BME 314 MIDTERM I REVIEW
Created By: Lonnissa Hong Nguyen
1.
Given a polymer sample with the following distribution of polymer molecules.
50 molecules of molar mass 1000
100 molecules of molar mass 3000
80 molecules of molar mass 5000
200 molecules of molar mass 7000
20 molecules of molar mass 10000
A. Calculate the number average
22
.
5222
450
000
,
350
,
2
20
200
80
100
50
)
10000
20
(
)
7000
200
(
)
5000
80
(
)
3000
100
(
)
1000
50
(
=
=
+
+
+
+
×
+
×
+
×
+
×
+
×
=
=
∑
∑
i
i
i
n
N
M
N
M
The
number average molecular weight
is a way of determining the molecular weight of a polymer.
Polymer molecules, even ones of the same type, come in different sizes (chain lengths, for linear
polymers), so the average molecular weight will depend on the method of averaging. The number
average molecular weight is the common, mean,
average of the molecular weights of the individual
polymers
. It is determined by measuring the molecular weight of
n
polymer molecules, summing the
weights, and dividing by
n
.
The number average molecular weight of a polymer can be determined by vapor pressure osmometry,
end-group titration, and colligative properties.
B. Calculate the weight average
59
.
6276
000
,
350
,
2
000
,
000
,
750
,
14
)
10000
20
(
)
7000
200
(
)
5000
80
(
)
3000
100
(
)
1000
50
(
)
10000
20
(
)
7000
200
(
)
5000
80
(
)
3000
100
(
)
1000
50
(
2
2
2
2
2
2
=
=
×
+
×
+
×
+
×
+
×
×
+
×
+
×
+
×
+
×
=
=
∑
∑
i
i
i
i
w
M
N
M
N
M
The
weight average molecular
weight is a way of
describing the molecular weight of a polymer
.
Polymer molecules, even if of the same type, come in different sizes (chain lengths, for linear polymers),
so we have to take an average of some kind.
where
N
i
is the number of molecules of molecular weight
M
i
.
Intuitively, if the weight average molecular weight is
w
, and you pick a random monomer, then the
polymer it belongs to will have a weight of
w
on average.
The weight average molecular weight can be determined by light scattering, small angle neutron
scattering (SANS), X-ray scattering, and sedimentation velocity.
C. Calculate the polydispersity Index (PI)
202
.
1
22
.
5222
59
.
6276
=
=
=
n
w
M
M
PDI
Polydispersity Index (PDI),
is a
measure of the distribution of molecular weights
in a given
polymer sample. The PDI calculated is the weight average molecular weight divided by the number
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