If we assume that the complex is decomposed so fast as to supply new silver ions rapidly enough, to allow us to consider the precipitation of silver and silver sulphide as direct actions of the silver ions, then we may, conservatively, consider TDecomposition to be about 1 / 100 second. Then TFormation would be only 1 / 1024 second. Considering the limiting results for the dimensions of atoms (and ions) and taking account of the fact that the formation of the complex involves electrical changes, that is, in modern terms, changes in position of electrons,[470] Haber finds, that to satisfy the above value for the time constant, such changes must involve a motion of electrical charges at a speed about a million times as great as the velocity of light. Such a velocity is, unquestionably, incompatible with our knowledge of the velocities of light and of electrical charges. We must draw the conclusion that the complex argenticyanide-ion probably cannot decompose fast enough into its ions, to enable the latter to be the only components which make it possible to precipitate silver sulphide or metallic silver from its solutions[471] (see above, p. [232]). That would make it necessary to assume direct action [p235] (as given in equation II, p. [232]) between the complex and the precipitating agent, to some extent, at least, the extent being dependent on the concentrations involved in a given case. If further investigations should confirm such a view, we would probably find that both the actions under consideration (equations I and II, p. [232]) must proceed simultaneously. The second one would have the advantage of enormously greater concentrations of the reacting components, e.g. of the complex ion; the first one would, probably, be found to have the advantage of an enormously greater velocity constant. The actual velocities of the two reactions have never been measured[472] and no final explanation of the relations can be offered. The problem is a very important one, involving the whole question of the mode of ionic action (cf. Chap. V, especially p. [83]).
Aside from the theoretical value of the problem that has been raised, the question of immediate moment to us, from the point of view of analytical chemistry, is the question whether such conclusions would invalidate, in any way, the use we have made of the theory of complex ions, in elucidating the question of the precipitation and nonprecipitation of salts of simple ions from solutions of their complex ions.
The existence of a precipitate in contact with a solution is a question of a condition of equilibrium; the question raised, as the result of Haber's calculations, deals simply with the problem of the path, the mechanism by which equilibrium is reached, but the answer to it does not affect the conditions, on which the maintenance of equilibrium depends. All the conclusions, drawn in our discussions of precipitation from solutions of complex ions, are concerned with final conditions for equilibrium, i.e. with the conditions under which a precipitate can exist, and not with the mechanism of its formation. The conclusions reached are valid, therefore, irrespective of what the decision may ultimately be in the question, whether the simple ions alone are acted upon, when their salts are precipitated, or whether the complex ions are also immediately concerned in the action. The precipitation of silver chloride from an ammoniacal solution[473] may serve to illustrate this point.
In the first place, the precipitation of silver chloride from an ammoniacal solution, say by sodium chloride, may be considered to be the result of the direct interaction of chloride ions with the small quantity of silver ions present, the complex serving only to renew the supply of silver ions, as the latter are removed from solution, by the precipitation. The course of the action would be expressed by the equations
[Ag(NH3)2]Cl ⇄ [Ag(NH3)2+] + Cl− ⇄
| 2 NH3 + Ag+ + Cl− ⇄ | AgCl | + 2 NH3. |
| ⇅ | ||
| AgCl ↓ |
(1)
When the precipitation is ended and equilibrium established, a trace of silver chloride is in solution, in contact with the precipitate, and, according [p236] to the principle of the solubility-product, we must have [Ag+] × [Cl−] = KAgCl. Bodländer's experiments,[474] on the solubility of silver chloride in ammonia, prove that this relation is in perfect agreement with the facts. For the silver-ammonium-ion, the free ammonia and the silver-ion present in the solution, we must have the relation [Ag+] × [NH3]2 / [Ag(NH3)2+] = KInstab. Const.. This relation, according to the experimental evidence, is also found to hold.
Now, we might, on the other hand, assume that the primary or main action, leading to the precipitation of silver chloride, is the interaction of the chloride ions with the complex ions, rather than with silver ions. Silver-ammonium chloride, [Ag(NH3)2]Cl, might first be formed, for instance, and then decompose directly into silver chloride and ammonia. This is the simplest assumption we can make for this kind of action and is sufficiently illustrative of any kind of direct action between the chloride ions and the complex ions. The path of the action would then be expressed by the equations
[Ag(NH3)2+] + Cl− ⇄ [Ag(NH3)2]Cl ⇄