18
DIFFERENCE
IN
POTENTIALS
where
e
denotes the
valency
of
the metal ion.
Integrating
over
V
and
taking
equations
(1)
into
account,
we
obtain
Next
we
imagine
that electrodes
made
of the solute metal
are
installed
in I
and
II,
and construct
the
following
ideal
cyclic
process:
1st
partial
process:
We
send
an
amount
of electricity
eE
infinitely
slowly
through
the
system,
taking
the
electrode
in
I
as
anode, and
the other
as
cathode.
2nd
partial
process:
The
metal thus
transported
electrolytically
from
z
= z1
to
z
=
z2,
which has
the
mass
of
one
gram-equivalent,
is
now
returned
mechanically to
the electrode
in
z
=
Z1.
By
applying
the
two
laws
of the mechanical
theory
of heat,
one
again
reaches the conclusion that the
sum
of
mechanical
and
electrical
energy
supplied
to the
system during
the cyclic
process
vanishes. Since,
as
one
can
readily
see,
the
second
step
does not
require
any
energy,
one
obtains the
equation
where
II2
and
II1
again
denote the potentials
of
the electrodes.
By
subtracting equations
(3)
and
(2),
one
obtains
and hence the
following
theorem:
The
potential difference
between
a
metal
and
a
completely
dissociated
solution of
a
salt of this metal
in
a
given
solvent is
independent
of the
nature
of
the
electronegative
component,
and
depends
solely
on
the
concentration of the metal ions. It is
assumed, however,
that the metal
ion
of these salts is
charged
with the
same
amount
of electricity.
(2)
(3)
II2 =
II1
,
(II2- r2)
-
(II1-
T1)
=
(MII)2 -
(AII)
1
=
0
+
thr
-fiT
A?A?
-cE~=O
dz
=2T.i