Solid alloys may be classed like liquid ones. Two metals or more dissolve one into the other, and form a solid solution quite analogous to the liquid solution. But the study of these solid solutions is rendered singularly difficult by the fact that the equilibrium so rapidly reached in the case of liquids in this case takes days and, in certain cases, perhaps even centuries to become established.

CHAPTER V

SOLUTIONS AND ELECTROLYTIC

DISSOCIATION

§ 1. SOLUTION

VAPORIZATION and fusion are not the only means by which the physical state of a body may be changed without modifying its chemical constitution. From the most remote periods solution has also been known and studied, but only in the last twenty years have we obtained other than empirical information regarding this phenomenon.

It is natural to employ here also the methods which have allowed us to penetrate into the knowledge of other transformations. The problem of solution may be approached by way of thermodynamics and of the hypotheses of kinetics.

As long ago as 1858, Kirchhoff, by attributing to saline solutions—that is to say, to mixtures of water and a non-volatile liquid like sulphuric acid—the properties of internal energy, discovered a relation between the quantity of heat given out on the

addition of a certain quantity of water to a solution and the variations to which condensation and temperature subject the vapour-tension of the solution. He calculated for this purpose the variations of energy which are produced when passing from one state to another by two different series of transformations; and, by comparing the two expressions thus obtained, he established a relation between the various elements of the phenomenon. But, for a long time afterwards, the question made little progress, because there seemed to be hardly any means of introducing into this study the second principle of thermodynamics.1 It was the memoir of Gibbs which at last opened out this rich domain and enabled it to be rationally exploited. As early as 1886, M. Duhem showed that the theory of the thermodynamic potential furnished precise information on solutions or liquid mixtures. He thus discovered over again the famous law on the lowering

1 The "second principle" referred to has been thus enunciated: "In every engine that produces work there is a fall of temperature, and the maximum output of a perfect engine—i.e. the ratio between the heat consumed in work and the heat supplied-depends only on the extreme temperatures between which the fluid is evolved."-Demanet, Notes de Physique Expérimentale, Louvain, 1905, fasc. 2, p. 147. Clausius put it in a negative form, as thus: No engine can of itself, without the aid of external agency, transfer heat from a body at low temperature to a body at a high temperature. Cf. Ganot's Physics, 17th English edition, § 508.-ED.

of the congelation temperature of solvents which had just been established by M. Raoult after a long series of now classic researches.

In the minds of many persons, however, grave doubts persisted. Solution appeared to be an essentially irreversible phenomenon. It was therefore, in all strictness, impossible to calculate the entropy of a solution, and consequently to be certain of the value of the thermodynamic potential. The objection would be serious even to-day, and, in calculations, what is called the paradox of Gibbs would be an obstacle.

We should not hesitate, however, to apply the Phase Law to solutions, and this law already gives us the key to a certain number of facts. It puts in evidence, for example, the part played by the eutectic point that is to say, the point at which (to keep to the simple case in which we have to do with two bodies only, the solvent and the solute) the solution is in equilibrium at once with the two possible solids, the dissolved body and the solvent solidified. The knowledge of this point explains the properties of refrigerating mixtures, and it is also one of the most useful for the theory of alloys. The scruples of physicists ought to have been removed on the memorable occasion when Professor Van t' Hoff demonstrated that solution can operate reversibly by reason of the phenomena of osmosis. But the experiment can only succeed in very rare cases;

and, on the other hand, Professor Van t' Hoff was naturally led to another very bold conception. He regarded the molecule of the dissolved body as a gaseous one, and assimilated solution, not as had hitherto been the rule, to fusion, but to a kind of vaporization. Naturally his ideas were not immediately accepted by the scholars most closely identified with the classic tradition. It may perhaps not be without use to examine here the principles of Professor Van t' Hoff's theory.

§ 2. OSMOSIS

Osmosis, or diffusion through a septum, is a phenomenon which has been known for some time. The discovery of it is attributed to the Abbé Nollet, who is supposed to have observed it in 1748, during some "researches on liquids in ebullition." A classic experiment by Dutrochet, effected about 1830, makes this phenomenon clear. Into pure water is plunged the lower part of a vertical tube containing pure alcohol, open at the top and closed at the bottom by a membrane, such as a pig's bladder, without any visible perforation. In a very short time it will be found, by means of an areometer for instance, that the water outside contains alcohol, while the alcohol of the tube, pure at first, is now diluted. Two currents have therefore passed through the membrane, one of water from the outside to the inside, and one of alcohol in the converse