We shall first consider the solubility relations of the single salts. The complete equilibrium curve for magnesium chloride and water is represented in Fig. 113 by the series of curves ABF_{1} G_{1} H_{1} J_{1} L_{1} N_{1}.

AB is the freezing-point curve of ice in contact with solutions containing magnesium chloride, and B is the cryohydric point at which the solid phases ice and MgCl_{2},12H_{2}O can co-exist with solution. BFG is the solubility curve of magnesium chloride dodecahydrate. This curve shows a point of maximum temperature at F_{1}, and a retroflex portion F_{1}G_{1}. The curve is therefore of the form exhibited by calcium chloride hexahydrate, or the hydrates of ferric chloride (Chapter VIII.). G_{1} is a transition point at which the solid phase changes from dodecahydrate to octahydrate, the solubility of which is represented by the curve G_{1}H_{1}. At H_{1} the octahydrate gives place to the hexahydrate, which is the solid phase in equilibrium with the solutions represented by the curve H_{1}J_{1}. J_{1} and L_{1} are also transition points at which the solid phase undergoes change, in the former case from hexahydrate to tetrahydrate; and in the latter case, {286} from tetrahydrate to dihydrate. The complete curve of equilibrium for magnesium chloride and water is, therefore, somewhat complicated, and is a good example of the solubility curves obtained with salts capable of forming several hydrates.

The solubility curve of pota.s.sium chloride is of the simplest form, consisting only of the two branches AC, the freezing-point curve of ice, and CO, the solubility curve of the salt. C is the cryohydric point. This point and the two curves lie in the YT-plane.

On pa.s.sing to the ternary systems, the composition of the solutions must be represented by points or curves situated _between_ the two planes. We shall now turn to the consideration of these. BD and CD are ternary eutectic curves (p. 284). They give the composition of solutions in equilibrium with ice and magnesium chloride dodecahydrate (BD), and with ice and pota.s.sium chloride (CD). D is a _ternary cryohydric point_. If the temperature is raised and the ice allowed to disappear, we shall pa.s.s to the solubility curve for MgCl_{2},12H_{2}O + KCl (curve DE). At E carnallite is formed and the pota.s.sium chloride disappears; EFG is then the solubility curve for MgCl_{2},12H_{2}O + carnallite (KMgCl_{3},6H_{2}O). This curve also shows a point of maximum temperature (F) and a retroflex portion. GH and HJ represent the solubility curves of carnallite + MgCl_{2},8H_{2}O and carnallite + MgCl_{2},6H_{2}O, G and H being transition points. JK is the solubility curve for carnallite + MgCl_{2},4H_{2}O. At the point K we have the _highest temperature at which carnallite can exist with magnesium chloride in contact with solution_. Above this temperature decomposition takes place and pota.s.sium chloride separates out.

If at the point E, at which the two single salts and the double salt are present, excess of pota.s.sium chloride is added, the magnesium chloride will all disappear owing to the formation of carnallite, and there will be left carnallite and pota.s.sium chloride. The solubility curve for a mixture of these two salts is represented by EMK; a simple curve exhibiting, however, a temperature maximum at M. This maximum point corresponds with the fact that dry carnallite melts at this temperature with separation of pota.s.sium chloride. _At all temperatures {287} above this point, the formation of double salt is impossible_. The retroflex portion of the curve represents solutions in equilibrium with carnallite and pota.s.sium chloride, but in which the ratio MgCl_{2} : KCl is greater than in the double salt.

Throughout its whole course, _the curve EMK represents solutions in which the ratio of MgCl_{2} : KCl is greater than in the double salt_. As this is a point of some importance, it will be well, perhaps, to make it clearer by giving one of the isothermal curves, _e.g._ the curve for 10, which is represented diagrammatically in Fig. 114. E and F here represent solutions saturated for carnallite plus magnesium chloride hydrate, and for carnallite plus pota.s.sium chloride. As is evident, the point F lies above the line representing equimolecular proportions of the salts (OD).

[Ill.u.s.tration: FIG. 114.]

Summary and Numerical Data.--We may now sum up the different systems which can be formed, and give the numerical data from which the model is constructed.[366]

I. _Bivariant Systems._

-------------------------------------- Solid phase.

Area of existence.

-------------------------------------- Ice

ABDC KCl

CDEMKLNO Carnallite

EFGHJKM MgCl_{2},12H_{2}O

BF_{1}G_{1}GFED MgCl_{2},8H_{2}O

G_{1}H_{1}HG MgCl_{2},6H_{2}O

H_{1}I_{1}IH MgCl_{2},4H_{2}O

I_{1}L_{1}LKI MgCl_{2},2H_{2}O

L_{1}N_{1}NL --------------------------------------

II. _Univariant Systems._--The different univariant systems have already been described. The course of the curves will be sufficiently indicated if the temperature and composition of the solutions for the different invariant systems are given.

{288}

III.--_Invariant Systems--Binary and Ternary._

-------------------------------------------------------------------------

Composition of solution.

Point.

Solid Phases.

Temper-

Gram-molecules of salt

ature.

per 1000 gram-mol. water.

------------------------------------------------------------------------- A

Ice

0

--

B

Ice; MgCl_{2},12H_{2}O

-33.6

49.2 MgCl_{2}

C

Ice; KCl

-11.1

59.4 KCl

D

{ Ice; MgCl_{2},12H_{2}O; }

-34.3

43 MgCl_{2}; 3 KCl

{ KCl }

E

{ MgCl_{2},12H_{2}O; KCl; }

-21

66.1 MgCl_{2}; 4.9 KCl

{ carnallite }

F_{1}

MgCl_{2},12H_{2}O

-16.4

83.33 MgCl_{2}

F

{ MgCl_{2},12H_{2}O; }

-16.6

{ Almost same as F_{1};

{ carnallite }

{ contains small amount

{ of KCl

G_{1}

{ MgCl_{2},12H_{2}O; }

-16.8

87.5 MgCl_{2}

{ MgCl_{2},8H_{2}O }

G

{ MgCl_{2},12H_{2}O; }

-16.9

{ Almost same as G_{1},

{ MgCl_{2},8H_{2}O; }

{ but contains small

{ carnallite }

{ quant.i.ty of KCl

H_{1}

{ MgCl_{2},8H_{2}O; }

-3.4

99 MgCl_{2}

{ MgCl_{2},6H_{2}O }

H

{ MgCl_{2},8H_{2}O; }

ca. -3.4

{ Almost same as H_{1},

{ MgCl_{2},6H_{2}O; }

{ but contains small

{ carnallite }

{ amount of KCl

J_{1}

{ MgCl_{2},6H_{2}O; }

116.67

161.8 MgCl_{2}

{ MgCl_{2},4H_{2}O }

J

{ MgCl_{2},6H_{2}O; }

115.7

162 MgCl_{2}; 4 KCl

{ MgCl_{2},4H_{2}O; }

{ carnallite }

K

{ MgCl_{2},4H_{2}O; KCl; }

152.5

200 MgCl_{2}; 24 KCl

{ carnallite }

L_{1}

{ MgCl_{2},4H_{2}O; }

181

238.1 MgCl_{2}

{ MgCl_{2},2H_{2}O }

L

{ MgCl_{2},4H_{2}O; }

176

240 MgCl_{2}; 41 KCl

{ MgCl_{2},2H_{2}O; KCl }

M

Carnallite; KCl

167.5

166.7 MgCl_{2}; 41.7 KCl

[N_{1}

MgCl_{2},2H_{2}O

186

ca. 241 MgCl_{2}]

N

MgCl_{2},2H_{2}O; KCl

186

240 MgCl_{2}; 63 KCl

[O

KCl

186

195.6 KCl]

With the help of the data in the preceding table and of the solid model it will be possible to state in any given case what will be the behaviour of a system composed of magnesium chloride, pota.s.sium chloride and water. One or two different cases will be very briefly described; and the reader should have no difficulty in working out the behaviour under other conditions with the help of the model and the numerical data just given. {289}

In the first place it may be again noted that at a temperature above 167.5 (point M) carnallite cannot exist. If, therefore, a solution of magnesium and pota.s.sium chlorides is evaporated at a temperature above this point, the result will be a mixture of pota.s.sium chloride and either magnesium chloride tetrahydrate or magnesium chloride dihydrate, according as the temperature is below or above 176. The isothermal curve here consists of only two branches.

Further, reference has already been made to the fact that all points of the carnallite area correspond to solutions in equilibrium with carnallite, but in which the ratio of MgCl_{2} to KCl is greater than in the double salt. A solution which is saturated with respect to double salt alone will be supersaturated with respect to pota.s.sium chloride. At all temperatures, therefore, carnallite is decomposed by water with separation of pota.s.sium chloride; hence all solutions obtained by adding excess of carnallite to water will lie on the curve EM. _A pure saturated solution of carnallite cannot be obtained._

If an unsaturated solution of the two salts in equimolecular amounts is evaporated, pota.s.sium chloride will first be deposited, because the plane bisecting the right angle formed by the X and Y axes cuts the area for that salt. Deposition of pota.s.sium chloride will lead to a relative increase in the concentration of magnesium chloride in the solution; and on continued evaporation a point (on the curve EM) will be reached at which carnallite will separate out. So long as the two solid phases are present, the composition of the solution must remain unchanged. Since the separation of carnallite causes a decrease in the relative concentration of the pota.s.sium chloride in the solution, the portion of this salt which was deposited at the commencement must _redissolve_, and carnallite will be left on evaporating to dryness. (_Incongruently saturated solution._)

Although carnallite is decomposed by pure water, it will be possible to crystallize it from a solution having a composition represented by any point in the carnallite area. Since during the separation of the double salt the relative amount of magnesium chloride increases, it is most advantageous to {290} commence with a solution the composition of which is represented by a point lying just above the curve EM (cf. p. 281).

From the above description of the behaviour of carnallite in solution, the processes usually employed for obtaining pota.s.sium chloride will be readily intelligible.[367]

Ferric Chloride--Hydrogen Chloride--Water.--In the case of another system of three components which we shall now describe, the relationships are considerably more complicated than in those already discussed. They deserve discussion, however, on account of the fact that they exhibit a number of new phenomena.

In the system formed by the three components, ferric chloride, hydrogen chloride, and water, not only can various compounds of ferric chloride and water (p. 152), and of hydrogen chloride and water be formed, each of which possesses a definite melting point, but various ternary compounds are also known. Thus we have the following solid phases:--

2FeCl_{3},12H_{2}O HCl,3H_{2}O 2FeCl_{3},2HCl,12H_{2}O 2FeCl_{3},7H_{2}O HCl,2H_{2}O 2FeCl_{3},2HCl,8H_{2}O 2FeCl_{3},5H_{2}O HCl,H_{2}O 2FeCl_{3},2HCl,4H_{2}O 2FeCl_{3},4H_{2}O FeCl_{3}

From this it will be readily understood that the complete study of the conditions of temperature and concentration under which solutions can exist, either with one solid phase or with two or three solid phases, are exceedingly complicated; and, as a matter of fact, only a few of the possible equilibria have been investigated. We shall attempt here only a brief description of the most important of these.[368]

If we again employ rectangular co-ordinates for the graphic {291} representation of the results, we have the two planes XOT and YOT (Fig.

115): the concentration of ferric chloride being measured along the X-axis, the concentration of hydrogen chloride along the Y-axis, and the temperature along the T-axis. The curve ABCDEFGHJK is, therefore, the solubility curve of ferric chloride in water (p. 152), and the curve A'B'C'D'E'F' the solubility curve of hydrogen chloride and its hydrates. B'

and D' are the melting points of the hydrates HCl,3H_{2}O and HCl,2H_{2}O.

In the s.p.a.ce between these two planes are represented those systems in which all three components are present. As already stated, only a few of the possible ternary systems have been investigated, and these are represented in Fig. 116. The figure shows the model resting on the XOT-plane, so that the lower edge represents the solubility curve of ferric chloride, the concentration increasing from right to left. The concentration of hydrogen chloride is measured upwards, and the temperature forwards. The further end of the model represents the isothermal surface for -30. The surface of the model on the left does not correspond with the plane YOT in Fig. 115, but with a parallel plane which cuts the concentration axis for ferric chloride at a point representing 65 gm.-molecules FeCl_{3} in 100 gm.-molecules of water. The upper surface corresponds with a plane parallel to the axis XOT, at a distance corresponding with the concentration of 50 gm.-molecules HCl in 100 gm.-molecules of water.

[Ill.u.s.tration: FIG. 115.]

Ternary Systems.--We pa.s.s over the binary system FeCl_{3}--H_{2}O, which has already been discussed (p. 152), and the similar system HCl--H_{2}O (see Fig. 115), and turn to the discussion of some of the ternary systems represented by {292} points on the surface of the model between the planes XOT and YOT. As in the case of carnallite, a plane represents the conditions of concentration of solution and temperature under which a ternary solution can be in equilibrium with a _single_ solid phase (bivariant systems), a line represents the conditions for the coexistence of a solution with two solid phases (univariant systems), and a point the conditions for equilibrium with three solid phases (invariant systems).

[Ill.u.s.tration: FIG. 116.]

In the case of a binary system, in which 2FeCl_{3},12H_{2}O is in equilibrium with a solution of the same composition, addition of hydrogen chloride must evidently lower the temperature at which equilibrium can exist; and the same holds, of course, {293} for all other binary solutions in equilibrium with this solid phase. In this way we obtain the surface I., which represents the temperatures and concentrations of solutions in which 2FeCl_{3},12H_{2}O can be in equilibrium with a ternary solution containing ferric chloride, hydrogen chloride, and water. This surface is a.n.a.logous to the curved surface K_{1}K_{2}_k__{4}_k__{3} in Fig. 97 (p. 256). Similarly, the surfaces II., III., IV., and V. represent the conditions for equilibrium between the solid phases 2FeCl_{3},7H_{2}O; 2FeCl_{3},5H_{2}O; 2FeCl_{3},4H_{2}O; FeCl_{3} and ternary solutions respectively. The lines CL, EM, GN, and IO on the model represent univariant systems in which a ternary solution is in equilibrium with two solid phases, viz. with those represented by the adjoining fields. These lines correspond with the ternary eutectic curves _k__{3}K_{1} and _k__{4}K_{2} in Fig. 97. Besides the surfaces already mentioned, there are still three others, VI., VII., and VIII., which also represent the conditions for equilibrium between one solid phase and a ternary solution; but in these cases, the solid phase is not a binary compound or an anhydrous salt, but a ternary compound containing all three components. The solid phases which are in equilibrium with the ternary solutions represented by the surfaces VI., VII., and VIII., are 2FeCl_{3},2HCl,4H_{2}O; 2FeCl_{3},2HCl,8H_{2}O; and 2FeCl_{3},2HCl,12H_{2}O respectively.

The model for FeCl_{3}--HCl--H_{2}O exhibits certain other peculiarities not found in the case of MgCl_{2}--KCl--H_{2}O. On examining the model more closely, it is found that the field of the ternary compound 2FeCl_{3},2HCl,8H_{2}O (VII.) resembles the surface of a sugar cone, and has a projecting point, the end of which corresponds with a higher temperature than does any other point of the surface. At the point of maximum temperature the composition of the liquid phase is the same as that of the solid. This point, therefore, represents the melting point of the double salt of the above composition.

The curves representing univariant systems are of two kinds. In the one case, the two solid phases present are both binary compounds; or one is a binary compound and the other is one of the components. In the other case, either one or both solid phases are ternary compounds. Curves belonging {294} to the former cla.s.s (so-called _border curves_) start from binary eutectic points, and their course is always towards lower temperatures, _e.g._ CL, EM, GN, IO. Curves belonging to the latter cla.s.s (so-called _medial curves_) would, in a triangular diagram, lie entirely within the triangle. Such curves are YV, WV, VL, LM, MV, NS, ST, SO, OZ. These curves do not always run from higher to lower temperatures, but may even exhibit a point of maximum temperature. Such maxima are found, for example, at U (Fig. 116), and also on the curves ST and LV.

Finally, whereas all the other ternary univariant curves run in valleys between the adjoining surfaces, we find at the point X a similar appearance to that found in the case of carnallite, as the univariant curve here rises above the surrounding surface. The point X, therefore, does not correspond with a eutectic point, but with a transition point. At this point the ternary compound 2FeCl_{3},2HCl,12H_{2}O melts with separation of 2FeCl_{3},12H_{2}O, just as carnallite melts at 168 with separation of pota.s.sium chloride.

The Isothermal Curves.--A deeper insight into the behaviour of the system FeCl_{3}--HCl--H_{2}O is obtained from a study of the isothermal curves, the complete series of which, so far as they have been studied, is given in Fig. 117.[369] In this figure the lightly drawn curves represent isothermal solubility curves, the particular temperature being printed beside the curve.[370] The dark lines give the composition of the univariant systems at different temperatures. The point of intersection of a dark with a light curve gives the composition of the univariant solution at the temperature represented by the light curve; and the point of intersection of two dark lines gives the composition of the invariant solution in equilibrium with three solid phases. The dotted lines represent metastable systems, and the points P, Q, and R represent solutions of {295} the composition of the ternary salts, 2FeCl_{3},2HCl,4H_{2}O; 2FeCl_{3},2HCl,8H_{2}O; and 2FeCl_{3},2HCl,12H_{2}O.

[Ill.u.s.tration: FIG. 117.]

The farther end of the model (Fig. 116) corresponds, as already mentioned, to the temperature -30, so that the outline evidently represents the isothermal curve for that temperature. Fig. 117 does not show this. We can, however, follow the isothermal for -20, which is the extreme curve on the right in Fig. 117. Point A represents the solubility of 2FeCl_{3},12H_{2}O in water. If hydrogen chloride is added, the concentration of ferric chloride in the solution first decreases and then increases, until at point 34 the ternary double salt 2FeCl_{3},2HCl,12H_{2}O is formed. If the addition of hydrogen chloride is continued, the ferric chloride disappears ultimately, and only the ternary double salt remains. This salt can coexist with solutions of the composition represented by the curve which pa.s.ses through the points 173, 174, 175. At the last-mentioned point, the ternary salt with 8H_{2}O is formed. The composition of the solutions with which this salt is in equilibrium at -20 is represented by the curve which pa.s.ses through a point of maximal concentration with respect to HCl, and cuts the curve SN at the point 112, at which the solution is in equilibrium with the two solid phases 2FeCl_{3},4H_{2}O and 2FeCl_{3},2HCl,8H_{2}O. The succeeding portion of the isotherm represents the solubility curve at -20 of 2FeCl_{3},4H_{2}O, which cuts the dark line OS at point 113, at which the solution is in equilibrium with the two solid phases 2FeCl_{3},4H_{2}O and 2FeCl_{3},2HCl,4H_{2}O. Thereafter comes the solubility curve of the latter compound.

The other isothermal curves can be followed in a similar manner. If the temperature is raised, the region of existence of the ternary double salts becomes smaller and smaller, and at temperatures above 30 the ternary salts with 12H_{2}O and 8H_{2}O are no longer capable of existing. If the temperature is raised above 46, only the binary compounds of ferric chloride and water and the anhydrous salt can exist as solid phases.

The isothermal curve for 0 represents the solubility curve for 2FeCl_{3},12H_{2}O; 2FeCl_{3},7H_{2}O; 2FeCl_{3},5H_{2}O; and 2FeCl_{3},4H_{2}O. {296}

Finally, in the case of the system FeCl_{3}--HCl--H_{2}O, we find _closed_ isothermal curves. Since, as already stated, the salt 2FeCl_{3},2HCl,8H_{2}O has a definite melting point, the temperature of which is therefore higher than that at which this compound is in equilibrium with solutions of other composition, it follows that the line of intersection of an isothermal plane corresponding with a temperature immediately below the melting point of the salt with the cone-shaped surface of its region of existence, will form a closed curve. This is shown by the isotherm for -4.5, which surrounds the point Q, the melting point of the ternary salt.

The following table gives some of the numerical data from which the curves and the model have been constructed:--

-------------------------------------------------------------------------

Composition of the sol-

ution in gm.-mols. salt Point.

Solid phases.

Temper-

to 100 gm.-mols. water.

ature.

------------------------

HCl

FeCl_{3} ------------------------------------------------------------------------- A

2FeCl_{3},12H_{2}O

-20

--

6.56

C

{ 2FeCl_{3},12H_{2}O; }

27.4

--

24.30

{ 2FeCl_{3},7H_{2}O }

E

{ 2FeCl_{3},7H_{2}O; }

30

--

30.24

{ 2FeCl_{3},5H_{2}O }

G

{ 2FeCl_{3},5H_{2}O; }

55

--

40.64

{ 2FeCl_{3},4H_{2}O }

J

2FeCl_{3},4H_{2}O; FeCl_{3}

66

--

58.40

{ 2FeCl_{3},12H_{2}O; }

L

{ 2FeCl_{3},7H_{2}O; }

-7.5

19.22

23.72

{ 2FeCl_{3},2HCl,8H_{2}O }

{ 2FeCl_{3},7H_{2}O; }

M

{ 2FeCl_{3},5H_{2}O; }

-7.3

23.08

28.55

{ 2FeCl_{3},2HCl,8H_{2}O }

{ 2FeCl_{3},5H_{2}O; }

N

{ 2FeCl_{3},4H_{2}O; }

-16

28.40

31.89

{ 2FeCl_{3},2HCl,8H_{2}O }

{ 2FeCl_{3},4H_{2}O; }

S

{ 2FeCl_{3},2HCl,8H_{2}O; }

-27.5

32.33

34.21

{ 2FeCl_{3},2HCl,4H_{2}O }

{ 2FeCl_{3},4H_{2}O; }

O

{ FeCl_{3}; }

29

33.71

49.84

{ 2FeCl_{3},2HCl,4H_{2}O }

U

{ 2FeCl_{3},7H_{2}O; }

-4.5

20.66

25.74

{ 2FeCl_{3},2HCl,8H_{2}O }

{ 2FeCl_{3},12H_{2}O; }

V

{ 2FeCl_{3},2HCl,12H_{2}O; }

-13

22.40

18.00

{ 2FeCl_{3},2HCl,8H_{2}O }

X

{ 2FeCl_{3},12H_{2}O; }

-12.5

22.14

16.69

{ 2FeCl_{3},2HCl,12H_{2}O }

Q

2FeCl_{3},2HCl,8H_{2}O

-3 (melting point) -------------------------------------------------------------------------

Basic Salts.--Another cla.s.s of systems in the study of {297} which the Phase Rule has performed exceptional service, is that of the basic salts.

In many cases it is impossible, by the ordinary methods of a.n.a.lysis, to decide whether one is dealing with a definite chemical individual or with a mixture. The question whether a solid phase is a chemical individual can, however, be answered, in most cases, with the help of the principles which we have already learnt. Let us consider, for example, the formation of basic salts from bis.m.u.th nitrate, and water. In this case we can choose as components Bi_{2}O_{3}, N_{2}O_{5}, and H_{2}O; since all the systems consist of these in varying amounts. If we are dealing with a condition of equilibrium at constant temperature between liquid and solid phases, three cases can be distinguished,[371] viz.--

1. The solutions in different experiments have the same composition, but the composition of the precipitate alters. In this case there must be two solid phases.

2. The solutions in different experiments can have varying composition, while the composition of the precipitate remains unchanged. In this case only one solid phase exists, a definite compound.

3. The composition both of the solution and of the precipitate varies. In this case the solid phase is a solid solution or a mixed crystal.

In order, therefore, to decide what is the nature of a precipitate produced by the hydrolysis of a normal salt, it is only necessary to ascertain whether and how the composition of the precipitate alters with alteration in the composition of the solution. If the composition of the solution is represented by abscissae, and the composition of the precipitate by ordinates, the form of the curves obtained would enable us to answer our question; for vertical lines would indicate the presence of two solid phases (1st case), horizontal lines the presence of only one solid phase (2nd case), and slanting lines the presence of mixed crystals (3rd case).

This method of representation cannot, however, be carried out in most cases. It is, however, {298} generally possible to find one pair or several pairs of components, the _relative amounts_ of which in the solution or in the precipitate undergo change when, and only when, the composition of the solution or of the precipitate changes. Thus, in the case of bis.m.u.th, nitrate, and water, we can represent the ratio of Bi_{2}O_{3} : N_{2}O_{5} in the precipitate as ordinates, and N_{2}O_{5} : H_{2}O in the solution as abscissae. A horizontal line then indicates a single solid phase, and a vertical line two solid phases. An example of this is given in Fig.

118.[372]