Similar conditions prevail when, for example, silver ions react with chloride ions, or barium ions react with sulphate ions.  In the former case the dissociation reaction of the silver nitrate is AgNO_{3} <—­> Ag^{+} + no_{3}^{-}, and as soon as the Ag^{+} ions unite with the Cl^{-} ions the concentration of the former is diminished, more of the AgNO_{3} dissociates, and this process goes on until the Ag^{+} ions are practically all removed from the solution, if the Cl^{-} ions are present in sufficient quantity.

For the sake of accuracy it should be stated that the mass law cannot be rigidly applied to solutions of those electrolytes which are largely dissociated.  While the explanation of the deviation from quantitative exactness in these cases is not known, the law is still of marked service in developing analytical methods along more logical lines than was formerly practicable.  It has not seemed wise to qualify each statement made in the Notes to indicate this lack of quantitative exactness.  The student should recognize its existence, however, and will realize its significance better as his knowledge of physical chemistry increases.

If we apply the mass law to the case of a substance of small solubility, such as the compounds usually precipitated in quantitative analysis, we derive what is known as the !solubility product!, as follows:  Taking silver chloride as an example, and remembering that it is not absolutely insoluble in water, the equilibrium expression for its solution is: 

(!Conc’n Ag^{+} x Conc’n Cl^{-})/Conc’n AgCl = Constant!.

But such a solution of silver chloride which is in contact with the solid precipitate must be saturated for the existing temperature, and the quantity of undissociated AgCl in the solution is definite and constant for that temperature.  Since it is a constant, it may be eliminated, and the expression becomes !Conc’n Ag^{+} x Conc’n Cl^{-} = Constant!, and this is known as the solubility product.  No precipitation of a specific substance will occur until the product of the concentrations of its ions in a solution exceeds the solubility product for that substance; whenever that product is exceeded precipitation must follow.

It will readily be seen that if a substance which yields an ion in common with the precipitated compound is added to such a solution as has just been described, the concentration of that ion is increased, and as a result the concentration of the other ion must proportionately decrease, which can only occur through the formation of some of the undissociated compound which must separate from the already saturated solution.  This explains why the addition of an excess of the precipitant is often advantageous in quantitative procedures.  Such a case is discussed at length in Note 2 on page 113.

Similarly, the ionization of a specific substance in solution tends to diminish on the addition of another substance with a common ion, as, for instance, the addition of hydrochloric acid to a solution of hydrogen sulphide.  Hydrogen sulphide is a weak acid, and the concentration of the hydrogen ions in its aqueous solutions is very small.  The equilibrium in such a solution may be represented as: