[33] This term ‹must not be confounded with the term osmotic pressure›, which has been defined on p. 10. [34] See Chapter VII on the law of physical or heterogeneous equilibrium, where the relations are discussed in detail. [35] ‹Z. phys. Chem.›, «5», 175 (1890). [36] ‹Ibid.›, «3», 119 (1889). [37] ‹Phil. Mag.›, «38», 206 (1894). [38] ‹Cf.› van 't Hoff's ‹Lectures on Physical Chemistry›, Vol. II, 40 (1899). [39] The molecules may have different masses in the different conditions, and the principle of the mean kinetic energy would always apply to them as ‹they are›, in the condition under observation, and not as they are in some other condition; any change in mass, in solution, for instance, would show itself in the osmotic pressure measurements (see p. 18), just as it is shown in the measurements of gases, when the gas molecules show a change in composition, as is the case with hydrogen fluoride (H_{2}F_{2} ⇄ 2 HF), nitrogen tetroxide (N_{2}O_{4} ⇄ 2 NO_{2}), phosphorus pentachloride (PCl_{5} ⇄ PCl_{3} + Cl_{2}) and other compounds. [40] The molecular weight of alcohol in dilute aqueous solution is the same (46) as in vapor form. Raoult, ‹Z. phys. Chem.›, «27», 656; Loomis, ‹ibid.›, «32», 592. [41] Nernst, ‹Theoretical Chemistry›, p. 245. [42] This assumption is not made in the rigorous development of the above relations on the basis of the kinetic theory, but it leads to the same net result. [43] Even for gases of ordinary concentration, the introduction of the same correction gives an expression for the relation of pressure and volume, which is more exact than Boyle's law and is used in all exact calculations with gases. [44] One may imagine, first, ‹n› molecules of the solute as a ‹gas›, with the pressure ‹P›_{gas}, in 1 c.c. Then, one may imagine, crudely, the ‹n› molecules of solute, in a free (gas) space of (1 − ‹v›) c.c., in the center of 1 c.c. of the solvent, and exerting by their impacts a pressure ‹P›_{osm.}, against the solvent. According to Boyle's law, we should then have, ‹P›_{gas} × 1 = ‹P›_{osm.} × (1 − ‹v›), and therefore ‹P›_{osm.} = ‹P›_{gas} / (1 − ‹v›). [45] ‹Vide› Nernst, ‹Theoretical Chemistry›, p. 245, for the detailed discussion of this relation. [46] This conclusion is reached more rigorously and more simply by thermodynamic analysis. [47] ‹Lectures on Physical Chemistry›, Part II, p. 35. [48] Rigorous developments of the relations between solute and solvent, for dilute and concentrated solutions, have been made by van der Waals, ‹Z. phys. Chem.›, «5», 133 (1890); van Laar, ‹ibid.›, «15», 457 (1894); G. N. Lewis, ‹J. Am. Chem. Soc.›, «30», 675 (1908), and Washburn, ‹ibid.›, «32», 653 (1910). An admirable review of the theories of osmotic pressure, by Lovelace, will be found in the ‹Am. Chem. J.›, «39», 546 (1908) («Stud.»). [p033] CHAPTER IV