120
MOLECULAR
DIMENSIONS
[54] (3)
p
=
RpT
,
where
T
is the absolute
temperature
and
R
=
8.31.107.
From equations
(1),
(2)
and
(3)
we
obtain for the
migration
velocity
of the dissolved substance
,
_
RT
_1_
1
So
6ik
NP
p ox
Finally,
the
amount
of
substance
passing per
unit
time
through
a
unit
cross
section in the direction
of
the X-axis is
(
(4)
wp
-'
m
m
'
w
1
fx
tip
•
Hence
we
obtain
for
the
coefficient
of
diffusion
D
n
-
RT
1
[55] D
~
6n%
'
NP
'
Thus,
from
the coefficient
of
diffusion
and
the coefficient
of viscosity of
the solvent
we can
calculate the
product
of the
number N
of
real molecules
in
one
gram-molecule
and
the
hydrodynamically
effective
molecular radius
P.
In
this derivation the osmotic
pressure
has been treated
as a
force
acting
on
the individual
molecules, which
obviously does
not
agree
with
the
point
of view of
the kinetic molecular
theory,
since
according
to
the latter
the osmotic
pressure
in
the
case
under consideration
has
to
be
conceived
as an
apparent
force
only.
However,
this
difficulty
disappears
when
one
considers
that the
(apparent)
osmotic forces
which correspond to
the concentration
differences
in
the solution
may
be
kept
in
(dynamic)
equilibrium
with
numeric-
ally
equal
forces
acting
on
the individual molecules in the
opposite
direc-
tion,
which
can
easily be
realized
on
the basis
of
thermodynamics.
1
qp
The
osmotic force
acting
on
the unit
mass
-
-
can
be
counter-
balanced
by
the
force
-Px
(exerted
on
the individual dissolved
molecules)
if
X
-
i
&
-
p
=
o
p
Ox x