If there really exist partitions permeable to one body and impermeable to another, it may be imagined that the homogeneous mixture of these two bodies might be effected in the converse way. It can be easily conceived, in fact, that by the aid of osmotic pressure it would be possible, for example, to dilute or concentrate a solution by driving through the partition in one direction or another a certain quantity of the solvent by means of a pressure kept equal to the osmotic pressure. This is the important fact which Professor Van t' Hoff perceived. The existence of such a wall in all possible cases evidently remains only a very legitimate hypothesis,—a fact which ought not to be concealed.
Relying solely on this postulate, Professor Van t' Hoff easily established, by the most correct method, certain properties of the solutions of gases in a volatile liquid, or of non-volatile bodies in a volatile liquid. To state precisely the other relations, we must admit, in addition, the experimental laws discovered by Pfeffer. But without any hypothesis it becomes possible to demonstrate the laws of Raoult on the lowering of the vapour-tension and of the freezing point of solutions, and also the ratio which connects the heat of fusion with this decrease.
These considerable results can evidently be invoked as a posteriori proofs of the exactitude of the experimental laws of osmosis. They are not, however, the only ones that Professor Van t' Hoff has obtained by the same method. This illustrious scholar was thus able to find anew Guldberg and Waage's law on chemical equilibrium at a constant temperature, and to show how the position of the equilibrium changes when the temperature happens to change.
If now we state, in conformity with the laws of Pfeffer, that the product of the osmotic pressure by the volume of the solution is equal to the absolute temperature multiplied by a coefficient, and then look for the numerical figure of this latter in a solution of sugar, for instance, we find that this value is the same as that of the analogous coefficient of the characteristic equation of a perfect gas. There is in this a coincidence which has also been utilized in the preceding thermodynamic calculations. It may be purely fortuitous, but we can hardly refrain from finding in it a physical meaning.
Professor Van t'Hoff has considered this coincidence a demonstration that there exists a strong analogy between a body in solution and a gas; as a matter of fact, it may seem that, in a solution, the distance between the molecules becomes comparable to the molecular distances met with in gases, and that the molecule acquires the same degree of liberty and the same simplicity in both phenomena. In that case it seems probable that solutions will be subject to laws independent of the chemical nature of the dissolved molecule and comparable to the laws governing gases, while if we adopt the kinetic image for the gas, we shall be led to represent to ourselves in a similar way the phenomena which manifest themselves in a solution. Osmotic pressure will then appear to be due to the shock of the dissolved molecules against the membrane. It will come from one side of this partition to superpose itself on the hydrostatic pressure, which latter must have the same value on both sides.
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. [17]
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.
§ 4. ELECTROLYTIC DISSOCIATION
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.