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662 19 PROCESSES AT SOLID SURFACES
19D Processes at electrodes
Answers to discussion questions
D19D.2 �is is discussed in Section 19D.3 on page 850.
Solutions to exercises
E19D.1(b) If the anodic process is dominant, the current density is given by [19D.5a–850],
ln j = ln j0 + (1 − α) f η, where f = F/RT . At 298.15 K
f = (96485Cmol−1)/[(8.3145 JK−1mol−1) × (298.15 K)] = 38.921 V−1
where the units are resolved by recalling 1 V = 1 JC−1. Taking the di�erence of
two expressions for ln j for di�erent overpotentials gives
ln( j2/ j1) = (1 − α) f (η2 − η1)
hence η2 =
ln( j2/ j1)
(1 − α) f
+ η1
= ln(72/17.0)
(1 − 0.42) × (38.921V−1)
+ 0.105 V = 0.17 V
E19D.2(b) If the anodic process is dominant, the current density is given by [19D.5a–850],
j = j0e(1−α) f η , where f = F/RT . At 298.15 K, f = 38.921V−1. Rearranging for
j0 and then using the data given
j0 = j e−(1−α) f η
= (17.0 mA cm−2) e−(1−0.42)×(38.921 V
−1)×(0.105 V) = 1.6 mA cm−2
E19D.3(b) If the anodic process is dominant, the current density is given by [19D.5a–850],
j = j0e(1−α) f η , where f = F/RT . At 298.15 K, f = 38.921V−1. Taking the ratio
of two expressions for j for di�erent overpotentials gives
j2/ j1 = j0e(1−α) f η2/ j0e(1−α) f η1
hence j2 = j1e(1−α) f (η2−η1)
= (1.22 mA cm−2) e(1−0.5)×(38.921 V
−1)×[(0.60−0.50) V)] = 8.5 mA cm−2
E19D.4(b) (i) �e Butler–Volmer equation is [19D.2–848], j = j0(e(1−α) f η − e−α f η).
For Fe3+ on Pt j0 = 2.5 × 10−3 A cm−2 and α = 0.58; at 298.15 K, f =
38.921V−1. For an overpotential of +0.30 V the current density is
j = (2.5 × 10−3 A cm−2)
× (e(1−0.58)×(38.921 V
−1)×(0.30 V) − e−0.58×(38.921 V
−1)×(0.30 V))
= 0.34 A cm−2