The analogy with a perfect gas naturally becomes much greater as the solution becomes more diluted. It then imitates gas in some other properties; the internal work of the variation of volume is nil, and the specific heat is only a function of the temperature. A solution which is diluted by a reversible method is cooled like a gas which expands adiabatically.
[Footnote 17: That is, without receiving or emitting any heat.—ED.]
It must, however, be acknowledged that, in other points, the analogy is much less perfect. The opinion which sees in solution a phenomenon resembling fusion, and which has left an indelible trace in everyday language (we shall always say: to melt sugar in water) is certainly not without foundation. Certain of the reasons which might be invoked to uphold this opinion are too evident to be repeated here, though others more recondite might be quoted. The fact that the internal energy generally becomes independent of the concentration when the dilution reaches even a moderately high value is rather in favour of the hypothesis of fusion.
We must not forget, however, the continuity of the liquid and gaseous states; and we may consider it in an absolute way a question devoid of sense to ask whether in a solution the solute is in the liquid or the gaseous state. It is in the fluid state, and perhaps in conditions opposed to those of a body in the state of a perfect gas. It is known, of course, that in this case the manometrical pressure must be regarded as very great in relation to the internal pressure which, in the characteristic equation, is added to the other. May it not seem possible that in the solution it is, on the contrary, the internal pressure which is dominant, the manometric pressure becoming of no account? The coincidence of the formulas would thus be verified, for all the characteristic equations are symmetrical with regard to these two pressures. From this point of view the osmotic pressure would be considered as the result of an attraction between the solvent and the solute; and it would represent the difference between the internal pressures of the solution and of the pure solvent. These hypotheses are highly interesting, and very suggestive; but from the way in which the facts have been set forth, it will appear, no doubt, that there is no obligation to admit them in order to believe in the legitimacy of the application of thermodynamics to the phenomena of solution.
From the outset Professor Van t’ Hoff was brought to acknowledge that a great number of solutions formed very notable exceptions which were very irregular in appearance. The analogy with gases did not seem to be maintained, for the osmotic pressure had a very different value from that indicated by the theory. Everything, however, came right if one multiplied by a factor, determined according to each case, but greater than unity, the constant of the characteristic formula. Similar divergences were manifested in the delays observed in congelation, and disappeared when subjected to an analogous correction.