DOC.
15
105
A NEW
DETERMINATION
OF MOLECULAR
DIMENSIONS
The
earliest
determinations of real sizes of molecules
were
made
possible
by
the kinetic
theory
of
gases,
whereas
the
physical
phenomena
observed in
liquids have
thus
far
not
served for the determination of
molecular sizes. This is
no
doubt due to
the fact that it has
not
yet
been
possible
to
overcome
the obstacles that
impede
the
development
of
a
detailed
molecular-kinetic
theory
of
liquids.
It will
be
shown
in this
paper
that the
size
of
molecules
of
substances
dissolved in
an
undissociated dilute solution
can
be
obtained
from
the
internal friction of the solution
and
the
pure
solvent
and from
the diffusion of the
dissolved
substance
within the solvent
if the
volume
of the molecule of
the dissolved substance is
large
compared
with the
volume of
the molecule of the solvent.
This is
because, with respect
to
its
mobility
in
the solvent and
its effect
on
the internal
friction of the
latter, such
a
molecule
will
behave
approximately
as a
solid
body suspended
in
a
solvent,
and
it will
be permissible to
apply
to
the
motion
of the solvent in
the
immediate
vicinity of
a
molecule the
hydrodynamic
equations
in
which
the
liquid is considered
to
be
homogeneous
and hence
its molecular
structure
is
not
taken into consideration.
For
the
shape
of the solid
body
that shall
represent the dissolved molecule,
we
will
choose the spherical
shape.
§1.
On
the
influence
on
the motion of
a
liquid
exercised
by a
very
small
sphere suspended in
it
Let
us
base
our
consideration
on
an
incompressible
homogeneous
liquid
with
a
coefficient of
viscosity
k, whose
velocity
components
u, v,
w
are
given
as
functions of
the
coordinates
x,
y,
z
and
of the time.
At
an
arbitrary point
x0, y0,
z0,
the
functions
u, v,
w
are
developed
as
functions of
x
-
x0,
y
-
y0, z
-
z0
according
to Taylor's theorem, and
around
this
point
there is demarcated
a region
G
that is
so
small that
within it
only
the linear
terms
of this
development
must be
taken into
consideration.
As
is well
known,
the
motion
of the liquid contained in
G
can
then
be
considered
as
a
superposition of
three
motions,
i.e.,
[5]