Sec. 3.  APPLICATION TO THE THEORY OF SOLUTION

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.