied by a diminution of volume.[^[344]]

As already mentioned, the decomposition of copper calcium acetate into the single salts and saturated solution is accompanied by a contraction, and it was therefore to be expected that increase of pressure would lower the transition point. This expectation of theory was confirmed by experiment, for van't Hoff and Spring found that although the transition point under atmospheric pressure is about 75°, decomposition of the double salt took place even at the ordinary temperature when the pressure was increased to 6000 atm.[^[345]]

Solubility Curves at the Transition Point.—At the transition point, as has already been shown, the double salt and the two constituent salts can exist in equilibrium with the same solution. The transition point, therefore, must be the point of intersection of two solubility curves; the solubility curve of the double salt and the solubility curve of the mixtures of the two constituent salts. It should be noted here that we are not dealing with the solubility curves of the single salts separately, for since the systems are composed of three components, a single solid phase can, at a given temperature, be in equilibrium with solutions of different composition, and two solid phases in contact with solution (and vapour) are therefore necessary to give an univariant system. The same applies, of course, to the solubility of the double salt; for a double salt also constitutes a single phase, and can therefore exist in equilibrium with solutions of varying composition. If, however, we make the restriction (which we do for the present) that the double salt is not decomposed by water, then the solution will contain the constituent salts in the same relative proportions as they are contained in the double salt, and the system may therefore be regarded as one of two components, viz. double salt and water. In this case one solid phase is sufficient, with solution and

vapour, to give an univariant system; and at a given temperature, therefore, the solubility will have a perfectly definite value.

Since in almost all cases the solubility is determined in open vessels, we shall in the following discussion consider that the vapour phase is absent, and that the system is under a constant pressure, that of the atmosphere. With this restriction, therefore, four phases will constitute an invariant system, three phases an univariant, and two phases a bivariant system.

It has already been learned that in the case of sodium sulphate and water, the solubility curve of the salt undergoes a sudden change in direction at the transition point, and that this is accompanied by a change in the solid phase in equilibrium with the solution. The same behaviour is also found in the case of double salts. To illustrate this, we shall briefly discuss the solubility relations of a few double salts, beginning with one of the simplest cases, that of the formation of rubidium racemate from rubidium d- and l-tartrates. The solubilities are represented diagrammatically in Fig. 100, the numerical data being contained in the following table, in which the solubility is expressed as the number of gram-molecules Rb₂C₄H₄O₆ in 100 gm.-molecules of water.[^[346]]

Temperature.	Solubility of tartrate mixture.	Solubility of racemate.
25°	13.03	10.91
35°	—	12.63
40.4°	—	13.48
40.7°	13.46	—
54°	13.83	—

In Fig. 100 the curve AB represents the solubility of the racemate, while A′BC represents the solubility of the mixed tartrates. Below the transition point, therefore, the solubility of the racemate is less than that of the mixed tartrates. The solution, saturated with respect to the latter, will be supersaturated with respect to the racemate; and if a nucleus of this is present, racemate will be deposited, and the mixed tartrates, if present in equimolecular amounts, will ultimately

entirely disappear, and only racemate will be left as solid phase. The solution will then have the composition represented by a point on the curve AB. Conversely, above the transition point, the saturated solution of the racemate would be supersaturated with respect to the two tartrates, and transformation into the latter would ensue. If, therefore, a solution of equimolecular proportions of rubidium d- and l-tartrates is allowed to evaporate at a temperature above 40°, a mixture of the two tartrates will be deposited; while at temperatures below 40° the racemate will separate out.

Similar relationships are met with in the case of sodium ammonium d- and l-tartrate and sodium ammonium racemate; but in this case the racemate is the stable form in contact with solution above the transition point (27°).[^[347]] Below the transition point, therefore, the solubility curve of the mixed tartrates will lie below the solubility curve of the racemate. Below the transition point, therefore, sodium ammonium racemate will break up in contact with solution into a mixture of sodium ammonium d- and l-tartrates. At a higher temperature, 35°, sodium ammonium racemate undergoes decomposition into sodium racemate and ammonium racemate.[^[348]]

The behaviour of sodium ammonium racemate is of interest from the fact that it was the first racemic substance to be resolved into its optically active forms by a process of crystallization. On neutralizing a solution of racemic tartaric acid, half with soda and half with ammonia, and allowing the solution to evaporate, Pasteur[^[349]] obtained a mixture of sodium ammonium

d- and l-tartrates. Since Pasteur was unaware of the existence of a transition point, the success of his experiment was due to the happy chance that he allowed the solution to evaporate at a temperature below 27°; for had he employed a temperature above this, separation of the racemate into the two enantiomorphous forms would not have occurred. For this reason the attempt of Staedel to perform the same resolution met only with failure.[^[350]]

Decomposition of the Double Salt by Water.—In the two cases just described, the solubility relationships at the transition point are of a simpler character than in the case of most double salts. If, at a temperature above the transition point, a mixture of rubidium d- and l-tartrates in equimolecular proportions is brought in contact with water a solution will be obtained, which is saturated with respect to both enantiomorphous forms; and since the solubility of the two optical antipodes is identical, and the effect of one on the solubility of the other also the same, the solution will contain equimolecular amounts of the d- and l-salt. If, now, the solution is cooled down in contact with the solid salts to just below the transition point, it becomes supersaturated with respect to the racemate, and this will be deposited. The solution thereby becomes unsaturated with respect to the mixture of the active salts, and these must therefore pass into solution. As the latter are equally soluble, equal amounts of each will dissolve, and a further quantity of the racemate will be deposited. These processes of solution and deposition will continue until the single tartrates have completely disappeared, and only racemate is left as solid phase. As a consequence of the identical solubility of the two tartrates, therefore, no excess of either form will be left on passing through the transition point. From this it will be evident that the racemate can exist as single solid phase in contact with its saturated solution at the transition point; or, in other words, the racemate is not decomposed by water at the transition point. The same behaviour will evidently be exhibited by sodium ammonium racemate at 27°, for the two enantiomorphous sodium ammonium tartrates have also identical solubility.

Very different, however, is the behaviour of, say, astracanite, or of the majority of double salts; for the solubility of the constituent salts is now no longer the same. If, for example, excess of a mixture of sodium sulphate and magnesium sulphate, in equimolecular proportions, is brought in contact with water below the transition point (22°), more magnesium sulphate than sodium sulphate will dissolve, the solubility of these two salts in a common solution being given by the following figures, which express number of molecules of the salt in 100 molecules of water.[^[351]]

Composition of Solutions saturated with respect to Na₂SO₄,10H₂O and MgSO₄,7H₂O.

Temperature.	Na₂SO₄.	MgSO₄.
18.5°	2.16	4.57
24.5°	3.43	4.68

At the transition point, then, it is evident that the solution contains more magnesium sulphate than sodium sulphate: and this must still be the case when astracanite, which contains sodium sulphate and magnesium sulphate in equimolecular proportions, separates out. If, therefore, the temperature is raised slightly above the transition point, magnesium sulphate and sodium sulphate will pass into solution, the former, however, in larger quantities than the latter, and astracanite will be deposited; and this will go on until all the magnesium sulphate has disappeared, and a mixture of astracanite and sodium sulphate decahydrate is left as solid phases. Since there are now three phases present, the system is univariant (by reason of the restriction previously made that the vapour phase is absent), and at a given temperature the solution will have a definite composition; as given in the following table:—

Composition of Solutions saturated with respect to Na₂Mg(SO₄)₂,4H₂O and Na₂SO₄,10H₂O.

Temperature.	Na₂SO₄.	MgSO₄.
22°	2.95	4.70
24.5°	3.45	3.62

From the above figures, therefore, it will be seen that at a temperature just above the transition point a solution in contact with the two solid phases, astracanite and Glauber's salt, contains a relatively smaller amount of sodium sulphate than a pure solution of astracanite would; for in this case there would be equal molecular amounts of Na₂SO₄ and MgSO₄. A solution which is saturated with respect to astracanite alone, will contain more sodium sulphate than the solution saturated with respect to astracanite plus Glauber's salt, and the latter will therefore be deposited. From this, therefore, it is clear that if astracanite is brought in contact with water at about the transition point, it will undergo decomposition with separation of Glauber's salt (supersaturation being excluded).

This will perhaps be made clearer by considering Fig. 101. In this diagram the ordinates represent the ratio of sodium sulphate to magnesium sulphate in the solutions, and the abscissæ represent the temperatures. The line AB represents solutions saturated with respect to a mixture of the single salts (p. [268]); BC refers to solutions in equilibrium with astracanite and magnesium sulphate; while BX represents the composition of solutions in contact with the solid phases astracanite and Glauber's salt. The values of the solubility are contained in the following table, and in that on p. [268], and are, as before, expressed in gm.-molecules of salt in 100 gm.-molecules of water.[^[352]]

Temperature.	Astracanite + sodium sulphate.		Astracanite + magnesium sulphate.
Temperature.	Na₂SO₄.	MgSO₄.	Na₂SO₄.	MgSO₄.
18.5°	—	—	3.41	4.27
22°	2.95	4.70	2.85	4.63
24.5°	3.45	3.62	2.68	4.76
30°	4.58	2.91	2.30	5.31
35°	4.30	2.76	1.73	5.88

At the transition point the ratio of sodium sulphate to magnesium sulphate is approximately 1 : 1.6. In the case of solutions saturated with respect to both astracanite and Glauber's salt, the relative amount of sodium sulphate increases as the temperature rises, while in the solutions saturated for astracanite and magnesium sulphate, the ratio of sodium sulphate to magnesium sulphate decreases.

If, now, we consider only the temperatures above the transition point, we see from the figure that solutions represented by points above the line BX contain relatively more sodium sulphate than solutions in contact with astracanite and Glauber's salt; and solutions lying below the line BC contain relatively more magnesium sulphate than solutions saturated with this salt and astracanite. These solutions will therefore not be stable, but will deposit in the one case, astracanite and Glauber's salt, and in the other case, astracanite and magnesium sulphate, until a point on BX or BC is reached. All solutions, however, lying to the right of CBX, will be unsaturated with respect to these two pairs of salts, and only the solutions represented by the line XY (and which contain equimolecular amounts of sodium and magnesium sulphates) will be saturated with respect to the pure double salt.

Transition Interval.—Fig. 101 will also render intelligible a point of great importance in connection with astracanite, and of double salts generally. At temperatures between those represented by the points B and X, the double salt when brought in contact with water will be decomposed with separation of sodium sulphate. Above the temperature of the point

X, however, the solution of the pure double salt is stable, because it can still take up a little of either of the components. At temperatures, then, above that at which the solution in contact with the double salt and the less soluble single salt, contains the single salts in the ratio in which they are present in the double salt, solution of the latter will take place without decomposition. The range of temperature between that at which double salt can begin to be formed (the transition point) and that at which it ceases to be decomposed by water is called the transition interval.[^[353]] If the two single salts have identical solubility at the transition point, the transition interval diminishes to nought.

In those cases where the double salt is the stable form below the transition point, the transition interval will extend downwards to a lower temperature. Fig. 101 will then have the reverse form.

Summary.—With regard to double salts we have learned that their formation from and their decomposition into the single salts, is connected with a definite temperature, the transition temperature. At this transition temperature two vapour pressure curves cut, viz. a curve of dehydration of a mixture of the single salts and the solubility curve of the double salt; or the dehydration curve of the double salt and the solubility curve of the mixed single salts. The solubility curves, also, of these two systems intersect at the transition point, but although the formation of the double salt commences at the transition point, complete stability in contact with water may not be attained till some temperature above (or below) that point. Only when the temperature is beyond the transition interval, will a double salt dissolve in water without decomposition (e.g. the alums).