Page 30 - Analytical Electrochemistry 2d Ed - Jospeh Wang

1-2 FARADAIC PROCESSES 15

FIGURE 1-8 Tafel plots for the cathodic and anodic branches of the current±potential
curve.

For small departures from E , the exponential term in equation (1-27) may be

linearized and the current is approximately proportional to Z:
i ˆ i nFZ=RT 1-30†
0
Hence, the net current is directly proportional to the overvoltage in a narrow
potential range near E .

Note also that when i net ˆ 0(i.e., when E ˆ E ) one can obtain the following
eq
from equation (1-24):

C 0; t† exp‰ anF E E †=RTŠˆ C 0; t† exp‰ 1 a†nF E E †=RTŠ 1-31†
eq
R
O
eq
Rearrangement of equation (1-31) yields the exponential form of the Nernst
equation:
C 0; t†
O

ˆ exp‰nF E E †=RTŠ 1-32†
eq
C 0; t†
R
expected for equilibrium conditions.
The equilibrium potential for a given reaction is related to the formal potential:
E ˆ E ‡ 2:3RT=nF† log Q 1-33†

eq
where Q is the equilibrium ratio function (i.e., ratio of the equilibrium concentra-
tions).