For the condition of equilibrium between ammonia, the silver-ion and the silver-ammonium-ion, we would have[426]:
[NH3] × [Ag+] / [NH3Ag+] = K.
Experimental investigations of the quantitative relations, obtaining in ammoniacal solutions containing silver compounds, show that no constant value is obtained for the ratio, as just developed. But the experimental data show equally conclusively,[427] that a constant is obtained, when the concentration of the ammonia is raised to the second power, in the mathematical statement.
The significance of this change in the mathematical relation, it will be recalled (p. [94]), is that two molecules of ammonia must combine with one silver ion to form an ion [(NH3)2Ag]+, whereas in the formation of the ammonium ion, NH4+, we have a single molecule of ammonia combining with one hydrogen ion. We have then
2 NH3 + Ag+ + HO− ⇄ [(NH3)2Ag]+ + HO− ⇄ [(NH3)2Ag]OH.
We would thus have a silver-ammonium ion, [(NH3)2Ag]+, and its hydroxide, silver-ammonium hydroxide, corresponding to the [p219] ammonium ion and its hydroxide, ammonium hydroxide. The properties of ammoniacal solutions of silver oxide are in entire agreement with this conception. The hydroxide is a stronger base than barium hydroxide.[428] It forms salts, [(NH3)2Ag]X, in which silver appears as part of a so-called positive "complex ion." The hydroxide, like ammonium hydroxide, is unstable and is only known in solution and in the presence of free ammonia, exactly as is the case for ammonium hydroxide. The mathematical equation expressing the equilibrium conditions for the complex ion,
[NH3]2 × [Ag+] / [(NH3)2Ag+] = KInstability,
gives a definite measure of the stability of this complex ion. It is clear, that the larger the constant, the more unstable the complex ion would be, and so the constant is called the Instability Constant[429] of the complex silver-ammonium-ion. Bodländer found the value of the constant to be 6.8E−8 at 25°.[430]
According to the composition of the complex ion, two molecules of ammonia should be required for every molecule of silver nitrate, to produce a solution containing the nitrate of the complex ion: Ag+ + NO3− + 2 NH3 ⇄ [(NH3)2Ag]+ + NO3−. As a matter of fact, 20 c.c. of a molar solution of ammonium hydroxide (= 200 c.c. of a 0.1 molar solution) must be added to 100 c.c. of a 0.1 molar solution of silver nitrate, to convert the silver nitrate into the salt of the complex silver-ammonium-ion. If the ammonium hydroxide solution is allowed to flow slowly, from a pipette, into the silver nitrate solution, we find that the last trace of the precipitated silver hydroxide redissolves just as the last drop or two of the 20 c.c. is added to the mixture (exp.). Working more exactly, Reychler[431] found that the addition of ammonia to a silver nitrate solution, in the proportion of two molecules of the former to one of the nitrate, does not change the freezing-point of the solution, and therefore [p220] does not increase the total number of molecules in the solution. This result agrees with the conception that two molecules of ammonia combine with one silver ion to form a complex ion.