Physical Chemistry Third Edition

594 13 Chemical Reaction Mechanisms II: Catalysis and Miscellaneous Topics

(b)

0.006

0.005

0.004

0.003

0.002

0.001

0

0 500 1000

Time, arbitrary units

0.6

W 1

W 100

W 500

W 1000

W

x

W

W (^2) x
W 3
W 5
0.5
0.4
0.3
0.2
0.1
0
0
Time, arbitrary units
12345
3
2
x
1
20 40
W
(^3) x
10
2
60 80 100
(a)
140 160
4
p 5 0.90
p 5 0.95
p 5 0.99
Figure 13.12 A Condensation Polymerization Distribution by Mass.(a) Conversions
of 90%, 95%, and 99%. The horizontal axis is labeled with x, the degree of polymerization.
The vertical axis is labeled with the mass fraction of molecules with x monomer units.
(b) The evolution of mass fractions. Note that all of the mass fractions shown except for
W 1 rise and then decline as molecules of larger size are formed. Part (a) from Allcock and
Lampe,op. cit., p. 261. Part (b) from T C. Tanford,Physical Chemistry of Macromolecules,
Wiley, New York, 1961, p. 595.
Exercise 13.18
Show that
〈M〉wM 0 (1+ 2 k′c 0 t) (13.4-22)
PROBLEMS
Section 13.4: The Reaction Kinetics of Polymer
Formation
13.27Find the number-average and mass-average molecular
masses for a sample of a polyvinyl alcohol that has equal
numbers of molecules with molecular masses 5000 amu,
10,000 amu, 15,000 amu, 20,000 amu, 25,000 amu,
30,000 amu, and 35,000 amu.
13.28Find the number-average and mass-average molecular
masses for a sample of a polyvinyl alcohol that has