[229] To accelerate the action, the mixture is shaken vigorously. After the separation of the layers, the bromine may be recognized in the aqueous layer by its color, or by the addition of potassium iodide (liberation of iodine). [230] [Br]_{aq.} and [Br]_{ch.} are used to express the actual concentrations at any given moment we wish to consider, for instance at the moment equilibrium is reached. The ratio ‹k›_{2} / ‹k›_{1} for any substance S is found to be equal to the ratio of the ‹solubilities› of the substance in the two solvents. That it must be so can be proved by applying the law of physical equilibrium to the mixed solvents in contact with an excess of the substance, ‹i.e.› to its ‹saturated› solutions (see below). [231] Similar relations hold for the condition of equilibrium between a liquid and its vapor. [232] Curie, ‹Bull. Soc. Min.›, «8», 145 (1885); Ostwald, ‹Grundlagen der Anal. Chem.›, p. 22 (1894). [233] Hulett, ‹Z. Phys. Chem.›, «37», 384 (1901). See also Ostwald, ‹ibid.›, «34», 495 (1900), on the solubilities of finely divided mercuric oxide ("yellow oxide") and of larger crystals ("red oxide"). [234] A 1 / 1000 solution of AuCl_{3}, 2 aq., and a 1.2 / 1000 solution of SnCl_{2}, 2 aq., may be used conveniently. When equal volumes of the solutions are mixed, the desired precipitate is formed. [235] Stannous chloride is usually sufficiently contaminated with stannic salt. Add a few drops of bromine- or chlorine-water to 100 c.c. of a ‹pure› stannous chloride solution. [236] The action is an exceedingly sensitive qualitative ‹test for gold›. By a modification of the test Donau was able to detect as little as 2E−9 gram of gold (‹Monatshefte f. Chem.›, «25», 545 (1904)). [237] The nature of the reduction reaction is discussed in Chapters XIV and XV. [238] Faraday, ‹Proc. Royal Soc.›, «8», 356 (1857), ‹Phil. Mag.› (4), «13», 401 (1857) (Stud.). [239] Zsigmondy, ‹Liebig's Annalen›, «301», 30 (1898). [240] Bredig, ‹Z. f. Elektrochem.›, «4», 514, 547 (1898), and ‹Anorganische Fermente›, 1901. Colloidal preparations of platinum, silver and many other metals may be prepared in the same way. In ether, colloidal preparations of the alkali metals may be made (Svedberg, ‹Ber. d. chem. Ges.›, «38», 3616 (1905), «39», 1708 (1906)). [241] ‹Argentum Credé› may be conveniently used. It contains, with the metallic silver, a small percentage of albumen, which is added for reasons discussed below. Brown solutions are formed at once. [242] First a thin ‹film of› black ‹carbon› is produced ‹round the metal›, then the latter appears in the form of a filigree of silver. [243] For details of the preparation, see A. A. Noyes, ‹J. Amer. Chem. Soc.›, «27», 94 (1905).