The Phase Rule and Its Applications Part 15

General.--With the conception of gaseous and liquid solutions, every one is familiar. Gases can mix in all proportions to form h.o.m.ogeneous solutions.

Gases can dissolve in or be "absorbed" by liquids; and solids, also, when brought in contact with liquids, "pa.s.s into solution" and yield a h.o.m.ogeneous liquid phase. On the other hand, the conception of a _solid solution_ is one which in many cases is found more difficult to appreciate; and the existence and behaviour of solid solutions, in spite of their not uncommon occurrence and importance, are in general comparatively little known.

The reason of this is to be found, to some extent, no doubt, in the fact that the term "solid solution" was introduced at a comparatively recent date,[254] but it is probably also due in some measure to a somewhat hazy comprehension of the definition of the term "solution" itself. As has already been said (p. 92), a solution is a h.o.m.ogeneous phase, the composition of which can vary continuously within certain limits; the definition involves, therefore, no condition as to the physical state of the substances. Accordingly, solid solutions are h.o.m.ogeneous solid phases, the composition of which can undergo continuous variation within certain limits. Just as we saw that the range of variation of composition is more limited in the case of liquids than in the case of gases, so also we find that the limits of miscibility are in general still more restricted in the case of solids. Examples of complete miscibility are, however, not unknown even in the case of solid substances.

Solid solutions have long been known, although, of course, {176} they were not defined as such. Thus, the phenomena of "occlusion" of gases by metals and other substances (occlusion of hydrogen by palladium; occlusion of hydrogen by iron) are due to the formation of solid solutions. The same is probably also true of the phenomena of "adsorption," as in the removal of organic colouring matter by charcoal, although, in this case, surface tension no doubt plays a considerable part.[255]

As examples of the solution of gases in solids there may be cited (in addition to the phenomena of occlusion already mentioned), the hydrated silicates and the zeolites. During dehydration these crystalline substances remain clear and transparent, and the pressure of the water vapour which they emit varies with the degree of hydration or the concentration of water in the mineral.[256] As examples of the solution of solids in solids we have the cementation of iron by charcoal, the formation of gla.s.s, and the crystallization together of isomorphous substances.

Although we have here spoken of the gla.s.ses as "solid solutions," it should be mentioned that the term "solid" is used in its popular sense. Strictly speaking, the gla.s.ses are to be regarded as supercooled liquids (see also p. 53, footnote).

In discussing the equilibria in systems containing a solid solution, it is of essential importance to remember that a solid solution const.i.tutes only _one_ phase, a phase of varying composition, as in the case of liquid solutions.

Solution of Gases in Solids.--Comparatively little work has been done in this connection, the investigations being limited chiefly to the phenomena of occlusion or adsorption of gases by charcoal.[257] We shall, therefore, indicate only briefly {177} and in a general manner, the behaviour which the Phase Rule enables us to foresee.[258]

In dealing with the systems formed by the two phases gas--solid, three chief cases call for mention:--

I. _The gas is not absorbed by the solid, but when the pressure reaches a certain value, combination of the two components can result._

[Ill.u.s.tration: Fig. 46.]

The graphic representation of such a system is shown in Fig. 46, the ordinates being the pressures of the gas, and the abscissae the concentrations of the gaseous component in the solid phase. Since there is no formation of a solid solution, the concentration of gas in the solid phase remains zero until the pressure has increased to the point A. At this point combination can take place. There will now be three phases present, viz. solid component, compound, and vapour. The system is therefore univariant, and if the temperature is maintained constant, the vapour pressure will be constant, irrespective of the amount of compound formed, _i.e._ irrespective of the relative amounts of gas and solid. This is indicated by the line AB. When the solid component has entirely disappeared, the system ceases to be univariant, and if no absorption occurs, the pressure will increase again, as shown by BC. If a second compound can be formed, then a second _pc_-line will be obtained, similar to the preceding. To this group belong the salt hydrates (Chap. VII.).

II. _The gas may be absorbed and may also form a compound._

If absorption of gas occurs with formation of a solid solution, then, as the system consists of two phases, solution--vapour, it is bivariant. At constant temperature, therefore, the pressure will still vary with the concentration of the gaseous component in the solid phase. This is represented by the curve AB in Fig. 47. When, however, the pressure has reached a certain value, combination can take place; and since there are now three phases present, the system is {178} univariant, and at constant temperature the pressure is constant, as shown by the line BC.

III. _Absorption of gas occurs, but at a certain concentration the solid solution can separate into two immiscible solid solutions._

We have seen, in Chapter VI., that two liquids can form two immiscible solutions, and the same has also been found true of solid solutions, as we shall presently learn more fully. If, now, two immiscible solutions are formed, then the system will become univariant, and at constant temperature the _pc_-curve will be a straight line, as in the case of the formation of a compound (cf. p. 86). The behaviour of this system will, therefore, also be represented diagrammatically by Fig. 47.

[Ill.u.s.tration: FIG. 47.]

_Palladium and Hydrogen._--The phenomenon of the absorption of hydrogen by palladium, to which Graham gave the name "occlusion," is one that has claimed the attention of several investigators. Although Graham was not of opinion that a compound is formed, but rather that the gas undergoes very great condensation, acts as a quasi-metal (to which he gave the name hydrogenium), and forms a h.o.m.ogeneous alloy with the palladium, later investigations, especially those of Troost and Hautefeuille,[259] pointed to the formation of a definite chemical compound, having the formula Pd_{2}H. This conclusion has, however, not been confirmed by subsequent investigation.[260]

Roozeboom and Hoitsema[261] sought to arrive at a final decision as to the nature of the phenomenon by an investigation of the equilibrium between hydrogen and palladium on the basis of the Phase Rule cla.s.sification given above. If a compound is formed, diminution of volume would cause no increase of pressure, but only an increase in the amount of the compound.

As this is the only case of gas absorption which has been {179} accurately studied from this point of view, a brief account of the results obtained will be given here, although these are not so clear and free from ambiguity as one would desire.

The scientists just mentioned investigated the variation of the pressure of hydrogen with the amount absorbed by the metal at different temperatures, and a few of their results, typical of all, are represented graphically in Fig. 48; the curves indicating the variation of the gas pressure with the concentration of the hydrogen in the palladium at the temperatures 120, 170, and 200. As can be seen, the curve consists of three parts, an ascending portion which pa.s.ses gradually and continuously into an almost horizontal but slightly ascending middle part, which in turn pa.s.ses without break into a second rapidly ascending curve. This, as Fig. 48 indicates, is the general form of the curve; but the length of the middle portion varies with the temperature, being shorter at higher than at lower temperatures.

[Ill.u.s.tration: FIG. 48.]

What is the interpretation to be put on these curves? With regard to the two end portions, these represent bivariant, two-phase systems, consisting of a solid solution and gas. They correspond, therefore, to curve AB in Fig. 47. If the middle portion were horizontal, it would indicate either the formation of a compound or of two immiscible solid solutions. If a compound Pd_{2}H were formed, then the middle portion would at all temperatures end at the same value of the concentration, viz. that corresponding to 0.5 atoms of hydrogen to 1 atom of palladium. As the figure shows, however, this is not the case; the higher the temperature, the lower is the concentration at which the middle pa.s.ses into the terminal portion of the curve. {180} Such a behaviour would, however, agree with the a.s.sumption of the formation of two solid solutions, the "miscibility" of which increases with the temperature, as in the case of the liquid solutions of phenol and water (p. 97). Nevertheless, although the a.s.sumption of the formation of two solid solutions is more satisfactory than that of the formation of a compound, it does not entirely explain the facts. If two solid solutions are formed, the pressure curve should be horizontal, but this is not the case; and the deviation from the horizontal does not appear to be due to impurities either in the gas or in the metal, but is apparently a peculiarity of the system. Further, the gradual instead of abrupt pa.s.sage of the three portions of the curve into one another remains unexplained. Hoitsema has expressed the opinion that the occlusion of hydrogen by palladium is a process of continuous absorption, the peculiar form of the curve--the flat middle portion--being possibly due to a condensation of the gas, even at temperatures far above the critical temperature of liquid hydrogen.

While, therefore, the occlusion of hydrogen by palladium still presents some unexplained phenomena, the behaviour found by Hoitsema would appear to disprove conclusively the formation of a definite chemical compound.[262]

SOLUTION OF SOLIDS IN SOLIDS. MIXED CRYSTALS.

The introduction by van't Hoff of the term "solid solution" resulted from the discovery of a number of deviations from the Raoult-van't Hoff law for the depression of the freezing point by dissolved substances. In all cases, the depression was too small; in some instances, indeed, the freezing point may be raised. To explain these irregularities, van't Hoff a.s.sumed that the dissolved substance crystallized out along with the solid solvent; and he showed how this would account for the {181} deviations from the law of the depression of the freezing point, which had been developed on the a.s.sumption that only the pure solvent crystallized out from the solution.[263]

The "mixed crystals" which were thus obtained, and which van't Hoff called dilute solid solutions, showed great resemblance in their behaviour to ordinary liquid solutions, and obeyed the laws applicable to these. These laws, however, can no longer be applied in the case of the concentrated solid solutions formed by the crystallization together of isomorphous substances, and known as isomorphous mixtures. Indeed, it has been contended[264] that these isomorphous mixtures should not be considered as solid solutions at all, although no sharp line of demarcation can be drawn between the two cla.s.ses. The differences, however, in the behaviour of the two groups are of a quant.i.tative rather than a qualitative nature; and since we are concerned at present only with the qualitative behaviour, we shall make no distinction between the crystalline solid solutions and the isomorphous mixtures, but shall study the behaviour of the two cla.s.ses under the head of "mixed crystals."

Mixed crystals can be formed either by sublimation[265] or from a liquid phase; and in the latter case the mixed crystals can be deposited either from solution in a common solvent or from a mixture of the fused components. In this method of formation, which alone will be discussed in the present chapter, we are dealing with the fusion curves of two substances, where, however, the liquid solution is in equilibrium not with one of the pure components, but with a solid solution or mixed crystal. The simple scheme (Fig. 29, p. 117) which was obtained in the case of two components which crystallize out in the pure state, is no longer sufficient in the case of the formation of mixed crystals. With the help of the Phase Rule, however, the different possible systems can be cla.s.sified; and examples of the different cases predicted by the Phase Rule have also been obtained by experiment.

{182}

We shall now consider briefly the formation of mixed crystals by isomorphous substances; the consideration of the formation of mixed crystals of isodimorphous substances will, on account of the complexity of the relationships, not be undertaken here.[266]

_Formation of Mixed Crystals of Isomorphous Substances._

For the purpose of representing the relationships found here we shall employ a temperature-concentration diagram,[267] in which the ordinates represent the temperature and the abscissae the concentration of the components. Since there are two solutions, the liquid and the solid, and since the concentration of the components in these two phases is not, in general, the same, two curves will be required for each system, one relating to the liquid phase, the other relating to the solid. The temperature at which solid begins to be deposited from the liquid solution will be called the _freezing point_ of the mixture, and the temperature at which the solid solution just begins to liquefy will be called the _melting point_ of the solid solution. The temperature-concentration curve for the liquid phase will therefore be the freezing-point curve; that for the solid solution, the melting-point curve. The latter will be represented by a dotted line.[268]

{183}

I.--THE TWO COMPONENTS CAN FORM AN UNBROKEN SERIES OF MIXED CRYSTALS.

Since, as has already been pointed out (p. 176), a mixed crystal (solid solution) const.i.tutes only one phase, it is evident that if the two components are miscible with one another in all proportions in the solid state, there can never be more than one solid phase present, viz. the solid solution or mixed crystal. If the components are completely miscible in the solid state, they will also be completely miscible in the liquid state, and there can therefore be only one liquid phase. The system can at no point become invariant, because there can never be more than three phases present. When, therefore, the two components form a continuous series of mixed crystals, the equilibrium curve must also be continuous. Of these systems three types are found.

[Ill.u.s.tration: FIG. 49.]

(_a_) _The freezing points of all mixtures lie between the freezing points of the pure components_ (Curve I., Fig. 49).

Examples.--This type of curve is represented by the mixed crystals of naphthalene and [beta]-naphthol.[269] The addition of [beta]-naphthol to naphthalene raises the freezing point of the latter, and the rise is directly proportional to the amount of naphthol added. The freezing point curve is therefore a straight line joining the melting points of the two components. This behaviour, however, is rather exceptional, the freezing-point curve lying generally above, sometimes also below, the straight line joining the melting points of the pure components. Thus the freezing-point curve of mixtures of [alpha]-monochlorocinnamic aldehyde and [alpha]-mon.o.bromocinnamic aldehyde[270] lies above the {184} straight line joining the melting points of the pure components (31.22 and 69.56), as is evident from the following table:--

---------------------------------------------------------------------- Molecules of bromo- cinnamic aldehyde in Freezing point. Deviation from straight 100 mols. of mixture. line.

---------------------------------------------------------------------- 0.00 31.22 -- 10.48 37.28 2.04 21.91 43.12 3.50 30.07 46.80 4.05 45.04 52.94 4.45 62.16 58.82 3.77 82.98 65.07 2.03 93.50 67.91 0.84 100.00 69.56 -- ----------------------------------------------------------------------

Melting-point Curve.--This curve, like the freezing-point curve, must also be continuous, and the melting points of the different solid solutions will lie between the melting points of the pure components. This is represented by the dotted line in Fig. 49, I. The relative position of the two curves, which can be deduced with the help of thermodynamics and also by experimental determination, is found in all cases to be in accordance with the following rule: At any given temperature, _the concentration of that component by the addition of which the freezing point is depressed, is greater in the liquid than in the solid phase_; or, conversely, _the concentration of that component by the addition of which the freezing point is raised, is greater in the solid than in the liquid phase_. An ill.u.s.tration of this rule is afforded by the two substances chloro- and bromo-cinnamic aldehyde already mentioned. As can be seen from the above table, the addition of chlorocinnamic aldehyde lowers the melting point of the bromo-compound. In accordance with the rule, therefore, the concentration of the chloro-compound in the liquid phase must be greater than in the solid phase; and this was found experimentally. At a temperature of 49.44, the liquid contained 58.52 per cent., the solid only 52.57 per cent. of the chlorocinnamic aldehyde.

From this it will also be clear that on cooling a fused mixture of two substances capable of forming mixed crystals, {185} the temperature of solidification will not remain constant during the separation of the solid; nor, on the other hand, will the temperature of liquefaction of the solid solution be constant. Thus, for example, if a liquid solution of two components, A and B, having the composition represented by the point _x_ (Fig. 50), is allowed to cool, the system will pa.s.s along the line _xx'_.

At the temperature of the point _a_, mixed crystals will be deposited, the composition of which will be that represented by b. As the temperature continues to fall, more and more solid will be deposited; and since the solid phase is relatively rich in the component B, the liquid will become relatively poorer in this. The composition of the liquid solution will therefore pa.s.s along the curve _ad_, the composition of the solid solution at the same time pa.s.sing along the curve _bc_; at the point _c_ the liquid will solidify completely.[271]

[Ill.u.s.tration: FIG. 50.]

Conversely, if mixed crystals of the composition and at the temperature _x'_ are heated, liquefaction will begin at the temperature _c_, yielding a liquid of the composition d. On continuing to add heat, the temperature of the ma.s.s will rise, more of the solid will melt, and the composition of the two phases will change as represented by the curves _da_ and _cb_. When the temperature has risen to _a_, complete liquefaction will have occurred. The process of solidification or of liquefaction is therefore extended over a temperature interval _ac_.

Even when the freezing-point curve is a straight line joining {186} the melting points of the pure components, the melting-point curve will not necessarily coincide with the freezing-point curve, although it may approach very near to it; complete coincidence can take place only when the melting points of the two components are identical. An example of this will be given later (Chap. XII.).

(_b_) _The freezing-point curve pa.s.ses through a maximum_ (Curve II., Fig.

49).

[Ill.u.s.tration: FIG. 51.]

This curve exhibits the greatest degree of contrast to the freezing-point curve which is obtained when the pure components crystallize out. For, since the curve pa.s.ses through a maximum, it is evident that the freezing point of each of the components must be _raised_ by the addition of the other component.

Example.--Very few cases belonging to this type are known. The best example is found in the freezing-point curve of mixtures of _d_- and _l_-carvoxime[272] (C_{10}H_{14}N.OH). The freezing points and melting points of the different mixtures of _d_- and _l_-carvoxime are given in the following table, and represented graphically in Fig. 51:--

---------------+----------------+-----------------+----------------- Per cent. of Per cent. of Freezing point. Melting point.

_d_-carvoxime. _l_-carvoxime. ---------------+----------------+-----------------+----------------- 100 0 72.0 72.0 99 1 72.4 -- 98 2 73.0 -- 95 5 75.4 73.0 90 10 79.0 75.0 80 20 84.6 80.0 70 30 88.2 85.0 60 40 90.4 -- 50 50 91.4 91.4 25 75 86.4 82.0 8 92 77.4 -- 1 99 72.4 -- 0 100 72.0 72.0 ---------------+----------------+-----------------+-----------------