[331] From equation (I) we obtain directly, by the application of a simple mathematical transformation, that [NH_{3}] + [NH_{4}OH] / [NH_{4}OH] = ‹k›_{NH_{3}} + 1 = ‹k′›, and, therefore, [NH_{4}OH] = [NH_{3}] + [NH_{4}OH] / ‹k′›. Inserting this value for [NH_{4}OH] in equation (II) and transferring ‹k′›, we have [NH_{4}^{+}] × [HO^{−}] / ([NH_{3}] + [NH_{4}OH]) = ‹k›_{base} / ‹k′› = K. [332] Water of crystallization, found in many of the precipitates used in qualitative analysis, will, as a rule, be indicated only in the formulas used in Part III, in the study of the reactions of ions. [333] See Part III as to the method of vaporizing magnesium. [334] ‹Cf.› Findlay, ‹Z. phys. Chem.›, «34», 409 (1900). [335] The solubility of barium sulphate at 18°, according to the table, is 0.0023 / 233, or 1E−5 mole per liter, and the salt may be considered completely ionized at this dilution. [336] The solubility (see the table) is 0.114 / 183.6, or 6.2E−4 mole per liter, 84% of which is ionized (according to conductivity determinations, Kohlrausch and Holborn, ‹loc. cit.›, p. 200). Hence [Sr^{2+}] = [SO_{4}^{2−}] = 0.00062 × 0.84 = 0.0005. [337] To establish equilibrium, prolonged "digesting" is sometimes required. Double salts, solid solutions and mechanical enclosures are liable to interfere with the completeness of such separations by fractional precipitation. Resolution and reprecipitation will then usually effect a sufficiently accurate separation for most purposes. On account of the possibility of such complications, the conditions for a successful separation, within limits such as those described in the text, must in all cases be investigated. [338] See the table at the end of Part IV. [339] The salt may be considered completely ionized at this dilution. Each molecule of silver chromate forms two silver ions when it is ionized. See p. 141 in regard to the form the solubility-product takes in the case of a salt of this type. [340] The complication, resulting from the hydrolysis of the chromate, is not included in this calculation. [341] ‹Cf.› Findlay, ‹loc. cit.› [342] Even Guldberg and Waage considered the ‹active› mass to be the fundamental factor and simply considered the total concentrations to be proportional to the "active masses," since they had no means of determining the proportion of "active" substances in the total concentrations. [343] See Nernst, ‹Theoretical Chemistry›, p. 533, for a fuller discussion of the relations between the new and the old views on this subject. [344] Dietrich and Wöhler, ‹Z. anorg. Chem.›, «34», 194 (1903). [345] On account of the formation of an ammonium salt in the reaction. [346] Loven, ‹Z. Anorg. Chem.›, «11», 404 (1896); Herz and Muks, ‹ibid.›, «38», 138 (1904).