the solution, it will be seen that nearly all of
the barium sulphate has been precipitated, and that the small amount
which then remains in the solution which is in contact with the
precipitate must represent a saturated solution for the existing
temperature, and that this solution is comparable with a solution of
sugar to which more sugar has been added than will dissolve. It
should be borne in mind that the quantity of barium sulphate in
this !saturated solution is a constant quantity! for the existing
conditions. The dissolved barium sulphate, like any electrolyte, is
dissociated, and the equilibrium conditions may be expressed thus:

(!Conc'n Ba^{++} x Conc'n SO_{4}^{--})/(Conc'n BaSO_{4}) = Const.!,

and since !Conc'n BaSO_{4}! for the saturated solution has a constant
value (which is very small), it may be eliminated, when the expression
becomes !Conc'n Ba^{++} x Conc'n SO_{4}^{--} = Const.!, which is
the "solubility product" of BaSO_{4}. If, now, an excess of the
precipitant, a soluble barium salt, is added in the form of a
relatively concentrated solution (the slight change of volume of a few
cubic centimeters may be disregarded for the present discussion)
the concentration of the Ba^{++} ions is much increased, and as a
consequence the !Conc'n SO_{4}! must decrease in proportion if the
value of the expression is to remain constant, which is a requisite
condition if the law of mass action upon which our argument depends
holds true. In other words, SO_{4}^{--} ions must combine with some
of the added Ba^{++} ions to form [BaSO_{4}]; but it will be recalled
that the solution is already saturated with BaSO_{4}, and this freshly
formed quantity must, therefore, separate and add itself to the
precipitate. This is exactly what is desired in order to insure
more complete precipitation and greater accuracy, and leads to the
conclusion that the larger the excess of the precipitant added the
more successful the analysis; but a practical limit is placed upon
the quantity of the precipitant which may be properly added by other
conditions, as stated in the following note.]

[Note 3: Barium sulphate, in a larger measure than most compounds,
tends to carry down other substances which are present in the solution
from which it separates, even when these other substances are
relatively soluble, and including the barium chloride used as the
precipitant. This is also notably true in the case of nitrates and
chlorates of the alk