Fundamentals of Electrochemistry - W.H. Freeman

1504T_ch14_270-297 1/23/06 11:35 Page 290
Solution Abbreviating dehydroascorbic acid as D, and ascorbic acid as H 2 A, we rewrite
the reduction as
for which the Nernst equation is
(14-33)
D is not an acid or a base, so its formal concentration equals its molar concentration:
F D [D]. For the diprotic acid H 2 A, we use Equation 14-29 to express [H 2 A] in terms
of F H2 A:
Putting these values into Equation 14-33 gives
E E°
which can be rearranged to the form
D 2H 2e T H 2 A H 2 O
E E°
0.059 16
2
0.059 16
log
2
0.059 16
1
E E° log
2 [H
14444444244444443
] 2 [H ]K 1 K 1 K 2
Formal potential ( E°¿ if pH 7)
0.062 V
£
[H 2 A]
log
[D][H ] 2
[H ] 2 F H2 A
[H 2 A]
[H ] 2 [H ]K 1 K 1 K 2
[H ] 2 F H2 A
[H ] 2 [H ]K 1 K 1 K 2 ≥
F D [H ] 2
0.059 16 F H2 A
log
2 F D
(14-34)
Putting the values of E°, K and into Equation 14-34 and setting [H ] 10 7.00 1 , K 2
, we
find E°¿ 0.062 V.
Curve a in Figure 14-11 shows how the calculated formal potential for Reaction 14-32
depends on pH. The potential decreases as the pH increases, until pH pK 2 . Above pK 2 ,
0.40
0.30
Formal potential (V)
0.20
0.10
(b)
(a)
0.00
–0.10
0
2 4 6 8 10 12 14
pH
Figure 14-11 Reduction potential of ascorbic acid, showing its dependence on pH. (a) Graph
of the function labeled formal potential in Equation 14-34. (b) Experimental polarographic halfwave
reduction potential of ascorbic acid in a medium of ionic strength 0.2 M. The half-wave
potential, discussed in Chapter 17, is nearly the same as the formal potential. At high pH (712), the
half-wave potential does not level off to a slope of 0, as Equation 14-34 predicts. Instead, a
hydrolysis reaction of ascorbic acid occurs and the chemistry is more complex than Reaction
14-32. [J. J. Ruiz, A. Aldaz, and M. Dominguez, Can. J. Chem. 1977, 55, 2799; ibid. 1978, 56, 1533.]
290 CHAPTER 14 Fundamentals of Electrochemistry