On Osmotic Pressure Against an Ideal Semipermeable Membrane¹

Abstract

To approach the subject of osmotic pressure against an ideal impermeable membrane by the easiest way, consider first a vessel filled with any particular fluid divided into two parts, A and B, by an ideal sur face, MM. Let a certain number of individual mole cules of the fluid in A, any one of which we shall call D (the dissolved substance), be endowed with the property that they cannot cross the surface MM (the semi-permeable membrane); but let them continue to be in other respects exactly similar to every other molecule of the fluid in A, and to all the molecules of the fluid in B, any one of which we shall call S (the solvent), each of which can freely cross the membrane. Suppose now the containing vessel and the dividing membrane all perfectly rigid.² Let the apparatus be left to itself for so long time that no further change is per ceptible in the progress towards final equilibrium of temperature and pressure. The pressures in A and B will be exactly the same as they would be with the same densities of the fluid if MM were perfectly impermeable, and all the molecules of the fluid were homogeneous in all qualities; and MM will be pressed on one side only, the side next A, with a force equal to the excess of the pressure in A above the pressure in B, and due solely to the impacts of D molecules striking it and rebounding from it.