ution which is equivalent to the volume of sodium hydroxide
solution used in this titration. Subtract this volume from the volume
of hydrochloric acid. The difference represents the volume of acid
used to react with the sodium carbonate. Divide the weight of sodium
carbonate by this volume in cubic centimeters, thus obtaining the
weight of sodium carbonate equivalent to each cubic centimeter of the
acid.

From this weight it is possible to calculate the corresponding weight
of HCl in each cubic centimeter of the acid, and in turn the relation
of the acid to the normal.

If, however, it is recalled that normal solutions are equivalent to
each other, it will be seen that the same result may be more readily
reached by dividing the weight in grams of sodium carbonate per cubic
centimeter just found by titration by the weight which would be
contained in the same volume of a normal solution of sodium carbonate.
A normal solution of sodium carbonate contains 53.0 grams per liter,
or 0.0530 gram per cc. (see page 29). The relation of the acid
solution to the normal is, therefore, calculated by dividing the
weight of the carbonate to which each cubic centimeter of the acid is
equivalent by 0.0530. The standardization must be repeated until the
values obtained agree within, at most, two parts in one thousand.

When the standard of the acid solution has been determined, calculate,
from the known ratio of the two solutions, the relation of the sodium
hydroxide solution to a normal solution (Notes 1 and 2).

[Note 1: In the foregoing procedure the acid solution is standardized
and the alkali solution referred to this standard by calculation. It
is equally possible, if preferred, to standardize the alkali solution.
The standards in a common use for this purpose are purified
oxalic acid (H_{2}C_{2}O_{4}.2H_{2}O), potassium acid oxalate
(KHC_{2}O_{4}.H_{2}O or KHC_{2}O_{4}), potassium tetroxalate
(KHC_{2}O_{4}.H_{2}C_{2}O_{4}.2H_{2}O), or potassium acid tartrate
(KHC_{4}O_{6}), with the use of a suitable indicator. The oxalic acid
and the oxalates should be specially prepared to insure purity,
the main difficulty lying in the preservation of the water of
crystallization.

It should be noted that the acid oxalate and the acid tartrate each
contain one hydrogen atom replaceable by a base, while the tetroxalate
contains three such atoms and the oxalic acid two. Each of the two
salts first named behave, therefore, as monobasic acids,