DOC.
15
119
times
larger
than the volume
of the
sugar
molecule
is attached
to
the
sugar [50]
molecule.
Hence
we may
say
that
a
dissolved
molecule of
sugar
(i.e.,
the
molecule
together
with the
water
held
by
it)
behaves
in the
hydrodynamic
sense as a
sphere
with
a
volume
of
2.45.342/N
cm3,
where 342
is the molecular
weight
of
[51]
sugar
and
N
is the
number
of real molecules in
one
gram-molecule.
§4.
On
the diffusion
of
an
undissociated
substance in
a
liquid solution
Let
us
consider
a
solution of the kind considered in
§3.
If
a
force
K
acts
upon
the
molecule, which
we
consider
as a
sphere
of
radius
P,
the
molecule will
move
with
a
velocity
w,
which
is determined
by
P and
the
coefficient
of viscosity
k
of
the
solvent,
since
we
have
the
equation1
)
K
(1)
w
= 6
ikP
We use
this relation
to
calculate the coefficient of diffusion of
an
undis-
sociated solution. If
p
denotes the osmotic
pressure
of the dissolved
substance,
which
is
to
be
regarded
as
the
only motion-producing
force in the
dilute
solution under
consideration,
then the force
acting in the direction
of
the X-axis
on
the dissolved substance
per
unit
volume
of the solution
equals
-Sp/Sx.
If there
are
p
grams
in
a
unit
volume, and
m
is the molecular
[53]
weight
of
the dissolved
substance
and
N
the
number
of real molecules in
one
gram-molecule,
then
(p/m).N
is the
number
of
(real)
molecules in
the unit
volume, and
the force exerted
on
the
molecule
by
virtue
of
the
concentration
gradient
is
(2)
pNox
If the solution is sufficiently diluted,
the osmotic
pressure
is
given
by
the
equation
1G.
Kirchhoff,
Vorlesungen
über
Mechanik.
26.Vorl.
[Lectures
on
Mechanics,
Lecture
26], equation
(22).
[52]