DOC.
2
13
One
remains
in
agreement
with
experience
when
one
applies the
second
law
to
physical
mixtures
whose
individual
components
are
acted
upon
by
arbitrary
conservative forces.
[2]
In
the
following
we
will
always
make
use
of
this
hypothesis,
even
when
this
does not
seem
absolutely
necessary.
§2. On
the
dependence
of
the
electric
potential difference of
a
completely
dissociated salt
solution
and
an
electrode
consisting
of
the solute metal
on
the concentration
of
the
solution
and the
hydrostatic
pressure
Let
a
solution of
a
completely
dissociated salt
be
contained in
a
cylindrical
vessel
whose
axis coincides with the z-axis of
a
Cartesian
coordinate
system.
Let
vdo
be
the
number
of
gram-molecules
of the salt
dissolved in the
volume
element do,
vm
do
the
number
of
metal ions,
and [3]
vs
do
the
number
of acid ions,
where
vm
and
vs
are
integral multiples
of
v, so
that
we
have
the
following
equations:
m
m
=71•l'
8 3
Further,
let n.v.E.do
be
the
magnitude
of
the total
positive
electric
charge
of
the ions in
do, and hence
also,
up
to
the infinitesimally small,
the
magnitude
of the
negative charge.
Here
n
is the
sum
of valencies of the
molecule's metal
ions, and
E
the
amount
of
electricity required for the
electrolytic separation of
one
gram-molecule
of
a
univalent ion.
[4]
These
equations
are
certainly
valid, since the
number
of
excess
ions of
one
kind
can
be neglected.
We
shall further
assume
that the metal
and
acid ions
are
acted
upon by
an
external conservative force
whose
potential
per
ion has
the
magnitude
Pm
and
Ps,
respectively. Furthermore,
we
neglect
the variability of
the
density
of the solvent with the
pressure
and density
of
the dissolved salt,
and
assume
that
a
conservative force,
whose
potential
per gram-equivalent
of the solvent
has
the
magnitude
P0,
acts
upon
the
parts
of
the
solvent; there shall
be
v0do
gram-molecules
of solvent in
do.
Suppose
that all force functions
depend
solely
on
the z-coordinate,
and
that the
system
is
in electrical, thermal, and mechanical equilibrium.
Then
[5]