Physical Chemistry Third Edition

13.5 Nonequilibrium Electrochemistry 595

molecules with the following percentages and molecular

masses:

10.00% 5000 amu

25.00% 15000 amu

60.00% 25000 amu

5.00% 35000 amu

13.29The hydroxy acid HO(–CH 2 –) 5 CO 2 H forms a polyester
by condensation polymerization.
a.Show that the same equations apply that were used for
the condensation polymerization of a diacid and a
dialcohol.
b.If the mass-average molecular mass is reported to
20,000 amu, find the fraction of carboxyl groups that
has been esterified.
c.Find the number-average molecular mass for part b.
d.Find the average degree of polymerization.

13.30The sum in Eq. (13.4-14) is similar to the geometric
progression

S

∑∞

n 0

pn

1

1 −p

This formula is valid only ifp<1. Show that the

result in Eq. (13.4-15) and that in Eq. (13.4-21)

can be obtained by differentiating the sum with

respect top.

13.31Carry out the solution of the kinetic equation for an

uncatalyzed polyesterification if the reaction is assumed

second order in carboxyl groups and first order in

hydroxyl groups:

dc

dt

kfc^3

13.32The amino acid 7-aminoheptanoic acid forms

a polyamide (nylon) inm-cresol solution, with the

second-order rate coefficients^28

temperature/◦C 150 187

k/kg mol−^1 min−^11. 0 × 10 −^32. 74 × 10 −^2

a.Find the times required at 150◦C to attain a value ofp

equal to 0.95 and a value ofpequal to 0.99.

b.Find the number-average and mass-average molecular

masses atp 0 .99.

c.Find the activation energy of the reaction and find the

time required to reach a value ofpequal to 0.95 at

175 ◦C.

13.5 Nonequilibrium Electrochemistry

Chapter 8 presented a discussion of the cell voltage of electrochemical cells at

equilibrium. There are many practical applications of electrochemistry, including the

commercial reduction of aluminum from its ore and the use of various batteries, but

nearly all of them involve nonzero currents. If a nonzero current is being drawn from

a galvanic cell or if a nonzero current is being passed through an electrolytic cell,

the cell voltage can differ from its equilibrium value. When you are cranking your

automobile engine, the voltage in the starting circuit might drop from its equilibrium

value of 12 volts to 10 or 11 volts. This deviation arises frompolarizationof the cell,

which is caused by nonequilibrium changes at the surface of the electrode and in the

solutions near the electrodes. An electrode that passes no current, even for a large

potential, is called anideal polarized electrode. An electrode that does not change its

potential no matter what current is passing is called anonpolarizable electrodeor an

ideal depolarized electrode. All real electrodes are intermediate between these two

nonexistent extremes.

(^28) B. A. Zhubanovet al.,Izv. Akad. Nauk. SSR Ser. Khim., 17 , 69 (1967), cited in H. R. Allcock and F. W. Lampe,op. cit., p. 268 (note 23).