~Sulphates.~--The sulphates of the rare earth elements are obtained by dissolving the oxides or hydroxides in sulphuric acid. From the solutions so obtained, various hydrated salts separate according to the temperature of crystallisation. By heating the hydrated salts to a temperature of 300°-400°, the anhydrous salts are prepared. These are extremely soluble in water at 0°, having a great tendency, which is indeed to be observed in the hydrated forms also, to form supersaturated solutions. When the temperature of such a solution is allowed to rise, larger or smaller quantities of an hydrated form separate out, the differences of solubility among the sulphate hydrates of the various elements being sometimes considerable. The hydrated sulphates of the cerium elements have been very closely studied in connection with the purification of thorium. Cerium sulphate itself forms hydrates with 12, 9, 8, 5, and 4 molecules of water, but sulphates of the other elements generally form fewer hydrates; the commonest have 12, 8, or 4 molecules of water, and numerous cases of isomorphism are known among them. The solubility curve of the cerium sulphate hydrates is shown in the diagram. Fig. 3. The sulphates of the yttrium elements have not yet been systematically investigated, and in most cases only the octohydrates are known. Scandium sulphate is notably different from the other sulphates, in that it is considerably more soluble, and crystallises with six molecules of water. [Illustration: FIG. 3.] It is an important characteristic of the rare earth elements that the solubility of the sulphates diminishes rapidly as the temperature rises. The study of the various equilibrium conditions is greatly complicated by the tendency to form supersaturated solutions, and the fact that many hydrates can exist throughout considerable ranges of temperature in the metastable condition; in consequence of this, also, the solubilities of many hydrates are known for temperatures far beyond the transition points. Foreign elements may be separated by taking advantage of the very great solubility of the anhydrous sulphates at 0°, and the rapid decrease in solubility with rise of temperature. For this purpose, a solution of the anhydrous sulphates saturated at 0° is prepared, and after filtration is slowly allowed to come to room temperature; the hydrated rare earth sulphates then separate, leaving in solution the foreign sulphates. This method may indeed be used instead of the oxalate separation (see p. 147).