CHAPTER XV

Chapter 341,573 wordsPublic domain

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 A_k__{1}B for the binary system; _k__{1}; 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 A_k__{2}C and B_k__{3}C. These curves give the composition of the binary liquid phases in equilibrium {254} 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 _k__{1}, 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 _k__{1}K, 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 _k__{2}K and _k__{3}K 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. A_k__{1}K_k__{2}, B_k__{1}K_k__{3}, and C_k__{1}K_k__{3} 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, {255} 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 _k__{1}K, _k__{2}K, and _k__{3}K 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]

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

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 {256} 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, K_{1} and K_{2}, 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 _k__{1}K and _k__{2}K 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 _k__{1}K_{1}K_{2}_k__{2} 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 [beta]-naphthol (C), obtained by Bruni.[333]

{257}

------------------------------------------------------------------------- | Temperature | Solid phases present. ------------------------------------------------------------------------- Point _k__{1} | 9.41deg | Ethylene bromide, picric acid. Curve _k__{1}K_{1} | -- | " " Point K_{1} | 9.32deg | Ethylene bromide, picric acid, and | | [beta]-naphthol picrate. Curve K_{1}D'K_{2} | -- | Ethylene bromide, | | [beta]-naphthol picrate. Point D' | 9.75deg | " " " " Point K_{2} | 8.89deg | " " [beta]-naphthol, | | and picrate. Curve K_{2}_k__{2} | -- | " " [beta]-naphthol. Point _k__{2} | 9.04deg | " " " -------------------------------------------------------------------------

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 103deg _i_-camphoroxime exists as a racemic compound, while above {258} 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