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4 GENERAL AND PHYSICO-CHEMICAL.
must also boil at the same temperature. The rise in the boiling-point
of a solution above the boiling-point of the solvent (elevation of the
boiling-point) is also, like the osmotic pressure, for dilute solutions pro-
portional to the concentration.
Solutions have a lower freezing-point than the pure solvent, and as
in dilute solutions the solvent can be frozen out from the dissolved body,
then isosmotic solutions have the same freezing-point. The depres-
sion of the freezing-point is also proportional to the concentration.
The determination of the elevation of the boiling-point for the esti-
mation of the osmotic pressure of animal fluids is applicable only in
exceptional cases, because on heating, precipitates often form. The
determination of the depression of the freezing-point has been found of
much greater use. This can be accomplished in an easy manner by aid of
the apparatus suggested by Beckmann. In regard to the use of this
method we must refer to more complete works.1
The above rule that equimolecular solutions of different bodies have
the same osmotic pressure is only applicable to non-electrolytes. The
electrolytes (bases, acids, salts) show in aqueous solution a much greater
pressure (i.e., a much lower depression of the freezing-point) than equi-
molecular solutions of non-electrolytes. As is known, Arrhenius has
explained this lack of correspondence by the assumption that the mole-
cule of the electrolyte is divided or dissociated into so-called ions hav-
ing an opposed electric charge. An ion exerts upon the osmotic pressure
the same influence as the non-dissociated molecule. The larger the
number of dissociated molecules the more does the osmotic pressure
of the solution rise above the pressure of an equimolecular solution of a
non-dissociated body. The osmotic action of a dissociated body is equal to
that of a non-dissociated body which in a given volume contains as many
molecules as the dissociated body contains ions plus non-dissociated mole-
cules. If we assume that a is the degree of dissociation, i.e., the number of
the molecules that are dissociated, then 1— a is the number that is not
dissociated. If in the dissociation of a molecule n ions are formed
then the relation of the molecules present before the dissociation to the
ions + molecules present after the dissociation is 1:(1— a-\-na) or
= l:(l-r-[n — l]a). The expression (l+[n — l]a) is generally denoted by
the letter i, and can be directly determined by estimating the freezing-
point of a solution of known molecular concentration.
A gram-molecule aqueous solution (one that contains as many grams per
liter as the molecular weight of the substance) of any non-electrolyte freezes
at about - 1.86°, or, the depression of the freezing-point A is =1.86°. For example,
1
Ostwald-Luther, Hand- und Hilfsbuch zur Ausfuhrung physik.-chemischer
Messung, 3 Aufl., 1910.
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