[A] The value of the constant, as given, is only an approximate estimation (p. [273]).
The significance of the constants is indicated by the ratios given in the table. The relation of these constants to those given in the first table may be seen from the following illustration. For hydrogen we have H2 ⇄ 2 H+. The first table tells us that hydrogen, at 18° under atmospheric pressure, is in equilibrium with its ion when the concentration of hydrogen-ion is 1.52E−5 (under KIon). Now, a mole of hydrogen at 18° occupies 22.4 × 291 / 273 = 23.9 liters under atmospheric pressure, and its concentration (per liter) is therefore 1 / 23.9 mole. Then equilibrium exists, when [H2] = 1 / 23.9 and [H+] = 1.52E−5 and Kequil. = [H+]2 : [H2] = (1.52E−5)2 × 23.9 = 5.6E−9.
Chapter XV Footnotes
[553] These constants are calculated from data given in Wilsmore's tables (loc. cit.) on the solution tension of hydrogen. Hydrogen, at 18° under one atmosphere pressure, produces a potential of εH2, H+ = +0.277 (see p. [261], in regard to the sign) against a solution containing hydrogen-ion in a concentration [H+] = 1 (see the table at the end of this chapter). Now, there must be some concentration of hydrogen-ion, which we will call [C], with which hydrogen at 18° and 760 mm. pressure is directly in equilibrium, with the potential 0. For any concentration of hydrogen-ion [H+], other than [C], a potential is produced according to εH2, H+ = 0.0575 log([H+] / [C]). If we insert into this equation the values [H+] = 1 and the potential ε = +0.277, and if we solve the equation for [C], we find [C] = 1.52E−5. That is the concentration of H+, with which hydrogen of one atmosphere pressure at 18° is directly in equilibrium. Since under these conditions of temperature and pressure [H2] = 1 / 23.9 mole, we have for the condition of equilibrium [H+]2 / [H2] = K : (1.52E−5)2 : (1 / 23.9) = 5.55E−9 = K.
[554] Experimentally the relations for an "oxygen electrode" are much more complicated than for a hydrogen electrode, as a result, apparently, of the oxidation of the metal (e.g. platinum), with the aid of which the electrode is prepared. For a critical review and summary of the more recent results on this point, vide Schoch, J. phys. Chem., 14, 665 (1910). For the purposes of this book it will be sufficient to limit our discussion to the behavior of an ideal oxygen electrode.
[555] The bivalent oxygen ions, O2−, combine with hydrogen ions (formed, for instance, by the ionization of water) and form the more stable hydroxide ions (p. [246]): O2− + H+ + HO− ⇄ 2 HO−, or simply, O2− + H+ ⇄ HO−. Then, [O2−] × [H+] / [HO−] = k and [O2−] = k × [HO−] / [H+]. But since we have [H+] × [HO−] = KHOH for the ionization of water (p. [176]), we also have:
[H+] = KHOH / [HO−] and [O2−] = (k / KHOH) × [HO−]2.
By substituting this value for the concentration [O2−] of the oxide-ion in equation (1), equation (2) is obtained. The constant K2 includes then the constants k and KHOH.
[556] The constants are calculated from the estimated potential of the oxygen-hydrogen cell, +1.231 volt, at 18°. (Vide G. N. Lewis, Z. phys. Chem., 55, 465 (1906); Nernst and Wartenberg, ibid., 56, 534 (1906); Brönsted, ibid., 65, 91 (1908); and a summary and discussion by Schoch, loc. cit.) At 18° oxygen, under one atmosphere pressure, gives an estimated potential εO2, HO− = +1.508 against an acid solution, in which the concentration of the hydrogen-ion [H+] = 1 (see the table at the end of this chapter). Since at 18° [H+] × [HO−] = 0.81E−14, the value for [HO−] in this acid solution is 0.81E−14. Now, for oxygen, at 18° and 760 mm., there must be some concentration of hydroxide-ion, which we will call [C], at which the tendency of the oxygen to ionize is exactly balanced by the tendency of the hydroxide-ion to form oxygen—at this point the potential is 0. For any concentration [HO−] of the hydroxide-ion, other than [C], a potential will exist εO2, HO− = 0.0575 log([C] / [HO−]). Since for [HO−] = 0.81E−14, we have a potential εO2, HO− = +1.508, these values can be introduced into the equation and the latter solved for [C]. We find thus [C] = 1.36E12, and oxygen, at 18° and 760 mm. pressure, would be directly in equilibrium with a solution in which [HO−] = 1.36E12. At 18° and 760 mm. pressure a liter of oxygen contains 1 / 23.9 mole, and thus we have for the condition of equilibrium [HO−]4 : [O2] = K : (1.36E12)4 : (1 / 23.9) = 8.2E49 = K.
[557] The most convenient form of electrode for this purpose consists (see Fig. 14) of a cylinder (about one inch long) of platinum gauze, which is fused to a glass tube and connected with a wire leading through the tube to some mercury, held in a small branch tube, fused into the main tube near its upper end. The gas is easily conducted to the platinum gauze electrode through such a tube. The cylinder of platinum gauze may be made by joining the ends of rolled gauze with pieces of molten glass. It is coated with platinum black.