322
THEORY OF BROWNIAN MOTION
,,,
RT
du
(4)
vv
-
-
-jt'
T1
The
left-hand side contains the
product
of the concentration
v
of
the
dissolved substance
and
the
velocity
with
which
the dissolved substance is
moved along
by
the
process
of
diffusion. This
product
represents
therefore
the
quantity
of the dissolved substance (in
gram-molecules)
transported
per
second
through
unit
cross
section
by
diffusion.
The
factor
of
dv/dx
on
the
right-hand
side
of
this
equation
is therefore1
nothing
other than the
coefficient
of
diffusion
D
of the solution considered.
Hence,
we
have
in
general
tr\ n
-
RT
1
(5)
D
-
T-
J
,
and,
in
case
the
diffusing
molecules
can
be
considered
as
spherical
and
large
compared
with the molecules
of
the solvent,
we
have
according
to
equation (3)
\ n
-
RT
1
(5a)
B
-
if
mrp
•
Thus,
in the
case
just
mentioned,
the coefficient
of diffusion does
not
depend
on any
constants
characteristic for the substances
in
question
other
than the viscosity
of
the solvent
7]
and
the radius
p
of
the molecule.2
1It should
be noted that the
numerical value
of
the coefficient
of
diffusion
is
independent
of
the choice
of
the unit for the concentration.
2This
equation permits
the
approximate
determination
of
the radius
of (large)
molecules from
the coefficient
of
diffusion if the latter is
know,
since
n
-
RT
1
^
6J7Wj'
Ü
'
where
we
have
to put
R =
8.31.107 and
N
=
6.1023.
To
be
sure,
the
value
of
N
has
a
margin
of uncertainty of about
50%.
This
relationship
might
be
of
significance
for the determination
of
the
approximate
size
of
molecules in
colloidal solutions.
[6]
[7]