[406] On account of the presence of a small, unknown amount of sulphuric acid in the original solution, resulting from the hydrolysis of ferrous sulphate, the exact value of [S^{2−}] in the first solution cannot be calculated without further examination; but, according to the values given in the table on page 202, the value of ‹x›, indicating the growth in the concentration of S^{2−}, is ‹at least› 10^{12}, if 2 equivalents of NaOH, and 10^9, if 2 equivalents of NH_{4}OH are used to convert the 0.1 molar hydrogen sulphide into the corresponding sulphide Me_{2}S, of 0.1 molar concentration. [407] [S^{2−}] is exactly the same in the two products, when equal volumes of the zinc and ferrous sulphate solutions are mixed and the mixture is saturated with hydrogen sulphide; ‹zinc sulphide› is precipitated. [408] The difference in the values obtained, when hydrolysis is considered or neglected, is very considerable. ‹Vide› Bodländer, on the solubility of calcium carbonate, ‹Z. phys. Chem.›, «35», 23 (1900), and Stieglitz, ‹Carnegie Institution Publications›, No. «107», 249 (1909). [409] In carrying out this ‹fractional precipitation› a very dilute solution of ammonium sulphide is used, so as to prevent the mechanical enclosure of black ferrous sulphide, which would discolor the white sulphide. The ammonium sulphide solution should be saturated with hydrogen sulphide, to prevent the precipitation of green ferrous-ferric oxide by an excess of free ammonia. It is best to prepare a set of the precipitates and to preserve them in well-stoppered vessels, and not to try to take the time and care necessary to effect a perfect fractionation as a lecture experiment. The presence of the ferrous sulphate, in the supernatant liquid above the first precipitate of zinc sulphide, may be readily demonstrated by pouring off some of the solution and adding an excess of ammonium sulphide to it. Of course, it is also perfectly legitimate, and easier, to precipitate first zinc sulphide from a pure zinc sulphate solution and then to add ferrous sulphate solution to the mixture and to preserve the mixture. If the zinc sulphide were not the less soluble, it would be rapidly converted into the black ferrous sulphide. (See p. 165, and see below, pp. 210, 213, where similar transformations are carried out as lecture experiments.)