20
DIFFERENCE
IN
POTENTIALS
Here
N
denotes the
number
of
molecules
per
unit
volume.
If
N0
denotes the
number
of molecules in
one
gram-equivalent,
then
N0/N
=
v
is the molecular
volume
of the liquid, and
if
we assume
that
the
investigation
involves
one
gram-equivalent
and neglect
the effect of the
liquid
surface,
our
expression
becomes
[8]
/2 P00
Const.
-
£
-
Aß
dT'-^ro,dT^
"00
We
shall
now
choose
the
unit
for
c
such
that this
expression
reduces
to
(d)
Const.
- c2/v,
hence
1/2
Aß
dr'
./?(
r0^T) =
1.
By
this
choice
one
obtains absolute
units
for
the quantities
c.
It
has been
shown
in the previously cited article that
one
remains in
agreement
with
experience
if
one
sets
c
=
Eca, where
the quantities
cQ
refer
to
the
atoms
composing
the molecule.
We now
want to
calculate the relative attraction
potential of
a gram–
molecule
of
an
ion with
respect to
its solvent, while
making
the
express
assumption
that the attraction fields of the solvent molecules
do
not act
upon
the electric
charges
of
the ions.
Methods to be
developed
later will
provide
the
means by
which to
decide
whether
this
assumption
is
permissible.
If
cj
is the molecular
constant
of the
ion and
Cl
that of the
solvent,
then the potential
of
one
molecule
of the
ion
with respect
to
the
solvent
has
the
form
Const.
-
^ c-Cg.(p(r)
=
const.
-
dr.(p(r
i)
,
J J
J
'
t
where Nl
denotes the
number
of solvent molecules
per
unit
volume.
Since
N0/Nl = Vl,
this
expression becomes
Nq
Const.
-
c
-.Cff.-lvt
J