[NH_{3}]^2 × [Ag^{+}] / [Ag(NH_{3})_{2}^{+}] = [‹x›^2 × 2E−10 / (0.1 × 0.87 × 1 / 11)] / (0.05 × 0.87 × 10 / 11) =  6.8E−8. Solving for ‹x›, we obtain ‹x› = [NH_{3}] = 0.33. The concentration of free ammonia, necessary to prevent precipitation of silver chloride in this system, is then [p223] 0.33, instead of 0.0018, present in the original solution. Now, 11 c.c. of 0.33 molar ammonia is equal to 11 × 0.33 / 6, or 0.61 c.c. hexamolar ammonia.[437] Calculations, based on the solubility-product constant of silver chloride and on the instability constant of silver-ammonium-ion, lead, thus, to the conclusion that an excess of 0.61 c.c. of hexamolar ammonia is required, in 10 c.c. of 0.05 molar [Ag(NH_{3})_{2}]NO_{3}, to prevent the precipitation of silver chloride by 1 c.c. of 0.1 molar sodium chloride. Conversely, this excess of ammonia will be required to ‹redissolve the precipitate› of silver chloride, formed when 1 c.c. of 0.1 molar sodium chloride solution is added to 10 c.c. of 0.05 molar [Ag(NH_{3})_{2}]NO_{3}. The following experiment shows that such is the case. EXP. 1 c.c. of 0.1 molar sodium chloride is added to 10 c.c. of 0.05 molar silver-ammonium nitrate, prepared as described on p. 220; hexamolar ammonia is slowly added to the mixture from a 1 c.c. pipette, graduated in twentieths of a cubic centimeter. The precipitate will be seen to be just about ‹completely dissolved› when 0.6 to 0.65 c.c. of the ammonia solution has been used. We find, in this way, that the equilibrium equation for the instability constant of the complex silver-ammonium-ion, together with the principle of the solubility-product, allows a ‹quantitative interpretation› of the problem of the behavior of ammoniacal silver solutions, as far as the detection of silver by the precipitation of its salts is concerned. If a still larger excess of ammonia is used (‹exp.›), even the addition of a 10% solution of sodium chloride fails to precipitate the chloride, and, ‹vice versa›, ammonia in excess will readily redissolve a heavy precipitate of silver chloride (‹exp.›). Advantage is taken of this fact in the separation and identification of silver-ion (Laboratory Manual, ‹q. v.›). It is interesting to note that the addition of potassium bromide, iodide or sulphide to the ammoniacal solution, in which sodium chloride fails to precipitate any silver chloride, will still precipitate silver bromide, iodide or sulphide readily (‹exp.›). Judged by the line of argument used above, in contrasting the behavior of silver bromate and silver chloride, these silver salts [p224] must be still less soluble than the chloride. Experiment proves, that such is, indeed, the case.[438]