Chemistry Reference
In-Depth Information
heterogeneity of the polymer, unlike light scattering data (
Section 3.2
).
Membrane osmometry measures the number average molecular weight of the
whole sample, including contaminants, although very low-molecular-weight mate-
rials will equilibrate on both sides of the membrane and may not interfere with
the analysis. Water-soluble polyelectrolyte polymers are best analyzed in aqueous
salt solutions, to minimize extraneous ionic effects.
Careful experimentation
wi
ll usually yield a precision of about
5% on
replicate measurements of
M
n
of the same sample in the same laboratory.
Interlaboratory reproducibility is not as good as the precision within a single lo
ca
-
tion and the variation in second virial coefficient results is greater than in
M
n
determinations.
The raw data in osmotic pressure experiments are pressures in terms of heights
of solvent columns at various polymer concentrations. The pressure values are
usually in centimeters of solvent (
h
) and the concentrations,
c
, may be in grams
per cubic centimeter, per deciliter (100 cm
3
), or per liter, and so on. The most
direct application of these numbers involves plotting (
h/c
) against
c
and extrapo-
lating to (
h/c
)
0
at zero concentration. The column height
h
is then converted to
osmotic pressure
6
π
by
π5ρ
hg
(3-28)
where
is the den
sity
of the solvent and
g
is the gravitational acceleration con-
stant. The value of
M
n
follows from
ρ
ðπ=
c
Þ
0
5
RT
=
M
n
(3-29)
(cf.
Eq. 3-26
). It is necessary to remember that the units of
R
must correspond to
those of (
(g cm
2
3
), and
g
(cm s
2
2
),
R
should be in
ergs mol
2
1
K
2
1
. For
R
in J mol
2
1
K
2
1
,
h
,
π
/c
)
0
. Thus, with
h
(cm),
ρ
ρ
, and
g
should be in SI units.
EXAMPLE 3-1
The following data is collected from an osmotic pressure experiment conducted at 298.2 K:
C
2
310
3
(g/cm
3
)
1.5
2.1
2.5
4.9
6.8
7.9
π (cm toluene)
0.30
0.45
0.55
1.20
2.00
2.40
where
C
2
i
s t
he concentration of a polystyrene sample in toluene, and
π
is the osmotic pres-
sure. Find M
n
.
Solution
5
RT
π
C
2
RT
lim
c
2
-0
C
2
Given lim
C
2
-0
M
n
.M
n
5
π
