litres, and the temperature in absolute degrees, the ‹gas-constant› ‹R› = ‹P› ‹V› / ‹T› = 1 × 22.4 / 273 = 0.082. FOOTNOTES: [3] Even after a solution of uniform concentration of the solute is formed, the tendency toward diffusion, and the diffusion itself, and the resulting pressure must still persist. But a state of ‹dynamic› (or flowing) ‹equilibrium› must be considered now to exist, the loss caused by the moving away of the solute, from a given part of the solution, being balanced by the diffusion (into that part) of the solute from the neighboring parts. Whether one ascribes the diffusion to inherent molecular velocities of the solute, or to an attraction between solvent and solute, the discrete particles of the solute in a solution of uniform concentration will continue to have such inherent velocities (Chap. III), and will also continue to be surrounded by pure solvent, exactly as in solutions of unequal concentrations, where the diffusion may be observed, because the net result, in such a case, is a one-sided action. [4] This again holds equally for the solvent. [5] See below. [6] At the same time, the change is also in the direction of an expansion of the ‹solvent in the solution›. The two changes are not opposed to each other, but supplementary. [7] ‹Am. Chem. J.›, «28», 1 (1902); «40», 266, 325 (1908) («Stud.»). [8] ‹Am. Chem. J.›, «34», 1 (1905); «36», 39 (1906); «37», 324, 425, 558 (1907); «38», 175 (1907). [9] The exact concentration of the solution at the point of equilibrium is determined by subsequent analysis. [10] ‹Cf.› Smith's ‹Inorganic Chemistry›, p. 287. [11] Berkeley and Hartley, ‹Phil. Trans. Roy. Soc.› A, «206», 481 (1906). [12] When appreciable ‹heat of dilution› is shown by a solution, some chemical change, resulting from dilution, is indicated (such as, dissociation of the solute, hydration, hydrolysis, etc.). In such a case, the Avogadro-van 't Hoff principle holds for each concentration for its actual composition, and the principle may often be used to determine the extent of the chemical change produced by dilution. But then the osmotic pressure will not obey Boyle's and Gay-Lussac's laws. The same exception applies also to gases which undergo chemical changes, as the result of dilution or change of temperature. In the case, for instance, of nitrogen tetroxide, which dissociates according to N_{2}O_{4} ⇄ 2 NO_{2}, the extent of the dissociation varies with changes of concentration (pressure) and of temperature, and the gas does not obey the laws of Gay-Lussac and of Boyle. In regard to the rôle of heat of dilution in connection with osmotic pressure, see Bancroft, ‹J. Phys. Chem.›, «10», 319 (1906). [13] See p. «15» for a more rigorous statement concerning the volume. ‹Cf.› Morse and Frazer, ‹Am. Chem. J.›, «34», 1 (1905).