Chemistry Reference
In-Depth Information
order of
6
0.2 mm so that the measurement uncertainty here is of the order of
6
2%. From
Eq.
(3-18)
the boiling point of
the solution would be about
10
2
4
C higher than that of the solvent at the same pressure. This is approxi-
mately at the limit of convenient temperature measuring
de
vices and thus boiling
point elevation is not a suitable method for measuring
M
n
of polymers of this
size. Similarly,
1
3
the vapor pressure lowering would be of
the order of
10
2
3
Pa) at 25
C(
Eq. 3-20
) and could not be measured
reliably. Toluene would not be used as a solvent for freezing point depression
measurements, because its freezing point is inconveniently low. If our sample
were dissolved instead in a material like naphthalene, the difference between the
freezing points of the solvent and that of a 1% (10 g/liter) solution would only be
about 4
10
2
4
mm Hg (2.7
2
3
3
10
2
4
C. It is obvious then that membrane osmometry is the only
c
olli-
gative property measurement that is practical for direct measurements of
M
n
of
high polymers.
Two other techniques that are also used to measure
M
n
are not colliga-
tive properties in the strict sense. These are based on end-group analysis
andonvaporphaseosmometry.Bothmethods,whicharelimitedtolower
molecular weight polymers, are described later i
n t
his chapter. Some general
details of the various procedures for measuring
M
n
directly are reviewed in
this section.
3
3.1.1
Ideal Solutions
[1]
An ideal solution is one in which the mixing volume and enthalpy effects are
zero. In th
e
range
o
f concentrations for which a solution is ideal, the partial molar
quantities
V
and
H
of the components are constant. In the case of solvent, these
partial molar quantities are equal to the molar quantities for pure solvent, since
dilute solutions approach ideality more closely than concentrated ones.
An appropriate definition of an ideal solution is one in which for each
component
d
μ
i
5
RT d
ln
x
i
(3-1)
where
μ
i
and
x
i
are the chemical potential and mole fraction, respectively, of the
i
th component. (Alternative definitions of ideality can be shown to follow from
this expression.) Integrating,
0
μ
i
5μ
i
1RT
ln
x
i
(3-2)
i
is the standard chemical potential. Dilute solutions tend to approach ide-
ality as they approach infinite dilution. That is,
Eq. (3-1)
becomes valid as the
solvent mole fraction approaches unity and all other mole fractions approach
zero. Then, if the solvent is labeled component 1:
where
μ
μ
1
5
G
1
the molar Gibbs free
i
energy of solvent. All other
μ
do not concern us here.
