Chemistry Reference
In-Depth Information
can be diluted by adding more solvent through A. It is then raised up into C, as
before, and a new flow is obtained.
The flow time is
related to the viscosity
η
of
the liquid by the
Hagen
Poiseuille equation:
η5πPr
4
t=
8
Ql
(3-87)
where
P
is the pressure drop along the capillary which has length
l
and radius
r
from
which a volume
Q
of liquid exits in time
t
. It is necessary to compare the flow behav-
ior of pure solvent with that of solution of concentration
c
. We will subscript the
terms related to solvent behavior with zeros. The average hydrostatic heads,
h
and
h
0
, are the same during solvent and solution flow in this apparatus, because
t
is the
time taken for the meniscus to pass between the same fiducial marks
a
and
b
. Then
the mean pressures driving the solvent and solution are
h
ρ
0
g
and
h
ρ
g
, respectively,
where
g
is the gravitational acceleration constant and
ρ
is a density (compare
Eq. 3-28
). For dilute solutions
ρ
is very close to
ρ
0
and it follows from
Eq. (3-87)
that
η=η
0
5
t
=
t
0
(3-88)
where
t
0
is flow time for the solvent and
t
that for the solution. Thus, the ratio of
viscosities needed in
Eq. (3-64)
can be obtained from flow times without measur-
ing absolute viscosities. The intrinsic viscosity [
η
] is defined in the above equa-
tion as a limit at zero concentration. The
η
0
ratios which are actually measured
are at finite concentrations, and there are a variety of ways to estimate [
η
/
η
] from
these data. The variation in solution viscosity (
) with increasing concentration
can be expressed as a power series in
c
. The equations usually used are the
Huggins equation
[9]
:
η
5
5 ½1
1
c
η
η
0
2
1
c
t
t
0
2
2
c
1
t
k
H
½η
(3-89)
and the Kraemer equation
[10]
:
c
2
1
ln
2
c
ðη=η
0
Þ 5 ½η 2
k
1
½η
(3-90)
EXAMPLE 3-2
The results of one lab group for the polystyrene/toluene solution at 25
C were as follows:
Solution
Flow times (s)
Pure toluene
72.9
73.6
73.8
Initial solution (0.7 g/100 mL toluene)
228.9
229.4
228.9
10 mL initial solution
1
10 mL toluene
137.6
136.8
137.4
values for the above solution from
Table 3.1
, estimate the
viscosity average molecular weight of the polymer.
Using given data and
K
and
a
