In investigating the equilibria between two components, three chief cla.s.ses of curves will be obtained according as--

I. No combination takes place between the two components.

II. The components can form definite compounds.

III. The components separate out in the form of mixed crystals.

The different types of curves which are obtained in these three cases are represented in Figs. 63, 64, 65. These different diagrams represent the whole series of equilibria, from the melting point of the one component (A) to that of the other component (B). The curves represent, in all cases, the composition of the solution, or phase of variable composition; the temperature being measured along one axis, and the composition along the other.

We shall now recapitulate very briefly the characteristics of the different curves.

[Ill.u.s.tration: FIG. 63.]

If no compound is formed between the two components, {209} the general form of the equilibrium curve will be that of curve I. or II., Fig. 63. Type I.

is the simplest form of curve found, and consists, as the diagram shows, of only two branches, AC and BC, meeting at the point C, _which lies below the melting point of either component_. The solid phase which is in equilibrium with the solutions AC is pure A; that in equilibrium with BC, pure B. C is the eutectic point. Although at the eutectic point the solution solidifies entirely without change of temperature, the solid which is deposited is not a h.o.m.ogeneous solid phase, but a mixture, or conglomerate of the two components. _The eutectic point, therefore, represents the melting or freezing point, not of a compound, but of a mixture_ (p. 119).

Curve II., Fig. 63, is obtained when two liquid phases are formed. C is an eutectic point, D and F are transition points at which there can co-exist the four phases--solid, two liquid phases, vapour. DEF represents the change in the composition of the two liquid phases with rise of temperature; the curve might also have the reversed form with the critical solution point below the transition points D and F.

[Ill.u.s.tration: FIG. 64.]

In the second cla.s.s of systems (Fig. 64), that in which combination between the components occurs, there are again two types according as the compound formed has a definite melting point (_i.e._ can exist in equilibrium with a solution of the same composition), or undergoes only partial fusion; that is, exhibits a transition point.

If a compound possessing a definite melting point is formed, the equilibrium curve will have the general form shown by curve I., Fig. 64. A, B, and D are the melting points of pure A, pure B, and of the compound A_{x}B_{y} respectively. AC {210} is the freezing point curve of A in presence of B; BE that of B in presence of A; and DC and DE the freezing point curves of the compound in presence of a solution containing excess of one of the components. C and E are eutectic points at which mixtures of A and A_{x}B_{y}, or B and A_{x}B_{y} can co-exist in contact with solution.

The curve CDE may be large or small, and the melting point of the compound, D, may lie above or below that of each of the components, or may have an intermediate position. If more than one compound can be formed, a series of curves similar to CDE will be obtained (_cf._ p. 152).

On the other hand, if the compound undergoes transition to another solid phase at a temperature below its melting point, a curve of the form II., Fig. 64, will be found. This corresponds to the case where a compound can exist only in contact with solutions containing excess of one of the components. The metastable continuation of the equilibrium curve for the compound is indicated by the dotted line, the summit of which would be the melting point of the compound. Before this temperature is reached, however, the solid compound ceases to be able to exist in contact with solution, and transition to a different solid phase occurs at the point E (_cf._ p. 134).

This point, therefore, represents the limit of the existence of the compound AB. If a series of compounds can be formed none of which possess a definite melting point, then a series of curves will be obtained which do not exhibit a temperature-maximum, and there will be only one eutectic point. The limits of existence of each compound will be marked by a break in the curve (_cf._ p. 143).

[Ill.u.s.tration: FIG. 65.]

Turning, lastly, to the third cla.s.s of systems, in which formation of mixed crystals can occur, five different types of curves can be obtained, as shown in Fig. 65. With regard to the first three types, curves I., II., and III., {211} these differ entirely from those of the previous cla.s.ses, in that they are continuous; they exhibit no eutectic point, and no transition point. Curve II. bears some resemblance to the melting-point curve of a compound (_e.g._ CDE, Fig. 64, I.), but differs markedly from it in not ending in eutectic points.

Further, in the case of the formation of a compound, the composition of the solid phase remains unchanged throughout the whole curve between the eutectic points; whereas, when mixed crystals are produced, the composition of the solid phase varies with the composition of the liquid solution. On pa.s.sing through the maximum, the relative proportions of A and B in the solid and the liquid phase undergo change; on the one side of the maximum, the solid phase contains relatively more A, and on the other side of the maximum, relatively more B than the liquid phase. Lastly, when mixed crystals are formed, the temperature at which complete solidification occurs changes as the composition of the solution changes, whereas in the case of the formation of compounds, the temperature of complete solidification for all solutions is a eutectic point.

The third type of curve, Fig. 65, can be distinguished in a similar manner from the ordinary eutectic curve, Fig. 63, I., to which it bears a certain resemblance. Whereas in the case of the latter, the eutectic point is the temperature of complete solidification of all solutions, the point of minimum temperature in the case of the formation of mixed crystals, is the solidification point only of solutions having one particular composition; that, namely, of the minimum point. For all other solutions, the temperature of complete solidification is different. Whereas, also, in the case of the simple eutectic curve, the solid which separates out from the solutions represented by either curve remains the same throughout the whole extent of that curve, the composition of the mixed crystal varies with variation of the composition of the liquid phase, and the relative proportions of the two components in the solid and the liquid phase are reversed on pa.s.sing through the minimum.[290]

In a similar manner, type IV., Fig. 65, can be distinguished from type II., Fig. 64, by the fact that it does not exhibit a {212} eutectic point, and that the composition of the solid phase undergoes continuous variation with variation of the liquid phase on either side of the transition point.

Lastly, type V., which does exhibit a eutectic point, differs from the eutectic curve of Fig. 63, in that the eutectic point does not const.i.tute the point of complete solidification for all solutions, and that the composition of the solid phase varies with the composition of the liquid phase.

Such, then, are the chief general types of equilibrium curves for two-components; they are the pattern curves with which other curves, experimentally determined, can be compared; and from the comparison it will be possible to draw conclusions as to the nature of the equilibria between the two components under investigation.

1. _Organic Compounds._

[Ill.u.s.tration: FIG. 66.]

The principles of the Phase Rule have been applied to the investigation of the equilibria between organic compounds, and Figs. 66-69 reproduce some of the results which have been obtained.[291]

{213}

Fig. 66, the freezing point curve (curve of equilibrium) for _o_-nitrophenol and _p_-toluidine, shows a curve of the simplest type[292]

(type I., Fig. 63), in which two branches meet at an eutectic point. The solid phase in equilibrium with solutions represented by the left-hand branch of the curve was _o_-nitrophenol (m.p. 44.1); that in equilibrium with the solutions represented by the right-hand branch, was _p_-toluidine (m.p. 43.3). At the eutectic point (15.6), these two solid phases could co-exist with the liquid phase. This equilibrium curve, therefore, shows that _o_-nitrophenol and _p_-toluidine do not combine with one another.

In connection with this curve, attention may be called to the interesting fact that although the solid produced by cooling the liquid phase at the eutectic point has a composition approximating to that of a compound of equimolecular proportions of the phenol and toluidine, and a constant melting point, it is nevertheless a _mixture_. Although, as a rule, the const.i.tuents of the eutectic mixture are not present in simple molecular proportions, there is no reason why they should not be so; and it is therefore necessary to beware of a.s.suming the formation of compounds in such cases.[293]

Fig. 67, on the other hand, indicates with perfect certainty the formation of a compound between phenol and [alpha]-naphthylamine.[294] (_Cf._ curve I., Fig. 64.)

Phenol freezes at 40.4, but the addition of [alpha]-naphthylamine lowers the freezing point as represented by the curve AC. At C (16.0) the compound C_{6}H_{5}OH,C_{10}H_{7}NH_{2} is formed, and the system becomes invariant. On increasing the amount of the amine, the temperature of equilibrium rises, the solid phase now being the compound. At D, the curve pa.s.ses through a maximum (28.8), at which the solid and liquid phases have the same composition. This is the melting point of the compound. Further addition of the amine lowers the temperature of equilibrium, until at E solid [alpha]-naphthylamine separates out, and a second eutectic point (24.0) is obtained. BE is the {214} freezing-point curve of [alpha]-naphthylamine in presence of phenol, the freezing point of the pure amine being 48.3.

On account of the great sluggishness with which the compound of phenol and [alpha]-naphthylamine crystallizes, it was found possible to follow the freezing point curves of phenol and the amine to temperatures considerably below the eutectic points, as shown by the curves CF and EG.

[Ill.u.s.tration: FIG. 67.]

Phenol can also combine with _p_-toluidine in equimolecular proportions; and this compound is of interest, from the fact that it exists in two crystalline forms melting at 28.5 and 30. Each of these forms now must have its own equilibrium curve, and it was found that the intermediate portion of the freezing point curve was duplicated, as shown in Fig.

68.[295]

{215}

[Ill.u.s.tration: FIG. 68.]

[Ill.u.s.tration: FIG. 69.]

{216}

Lastly, a curve is given, Fig. 69,[296] which corresponds with curve II., Fig. 64. Picric acid and benzene can form a compound, which, however, can exist only in contact with solutions _containing excess of benzene_. When the temperature is raised, a point (K) is reached at which the compound melts with separation of solid picric acid. The point, K, is, therefore, a _transition point_; a.n.a.lysis, however, showed that the composition of the solution at this point is very nearly that of the compound C_{6}H_{2}(NO_{2})_{3}OH,C_{6}H_{6}, so that the melting point of the compound can almost be reached. The fusion of the compound of benzene and picric acid with separation of the latter is a.n.a.logous to the (partial) fusion of Glauber's salt with separation of anhydrous sodium sulphate.

2. _Optically Active Substances._

The question as to whether a resolvable inactive body is a mixture of the two oppositely active const.i.tuents (a _dl_-mixture), or a racemic compound, is one which has given rise to considerable discussion during the past decade; and several investigators have endeavoured to establish general rules by which the question could be decided. In the case of inactive liquids it is a matter of great difficulty to arrive at a certain conclusion as to whether one is dealing with a mixture or a compound, for in this case the usual physical methods give but a dubious answer; and although the existence of a racemate in the liquid state (in the case of conine) has been a.s.serted,[297] most chemists incline to the belief that such a thing is improbable.

Even in the case of crystalline substances, where the differences between the various forms is greater, it was not always easy to discriminate between the _dl_-mixture and the racemic compound. The occurrence of hemihedral faces was considered by Pasteur to be a sufficient criterion for an optically active substance. It has, however, been found that hemihedry in crystals, although a frequent accompaniment of {217} optical activity, is by no means a necessary or constant expression of this property. Other rules, also, which were given, although in some cases reliable, were in other cases insufficient; and all were in so far unsatisfactory that they lacked a theoretical basis.

With the help of the Phase Rule, however, it is possible from a study of the solubility or fusion curves of the optically active and inactive substances, to decide the nature of the inactive substance, at least under certain conditions. On account of the interest and importance which these compounds possess, a brief description of the application of the Phase Rule to the study of such substances will be given here;[298] the two optical antipodes being regarded as the two components.

In the present chapter we shall consider only the fusion curves, the solubility curves being discussed in the next section on three-component systems. The rules which are hereby obtained, have reference only to the nature of the inactive substance in the neighbourhood of the melting points.

I. _The inactive substance is a _dl_-mixture._

In this case the fusion curves will have the simple form shown in type I, Fig. 63. A and B are the melting points of the two optical isomerides, and C the eutectic point at which the inactive mixture consisting of equal amounts of d- and l-form melts. Owing to the similar effect of the one form on the freezing point of the other, the figure is symmetrical. No example of this simple case has been investigated.

II. _The two components form a racemic compound._

In this case there will be three melting point curves as in Fig. 64, type I. In this case also the figure must be symmetrical.

Examples.--As examples of this, may be taken dimethyl tartrate and mandelic acid, the freezing point curves of which are given in Figs. 70 and 71.[299]

As can be seen, the curve for the racemic tartrate occupies a large part of the diagram, {218} while that for racemic mandelic acid is much smaller. In the case of dimethyldiacetyl tartrate, this middle portion is still less.

[Ill.u.s.tration: FIG. 70.]