[418] The value of the solubility-product constant for cupric sulphide, at 25°, was determined by Knox (‹loc. cit.›): [Cu^{2+}] × [S^{2−}] = 1.2E−42, corresponding to a concentration of 1.1E−21 of cupric-ion. Mercuric sulphide was found even less soluble: [Hg^{2+}] × [S^{2−}] = 2.8E−54, and its behavior agrees with such a relation (Lab. Manual, p. 50, § 2). The solubility-product constant for lead sulphide, which resembles cadmium sulphide in the fact that a large excess of acid prevents its precipitation, was found to be [Pb^{2+}] × [S^{2−}] = 2.6E−15, the constant being about 10^{27} times as large as the constant for cupric sulphide. This value for the solubility-product constant for lead sulphide must either be considerably larger than the true value or lead must be easily precipitated as a hydrosulphide, Pb(SH)_{2}, since solutions in which the product of the ion concentrations, [Pb^{2+}] × [S^{2−}], is very much smaller than the constant given, readily precipitate lead sulphide. Thus Noyes and Bray [‹J. Am. Chem. Soc.›, «29», 137 (1907)] report it possible to precipitate 1 to 2 milligrams of lead-ion in 100 c.c. of solution (say [Pb^{2+}] = 1E−4) with hydrogen sulphide in the presence of 4 c.c. of hydrochloric acid (sp. gr. 1.12), for which, approximately, [H^{+}] = 0.25. Then (equation (IV), p. 201) [S^{2−}] = (1.1E−23) / (0.25)^2 = 1.8E−22, and [Pb^{2+}] × [S^{2−}] = 1E−4 × 1.8E−22 = 1.8E−26, which is a much lower value than that given by Knox, and which still is not claimed to represent the limit of insolubility. Experiments, made in this laboratory, confirm this result and show further, that lead-ion in a concentration of 1E−5 is precipitated in the presence of 0.25 molar hydrochloric acid ([H^{+}] = 0.22). Then [S^{2−}] = 2.3E−22 and [Pb^{2+}] × [S^{2−}] = 2.3E−22 × 10^{−5} = 2E−27, which does not yet express the limit of insolubility. [419] The fractions are not prepared in the lecture, but the first fraction is kept suspended in part of the solution of the two sulphates and may be kept so for years. The last fraction is kept in a separate container. [420] A large excess of acid is liable to interfere with the precipitation of the ‹last traces› of cupric sulphide and is avoided in exact work. [421] Noyes and Bray use, approximately, [H^{+}] = 0.25 [‹J. Am. Chem. Soc.›, «29», 137 (1907)]. Tests in this laboratory showed that 1 milligram of cadmium-ion, or of lead-ion, in 100 c.c., is readily precipitated by hydrogen sulphide in the presence of 0.25 molar hydrochloric acid, ([H^{+}] = 0.22). [422] Kahlbaum's "Krystallviolett," [(CH_{3})_{2}NC_{6}H_{4}]_{2}C : C_{6}H_{4}N(CH_{3})_{2}Cl, is referred to. [423] An indelible ink pencil (violet) may, in most cases, be used in place of the solution. The details for the application of the indicator are given in the instructions for laboratory practice, Lab. Manual, pp. 31, 102, 103.