Fig. 46Fig. 46.
The graphic representation of such a system is shown in Fig. 46, the ordinates being the pressures of the gas, and the abscissæ 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 secondpc-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 isunivariant, 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 thepc-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.
Fig. 47Fig.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 homogeneous 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 Pd2H. 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 classification 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 beenaccurately 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 passes gradually and continuously into an almost horizontal but slightly ascending middle part, which in turn passes 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.
Fig. 48Fig. 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 Pd2H 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 passes into the terminal portion of the curve.Such a behaviour would, however, agree with the assumption 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 assumption 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 passage 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 assumed that the dissolved substance crystallized out along with the solid solvent; and he showed how this would account for thedeviations from the law of the depression of the freezing point, which had been developed on the assumption 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 classes. The differences, however, in the behaviour of the two groups are of a quantitative 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 classes 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 classified; and examples of the different cases predicted by the Phase Rule have also been obtained by experiment.
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 abscissæ 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 thefreezing pointof the mixture, and the temperature at which the solid solution just begins to liquefy will be called themelting pointof 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]
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) constitutes 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.
Fig. 49Fig.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 andβ-naphthol.[269]The addition ofβ-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 ofα-monochlorocinnamic aldehyde andα-monobromocinnamic aldehyde[270]lies above thestraight line joining the melting points of the pure components (31.22° and 69.56°), as is evident from the following table:—
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 illustration 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,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 pointx(Fig. 50), is allowed to cool, the system will pass along the linexx′. At the temperature of the pointa, mixed crystals will be deposited, the composition of which will be that represented byb. 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 pass along the curvead, the composition of the solid solution at the same time passing along the curvebc; at the pointcthe liquid will solidify completely.[271]
Fig. 50Fig.50.
Conversely, if mixed crystals of the composition and at the temperaturex′are heated, liquefaction will begin at the temperaturec, yielding a liquid of the compositiond. On continuing to add heat, the temperature of the mass will rise, more of the solid will melt, and the composition of the two phases will change as represented by the curvesdaandcb. When the temperature has risen toa, complete liquefaction will have occurred. The process of solidification or of liquefaction is therefore extended over a temperature intervalac.
Even when the freezing-point curve is a straight line joiningthe 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 passes through a maximum(Curve II., Fig. 49).
Fig. 51Fig.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 passes through a maximum, it is evident that the freezing point of each of the components must beraisedby 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 ofd- andl-carvoxime[272](C10H14N.OH). The freezing points and melting points of the different mixtures ofd- andl-carvoxime are given in the following table, and represented graphically in Fig. 51:—
In this figure, the melting-point curve,i.e.the temperature-concentration curve for the mixed crystals, is represented by the lower curve. Since the addition of the lævo-form to the dextro-form raises the melting point of the latter, the concentration of the lævo-form (on the right-hand branch of the curve) must, in accordance with the rule given, be greater in the solid phase than in the liquid. Similarly, since addition of the dextro-form raises the melting point of the lævo-form, the solid phase (on the left-hand branch of the curve) must be richer in dextro- than in lævo-carvoxime. At the maximum point, the melting-point and freezing-point curves touch; at this point, therefore, the composition of the solid and liquid phases must be identical. It is evident, therefore, that at the maximum point the liquid will solidify, or the solid will liquefy completely without change of temperature; and, accordingly, mixed crystals of the composition represented by the maximum point will exhibit a definite melting point, and will in this respect behave like a simple substance.
(c)The freezing-point curve passes through a minimum(Curve III., Fig. 49).
In this case, as in the case of those systems where the pure components are deposited, a minimum freezing point is obtained. In the latter case, however, there are two freezing-point curves which intersect at a eutectic point; in the case where mixed crystals are formed there is only one continuous curve. On one side of the minimum point the liquid phase contains relatively more, on the other side relatively less, of the one component than does the solid phase; while at the minimum point the composition of the two phases is the same. At this point, therefore, complete solidification or complete liquefaction will occur without change of temperature, and the mixed crystals will accordingly exhibit a definite melting point.
Fig. 52Fig.52.
Example.—As an example of this there may be taken the mixed crystals of mercuric bromide and iodide.[273]Mercuric bromide melts at 236.5°, and mercuric iodide at 255.4°. The mixed crystal of definite constant melting point (minimum point) contains 59 mols. per cent. of mercuric bromide, the melting point being 216.1°.
The numerical data are contained in the following table, and represented graphically in Fig. 52:—
Fig. 53Fig.53.
Fractional Crystallization of Mixed Crystals.—With the help of the diagrams already given it will be possible to predict what will be the result of the fractional crystallization of a fused mixture of two substances which can form mixed crystals. Suppose, for example, a fused mixture of the compositionx(Fig. 53) is cooled down; then, as we have already seen, when the temperature has fallen toa, mixed crystals of composition,b, are deposited. If the temperature is allowed to falltox′, and the solid then separated from the liquid, the mixed crystals so obtained will have the composition represented bye. If, now, the mixed crystalseare completely fused and the fused mass allowed to cool, separation of solid will occur when the temperature has fallen to the pointf. The mixed crystals which are deposited have now the composition represented byg, i.e.they are richer in B than the original mixed crystals. By repeating this process, the composition of the successive crops of mixed crystals which are obtained approximates more and more to that of the pure component B, while, on the other hand, the composition of the liquid phase produced tends to that of pure A. By a systematic and methodical repetition of the process of fractional crystallization, therefore, apracticallycomplete separation of the components can be effected; a perfect separation is theoretically impossible.
From this it will be readily understood that in the case of substances the freezing point of which passes through a maximum, fractional crystallization will ultimately lead to mixed crystals having the composition of the maximum point, while the liquid phase will more and more assume the composition of either pure A or pure B, according as the initial composition was on the A side or the B side of the maximum point. In those cases, however, where the curves exhibit a minimum, the solid phase which separates out will ultimately be one of the pure components, while a liquid phase will finally be obtained which has the composition of the minimum point.
II.—The Two Components do not form a Continuous Series of Mixed Crystals.
This case corresponds to that of the partial miscibility of liquids. The solid component A can "dissolve" the component B until the concentration of the latter in the mixed crystal has reached a certain value. Addition of a further amount of B will not alter the composition of the mixed crystal, but there will be formed a second solid phase consistingof a solution of A in B. At this point the four phases, mixed crystals containing excess of A, mixed crystals containing excess of B, liquid solution, vapour, can coexist; this will therefore be an invariant point. The temperature-concentration curves will therefore no longer be continuous, but will exhibit a break or discontinuity at the point at which the invariant system is formed.
(a)The freezing-point curve exhibits a transition point(Curve I., Fig. 54).
As is evident from the figure, addition of B raises the melting point of A, and, in accordance with the rule previously given, the concentration of B in the mixed crystals will be greater than in the solution. This is represented in the figure by the dotted curve AD. On the other hand, addition of A lowers the melting point of B, and the two curves BC and BE are obtained for the liquid and solid phases respectively. At the temperature of the line CDE the liquid solution of the composition represented by C is in equilibrium with the two different mixed crystals represented by D and E. At this temperature, therefore, thetc-curve for the solid phase exhibits a discontinuity; and, since the solid phase undergoes change at this point, the freezing-point curve must show a break (p.111).
Fig. 54Fig. 54.
Example.—Curves of the form given in Fig. 54 I. have been found experimentally in the case of silver nitrate and sodium nitrate.[274]The following table contains the numerical data, which are also represented graphically in Fig. 55:—
The temperature of the transition point is 217.5°; at this point the liquid contains 19.5, and the two conjugate solid solutions 26 and 38 molecules of sodium nitrate per cent. respectively.
Fig. 55Fig.55.
Fig. 56Fig.56.
(b)The freezing-point curve exhibits a eutectic point(Curve II., Fig. 54).
In this case the freezing point of each of the components is lowered by the addition of the other, until at last a point is reached at which the liquid solution solidifies to a mixture or conglomerate of two mixed crystals.
Examples.—Curves belonging to this class have been obtained in the case of potassium and thallium nitrates[275]and of naphthalene and monochloracetic acid.[276]The data for the latter are given in the following table and represented in Fig. 56:—
At the eutectic point the liquid solution is in equilibrium with two different mixed crystals the composition of which is represented by D and E respectively. If, therefore, a fused mixture containing the two components A and B in the proportions represented by C is cooled down, it will, when the temperature has reached the point C, solidify completely to aconglomerateof mixed crystals, D and E.