Demonstration of the Nature of Osmotic Pressure Using a Mechanical Model

(With 3 figures in the text.)

Ya. I. Mikhailenko.

1. If into an airless space there is introduced some volume of a substance in the solid, liquid, or gaseous state, then the separate masses making up this volume will begin to move from places of greater concentration to places of lesser concentration, the result of which will be an increase in the volume of the substance.

In order to stop this motion, or, in other words, to fix for the substance some definite volume, forces equal and opposite to the forces moving the masses must be applied to the masses making up the substance. The simplest way to accomplish this is to enclose the substance with walls impermeable to this substance and to apply forces to these walls. When equilibrium is reached, the space bounded by the impermeable walls will be filled uniformly by the substance, and the impermeable walls bounding the substance will experience at every point a definite pressure. This pressure, which may in general be called the pressure of diffusion, here bears the name of the pressure of a gas or vapor.

2. If into a space filled with a liquid there is introduced some volume of a solid nonvolatile body, then here too there begins a motion of the masses of the solid body in the direction from places of greater concentration of the substance to places of lesser concentration, i.e., likewise in such a direction that the volume occupied by the body will increase.

In order to stop the motion of these masses, it is evident that here too forces equal and opposite to the moving forces must be applied to them. This is what will happen when the moving masses reach the boundary of the liquid. Since, by hypothesis, the body is soluble only in the liquid, the boundaries of the liquid are for it impermeable walls. The moving masses of the dissolved body will come up against these walls and will press upon them. This pressure of diffusion of the substance bears the name of the osmotic pressure of dissolved bodies.

3. Thus, when a solution is in an ordinary vessel (i.e., in a vessel with walls impermeable to the dissolved body)

and the solvent), under the pressure of its saturated vapor, then the dissolved substance is enclosed as though in a vessel whose walls are formed by an infinitely thin layer of liquid, impermeable to the dissolved substance. The osmotic pressure of the dissolved substance on these walls is balanced by the elastic forces arising in these walls.

The solvent is thus under the action of the osmotic forces of the dissolved substance, which act from within outward, i.e., they stretch the solvent. These forces have changed the properties of the solvent in the solution and the lowering, as compared with the pure solvent, of the vapor pressure, the freezing point, the density, etc., are the result of the action of these forces on the solvent.

1. If the solution is in an ordinary vessel, under an external pressure (compressing the liquid) equal to the osmotic pressure of the dissolved substance, then the osmotic pressure of the dissolved substance is balanced by this pressure.

The solvent of the solution is no longer stretched. Its properties are now identical with those of the pure solvent.

The pressure by which the solution must be compressed in order that its properties become identical with those of the pure solvent—for example, in order that the vapor pressure of the solution rise to the value of the vapor pressure of the pure solvent—will be equal to the osmotic pressure of the dissolved substance.

1. If the solution fills a vessel with walls permeable to the solvent but impermeable to the dissolved substance (Pfeffer’s cell), and the vessel itself is placed in a medium of pure solvent, then at the boundary between the solution and the pure solvent masses of solvent meet: some are under the action of the osmotic forces of the dissolved substance, others are not. And, since the transfer of masses of solvent to one side or the other of the boundary is free, this transfer begins, as always, in the direction from the higher concentrations of substance toward the lower ones, i.e., a current of pure solvent is directed into Pfeffer’s cell. Here the same thing occurs as is observed when the partition separating two masses of gas compressed to unequal degrees is removed. The flow of solvent into the cell will cease when the spatial concentrations of the solvent on the two sides of the boundary become equal. Now the osmotic pressure of the dissolved substance, because it is impossible to find a point of application for the force, cannot be balanced by the elastic forces of the solvent—it will manifest itself as a pressure on the semipermeable walls—

of the vessel, and, if equilibrium is reached, it will be balanced by the elastic forces of the walls of the vessel or by a load placed upon the movable piston closing the cell, if there is one.

1. These relations are conveniently demonstrated on the following mechanical model, whose construction is clear from the figures (1, 2, 3). The springs represent the dissolved substance—which is thus compared with an unfolding spring. Water is represented in the model by a rubber band (for example, a rubber tube), which, by means of rings attached to the rubber band and to studs driven into the frame of the model, may, as desired, be fastened or left unfastened.

In order to fix the spring—the dissolved substance—a definite volume, it is necessary to apply to the spring a force equal and opposite to the force unfolding the spring.

In Fig. (1) the spring is restrained from unfolding by the elastic forces of the rubber band, which is fastened. The rubber band is stretched (its stretch is deliberately exaggerated).

Fig. 1.

This is the scheme of forces for the case when the solution is in a vessel with impermeable walls under the pressure of its vapor.

In Fig. (2) the spring is restrained from unfolding by a load. The rubber band remains fastened. But now it is not stretched.

Fig. 2

This is the scheme of forces for the case when the solution is in a vessel with impermeable walls under external pressure upon the surface of separation

between the liquid and its vapor, equal to the osmotic pressure of the dissolved substance.

In Fig. (3) the spring is kept from expanding by a weight, but the rubber band is not fixed. It is now not stretched, and part of it is drawn into the frame (representing the volume of the solution).

This is the scheme of forces for the case when the solution is in Pfeffer’s cell, immersed in pure solvent.

Fig. 3.

The volume of the solution in case (2) is obviously smaller than in cases (1) and (3). The weight (osmotic pressure) in case (2) is obviously greater than in case (3).

The material for the view set forth above regarding the scheme of forces in the experiment on osmotic pressure was provided by the articles: N. N. Schiller, Zh. R. F. Kh. O. 29, 7. 1897; Wied. Ann. 53, 396. 1894; 60, 755. 1897. Ya. I. Mikhailenko. On the elasticity of the vapor of solutions. Kiev Univ. Izv. 1904. On the question of the relation between the partial density of the solvent in the solution and the vapor pressure of the solution. Kiev. 1905.

Tomsk, October 23, 1909.

Ya. Mikhailenko.