[548] Vide Peters, loc. cit., p. 236.
[549] Ostwald [Lehrbuch d. allgem. Chem., 2d Ed., II, 883 (1893)], first emphasized the fact that potential differences are a measure of oxidizing and reducing powers.
[550] The constant is calculated from the data of Küster and Crotogino on the potential of solutions of iodine in potassium iodide [Z. anorg. Chem., 23, 88 (1900)]. Owing to the formation of complex ions I3−, for which due allowance has not been made in the calculation, and owing to some uncertainty as to the vague definition of the concentration of iodine used, the estimation of the constant can only be considered a rough one. The value given expresses the order of the equilibrium ratio sufficiently well for our present purposes. In a recent paper, Bray and MacKay [J. Am. Chem. Soc., 32, 914 (1910)] have determined the constant for the formation of the complex ion according to I3− ⇄ I2 + I−, which might be used to correct the data of Küster and Crotogino; but in view of other uncertainties and inaccuracies, the correction has not been considered advisable.
Several related methods may be used to calculate the equilibrium constant for [I−]2 : [I2] = K from the data of Küster and Crotogino. Perhaps the simplest method is the following: A solution of iodine ([I] = 1 / 32 normal, and therefore [I2] = 1 / 64 molar) in 1/8 molar potassium iodide, in which, the degree of ionization being taken into account, [I−] = 0.109, was observed to show a potential εI2, I− = +0.860 (the convention as to signs, discussed on p. [261], is used here and the potential, observed against a so-called "calomel electrode," is reduced to the so-called "absolute potential"; cf. Le Blanc, Lehrbuch der Elektrochemie, p. [214]). Now, there must be a certain concentration of iodide-ion, which we will call [C], with which iodine of the above concentration would be directly in equilibrium and would give no potential at all (cf. pp. [261] and 258 in regard to copper). With a change in the concentration of the iodide-ion, a potential would be produced according to εI2, I− = 0.0575 log([C] / [I−]). This relation is of exactly the same nature as that developed for the potential of copper plates, immersed in solutions of cupric-ion of different concentrations (but see footnote 1, p. [261], concerning the sign of the new relation). In the present case, we are dealing with univalent ions, I−, in place of bivalent ions Cu2+, and the factor 0.0575 is used instead of 0.0575 / 2 (see p. [261]). If we insert the observed values, [I−] = 0.109 and ε = 0.860, of the experiment described above, into the equation εI2, I− = 0.0575 log([C] / [I−]) and solve the equation for [C], we find [C] = 1014. That means, 1 / 64 molar iodine would be directly in equilibrium with a concentration of iodide-ion = 1014 (if this value is inserted for [I−] in the logarithmic equation, the potential is found to be 0). For the condition of equilibrium for I2 ⇄ 2 I−, according to [I−]2 : [I2] = K, we have then (1014)2 : (1 / 64) = K = 6.4E29. Similarly, for [I−] = 0.109 and [I2] = 1 / 512 the potential ε = 0.831 is observed, and the equilibrium constant is found to be 5.1E29. When [I−] = 0.109 and [I2] = 1 / 128, the potential is 0.850 and the constant is calculated to be 5.3E29. The mean value for K is 5.6E29. In these calculations, the formation of ions I3−, affecting the values for [I−] and [I2], has not been considered, and there is some doubt whether the concentrations of iodine, given by Küster and Crotogino, do not represent [I2] rather than [I], as assumed in the calculations. If the former be the case, the mean value of the above experiments would be 2.8E29. The value, used in the text, is considered sufficiently accurate for the purposes of this book.
[551] This relation of the equilibrium constant and the solution-tension constants may be deduced in a manner similar to that for the analogous equilibrium constant for the oxidation of zinc by the cupric-ion, as given in footnote 1, on page [267]. The exact value of the equilibrium constant is uncertain, since KI−, Iodine has not yet been determined with a sufficient degree of accuracy; but the value, used, gives the order of the constant sufficiently well for our purposes, especially when it is considered in connection with the constant given below for the same relation, when the chloride-ion is substituted for the iodide-ion.
[552] This is the value of the constant as calculated from the data given by Wilsmore (Z. phys. Chem., 36, 91 (1900)) for the solution-tension of chlorine under atmospheric pressure at 18°. The calculation may be made exactly as in the case of the similar constant for iodine (p. [273]). There must be a concentration of chloride-ion, which we will call [C], with which chlorine, of one atmosphere pressure at 18°, would be directly in equilibrium. The potential of chlorine, against any other concentration of chloride-ion, would be εCl2, Cl− = 0.0575 log([C] / [Cl−]). For [Cl−] = 1, ε is +1.694 (see the table at the end of Chapter XV), and inserting these values in our equation and solving it for [C], we find [C] = 2.88E29. That means, that chlorine, at 18° and of atmospheric pressure, would be in equilibrium with chloride-ion of the concentration given. Since chlorine, at this temperature and pressure, has a concentration of 1 / 23.9 moles (at 18°, one mole is contained in 23.9 liters, instead of in 22.4 liters, at O°), we have for the condition of equilibrium: [Cl−]2 : [Cl2] = (2.88E29)2 : (1 / 23.9) = 2E60. [Cl2] represents, thus, in the calculation of this constant, the concentration of chlorine gas (see Chapter XV concerning gas electrodes) and not the concentration of the dissolved chlorine; the latter, however, is proportional to the gas concentration (Chapter VII).
CHAPTER XV OXIDATION AND REDUCTION. II. OXIDATION BY OXYGEN, PERMANGANATES, ETC.; OXIDATION OF ORGANIC COMPOUNDS
We will turn now to the consideration of the question, how the principles of the theory of electric oxidation and reduction may be applied to the most important oxidizing agent, oxygen, and to such vigorous and common oxidizing agents as permanganates, dichromates, nitric acid, and similar substances.