This equilibrium pressure is called the osmotic pressure of the solution, and thermodynamic theory shows that, in an ideal case of perfect separation between solvent and solute, it should have the same value as the pressure which a number of molecules equal to the number of solute molecules in the solution would exert if they could exist as a gas in a space equal to the volume of the solution, provided that the space was large enough (i.e.
Membranes which allow a solvent to pass freely but are impervious to a solute when dissolved in that solvent.
The solubilities of solids may be expressed in terms of the mass of solute which will dissolve in loo grammes of water.
If each molecule of the solute combines with a certain number of molecules of the solvent in such a way as to render them inactive for evaporation, we get a lowering of vapour pressure.
When the solution ceases to be dilute in the thermodynamic sense of the word, that is, when the spheres of influence of the solute particles intersect each other, this reasoning ceases to apply, and the resulting modification of the gas laws as applied to solutions becomes a matter for further investigation, theoretical or experimental.
The result of our consideration, therefore, is that the osmotic pressure of a dilute solution of a volatile solute must have the same value as the gaseous pressure the same number of solute particles would exert if they occupied as gas a volume equal to that of the solution.
If solvent be allowed to enter through a semipermeable wall into an engine cylinder, the work done when the solution within is already dilute will be the same whatever the nature of the interaction between solute and solvent, that is, whatever be the nature of the solvent itself.
In the case of solutions, if the absorption of the solvent is negligible, the effect of increasing the concentration of the absorbing solute is the same as that of increasing the thickness in the same ratio.
It will even be the same in those cases where, with a volatile solute, the presence of a solvent may be dispensed with, and the solute exist in the same volume as a gas.
Artificial membranes are seldom or never perfectly semi-permeable - some leakage of solute nearly always occurs, but the imperfections of actual membranes need no more prevent our use of the ideal conception than the faults of real engines invalidate the theory of ideal thermodynamics founded on the conception of a perfect, reversible, frictionless, heat engine.