Chemistry Reference
In-Depth Information
(a) Calculate the number average diameter
ð
D
n
Þ:
(b) Calculate the volume average diameter
ð
D
v
Þ:
(c) Calculate the weight average diameter
ð
D
w
Þ:
α
[weight of a sphere
(diameter)
3
].
volume
α
2-9 The measured diameters of a series of spheres follow:
Number of spheres
Diameter (cm)
2
1
3
2
4
3
2
4
ð
D
n
Þ:
(b) Calculate the weight average diameter
(a) Calculate the number average diameter
ð
D
w
Þ:
[Weight of a sphere
(diameter)
3
.]
~
volume
~
2-10 A chemist dissolved a 50-g sample of a polymer in a solvent. He added
nonsolvent gradually and precipitated out successive polymer-rich phases,
which he separated and freed of solvent. Each such specimen (which is
ca
lled a fraction) was weighted, and its number average molecular weight
M
n
was determined by suitable methods. His results follow:
Fraction no.
Weight (g)
M
n
1
1.5
2,000
2
5.5
50,000
3
22.0
100,000
4
12.0
200,000
5
4.5
500,000
6
1.5
1,000,000
and a
measure of the breadth of the number distribution for the recovered poly-
mer. (Note: This is not a recommended procedure for measuring molecular
weight distributions. The fractions obtained by the method described will
not be monodisperse and the molecular weight distributions of successive
fractions will overlap. The assignment of a single average molecular
weight to each fraction is an approximation that may or may not be useful
in particular cases.)
Assume that each fraction is monodisperse and calculate M
n
;
M
w
;
2-11 The degree of polymerization of a certain oligomer sample is described by
the distribution function
w
i
5
K
ð
i
3
2
i
2
1
Þ
1
