n 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,