The bearing of these relations, which, it will be noted, concern concentrations of silver-ion, can best be seen by working with solutions of definite concentrations.
If the solution we have just prepared is diluted with water to 200 c.c., a 0.05 molar solution of [(NH3)2Ag]NO3 is formed. In such a solution, the concentration, [Ag+], of the silver-ion is only 0.0009,[432] whereas in 0.05 molar silver nitrate solution it is 0.0435. It is clear that the reactions of the silver-ion will not be observed as readily in such an ammoniacal solution as in a solution of silver nitrate, which contains the same concentration of total silver. That such is the case, may be readily demonstrated as follows: the addition of 1 c.c. of molar sodium bromate to 10 c.c. of 0.05 molar silver nitrate immediately forms a heavy precipitate of the moderately difficultly soluble bromate, AgBrO3, while the same addition to 10 c.c. of the 0.05 molar silver-ammonium nitrate solution produces no precipitate whatever (exp.). [p221]
A liter of water dissolves 0.025 mole (6 grams) of silver bromate[433] at 18°. If the same degree of ionization be assumed for it as for a 0.025 molar solution of the analogous salt, silver nitrate, AgNO3, 90% of the silver bromate in the saturated solution is ionized. The solubility-product constant then is [Ag+] × [BrO3−] = (0.025 × 0.9)2 = 0.0005.
When 1 c.c. of molar sodium bromate is added to 10 c.c. of 0.05 molar silver nitrate, each salt is ionized 80% in the mixture, and [Ag+] = 0.05 × 0.8 × 10 / 11 = 0.037 and [BrO3−] = (1 × 1 / 11) × 0.8 = 0.072. Then the product of the ion concentrations, [Ag+] × [BrO3−] = 0.037 × 0.072 = 0.0027, is considerably larger than the constant 0.0005 and precipitation follows.
But, when 1 c.c. of molar sodium bromate is added to 10 c.c. of a 0.05 molar silver-ammonium nitrate solution, the concentration of silver-ion[434] is 0.00085 and the product of the ion concentrations, [Ag+] × [BrO3−] = 0.00085 × 0.072 = 6E−5, is smaller than the constant; the solution will not be saturated with silver bromate and no precipitate is formed.
On the other hand, if 1 c.c. of a 0.1 molar solution of sodium chloride is added to 10 c.c. of 0.05 molar silver-ammonium nitrate solution, a very decided precipitate of silver chloride is formed (exp.). The difference in the action of the sodium bromate and the chloride lies in the fact that silver chloride is 2500 times as insoluble as is silver bromate, and the chloride may be precipitated from solutions containing a very much smaller concentration of the silver-ion than is required for the precipitation of silver bromate.
The quantitative relations for the chloride are as follows: a liter of water dissolves 0.002 gram, or 1.4E−5 mole, of silver chloride at 25°,[435] and the solubility-product constant at 25° is [Ag+] × [Cl−] = (1.4E−5)2 = 2E−10. Now, if 1 c.c. of 0.1 molar sodium chloride is added to 10 c.c. of 0.05 molar silver-ammonium nitrate, we have,[436] for the first moment, [Ag+] = 8.9E−4 and [p222] [Cl−] = 0.008, and [Ag+] × [Cl−] = 8.9E−4 × 0.008 = 7E−6, which is much larger than the solubility-product constant, and precipitation must take place. The precipitate will be quite a heavy one: as silver-ion is removed from solution, the complex ion must decompose and furnish a new supply of silver-ion, and precipitation must continue until the excess of ammonia, which is liberated by the decomposition of the complex ion (Ag(NH3)2+ + Cl− → AgCl ↓ + 2 NH3), suppresses the silver-ion sufficiently to satisfy, with the diminished concentration of chloride-ion, the solubility-product constant of silver chloride.
It is clear that, while the reactions of silver-ion are not obtained as readily in the ammoniacal solution as in an equivalent solution of silver nitrate (bromate experiment), nevertheless more sensitive tests show that a small portion of the silver still is present as silver-ion in the ammoniacal solution (chloride experiment).
This brings us to our third point, the influence of an excess of ammonia on the concentration of silver-ion and on its reactions. It is evident, from the form of the equilibrium equation (p. [219]), that any excess of ammonia must very rapidly reduce the concentration of silver-ion. We may ask what excess will be required to prevent the precipitation of silver chloride in the experiment just tried.
The question may be answered as follows: The concentration of chloride-ion, when 1 c.c. of 0.1 molar sodium chloride is added to 10 c.c. of 0.05 molar [Ag(NH3)2]NO3, no precipitate being formed, will be 0.1 × (1 / 11) × 0.87, the solution being diluted 1 to 11 and the percentage of ionization of a salt MeX being approximately 87% in 0.05 to 0.06 molar concentration. For a solution containing this concentration of chloride-ion, the concentration [Ag+] of silver-ion, which may just be present without leading to the precipitation of silver chloride (i.e. for the saturated solution) is, according to the principle of the solubility-product,