DOC.
50
325
^2
-
vx
_
du
A
"
Sx
'
and from
this
a
du
"
v1 ~
~
lx
'
so
that
the
amount
of
substance
diffusing
during
r
through E
equals
(6a)
1/2A2dvdx•
The amount
of substance,
expressed
in
gram-molecules,
diffusing
through
E
in
unit time hence
equals
1
A2
du
2
r
Jx
'
With
this
we
have
obtained
a
second
value for
the
coefficient
of
diffusion
D.
We
have
(7) d
=
\t
where
A
denotes the
path
travelled
on
the
average1
by a
dissolved
molecule
during
time
r
in the direction
of
the x-axis.
Solving (7)
for
A,
we
obtain
(7a)
A
=
fD
Jr.
[10]
§3.
Motion
of individual molecules.
Brownian motion
If
we
equate
the values for the diffusion coefficient
in equations
(5)
and
(7),
we
obtain
by
solving
for
A
1To
be
more
precise,
A
equals
the
square
root
of the
mean
of
the
squares
of
the individual
displacements
A21, A22,
etc. For greater
accuracy,
we
should
therefore write A2 instead
of
A.
[9]