118
MOLECULAR DIMENSIONS
radius
P.
In that
case
we
can
apply
the result obtained
in
§2.
If k*
denotes
the coefficient
of viscosity
of the solution
and
k
that
of
the
pure
solvent,
we
have
k*
[45]
/k
=
1 +
p ,
where
ip
is the total
volume
of the
molecules
per
unit
volume
of the
solution.
We
wish to
calculate
(p
for
a
1%
aqueous
solution
of
sugar. According
to
Burkhard's observations
(Landolt
and
Börnstein Tables),
k*/k
=
1.0245 (at
20°C)
for
a
1%
aqueous
sugar
solution,
hence
cp
=
0.0245
for
(almost exactly)
[46]
0.01
g
of
sugar.
Thus,
one
gram
of
sugar
dissolved
in
water has
the
same
effect
on
the coefficient
of
viscosity
as
do
small
suspended
rigid
spheres of
[47]
a
total
volume
of
2.45
cm3.
This consideration
neglects
the effect exerted
on
the internal friction
of the
solvent
by
the
osmotic
pressure
resulting from
the dissolved
sugar.
Let
us
remember
that
1
g
of
solid
sugar
has
a
volume
of 0.61
cm3.
This
same
volume
is also
found
for the
specific
volume
s
of
sugar
in
solution if
one
considers the
sugar
solution
as a
mixture of
water
and sugar
in
dissolved
form.
I.e.,
the
density of
a
1%
aqueous sugar
solution (referred
to water of
[48]
the
same
temperature) at 17.5°
is
1.00388.
Hence
we
have (neglecting
the
difference
between
the
density of water at
4°
and at
17.5°)
and
thus
1.00388 1
=
0.99
+
0.01
s ,
s
=
0.61.
Thus,
while the
sugar
solution
behaves
as
a
mixture
of water and
solid
[49] sugar
with
respect
to
its
density,
the effect
on
internal friction is four
times
larger
than
that which
would
result
from
the
suspension
of the
same
amount
of
sugar.
It
seems
to
me
that
from
the
point
of view of
the
molecular
theory,
this result
can
hardly
be interpreted
otherwise than
by assuming
that
the
sugar
molecule in
the
solution
impedes
the
mobility
of
the
water
in its
immediate
vicinity,
so
that
an
amount
of
water
whose volume
is about three