14
DIFFERENCE
IN
POTENTIALS
the
quantities
concentration
v,
electric
potential
t,
osmotic
pressures
of
the
two
ion
types
pm
and
ps,
and
hydrostatic
pressure
p0
will
be
func
tions of
z
only.
At
each
location of the electrolyte,
each of
the
two types
of
electrons
must
then
be
in
equilibrium
separately, which
is
expressed
by
the
equations
^tn
1
^n?
F
di
_
n
dz '
v
m
dz
Jz
'
dp,
i
dP
A
U
#
u
~
7F
+ nE
Tz
~
0
'
where
P«,= vnmRT
'
Ps =
vn
'iT
,
and where
R
is
a
constant
common
to
all ionic
species.
Hence
the
equations
take the form
(1)
If
Pm
and
Ps
are
known
for
all
z,
and
v
and
x
for
a
particular
z,
then
equations (1)
yield
v
and
i
as
functions
of
z.
Also, the condition
that the solution
as a
whole
is in
equilibrium would
result
in
an
equation
for
the determination of the
hydrostatic
pressure
p0,
which need not be
written
down.
We
only
note
that the
reason
that
dp0
is
independent
of
dv and
di
is that
we
are
free
to postulate
arbitrary conservative forces that
act
on
the
molecules
of the solvent.
We now
imagine
that electrodes
made
of
the solute metal
and
occupying
a
vanishingly
small
part of
the
cross
section
of
the
cylindric
vessel
are
placed
in
the solution
at
z
= z1
and
z
=
z2.
The
solution
and
the electrodes
to
gether form
a
physical
system,
which
we
take
through
the
following
reversible
isothermal cyclic
process:
1st
partial
process:
We
pass
the
amount
of
electricity
nE
infinitely
slowly through
the
solution,
using
the electrode
at
z
=
z1
as
anode, and
that
at
z
=
z2
as
cathode.
dP
m
dP
tF
+
IF

'E
Tz

0
•
[6]