for this effect, ‹P› = ‹n› / 3 × ‹m› ‹u›^2 / (1 − ‹b›), where ‹b› represents the volume actually occupied by the molecules in 1 c.c. of the gas.[43] [Illustration: FIG. 7.] Now, for solute molecules, the "free space" of movement, as we may call it, is, similarly, very considerably reduced by the presence [p031] of the solvent, and the reduction of this free space, as Nernst has shown, will have the same effect on the pressure produced against unit surface of the solvent by the bombardment of the solvent by the solute, as the reduction of the free space has on the gas pressure when a gas is strongly compressed. The resulting pressure on unit surface of the solution must thus be increased, from the pressure ‹P›_{gas}, which would be exerted by the solute against the walls of a vessel, if it were present as a gas of the same concentration, at the same temperature, to ‹P›_{gas} / (1 − ‹v›), where ‹v› represents the real volume occupied by the solvent and (1 − ‹v›) the ‹free space› for the solute molecules ‹in unit volume› of solution.[44] If osmotic pressure is the result of such a bombardment of the solvent by the molecules of the solute, one might, therefore, expect to find the osmotic pressure ‹very much greater› than the gas pressure of the same substance in the same volume at the same temperature. However, in all the ‹experimental determinations› (by means of semipermeable membrane, vapor pressure, boiling-point and freezing-point measurements) of the osmotic pressure as defined on p. 10, this ‹corrective factor cancels› out again.[45] ‹According to the kinetic theory›, the osmotic pressure of a substance in ‹dilute solution should, consequently, be found by experiment to be equal to the gas pressure which a gas, of the same molecular concentration, would exert at the same temperature›.[46] We find thus that the significant coincidence between the osmotic pressure of a substance in dilute solution, as defined and measured according to van 't Hoff, and the gas pressure which the substance would exert, if it were present as a gas in the same volume and at the same temperature, is in agreement with the fundamental assumptions of the kinetic theory. This theory, consequently, gives us an adequate theoretical explanation of [p032] osmotic pressure, as it does of gas pressure. As van 't Hoff says,[47] "if the osmotic pressure follows Gay-Lussac's law and is proportional to the absolute temperature, then, like gas pressure, it will become zero at 0° absolute temperature and will vanish when molecular movements come to rest. It is therefore natural to look for the cause of osmotic pressure in kinetic phenomena and not in attractions."[48] FOOTNOTES: [29] L'Hermite, ‹Compt. rend.›, «39», 1177 (1854); van 't Hoff, ‹Lectures on Physical Chemistry›, ‹Part II›, p. 37. [30] Nernst, ‹Theoretical Chemistry›, p. 103. [31] Van 't Hoff, ‹Lectures on Physical Chemistry, Part II›, p. 37. [32] ‹J. Phys. Chem.›, «10», 141 (1906).