Callister - An introduction - 8th edition

680 • Chapter 17 / Corrosion and Degradation of Materials
Consider the generalized reactions involving the oxidation of metal M 1 and the
reduction of metal M 2 as
Electrochemical cell
potential for two
standard half-cells
that are electrically
coupled
Nernst equation—
Electrochemical cell
potential for two
half-cells that are
electrically coupled
and for which
solution ion
concentrations are
other than 1M
Simplified form of
Equation 17.19 for
T 25ºC (room
temperature)
(17.16a)
(17.16b)
where the V 0 s are the standard potentials as taken from the standard emf series.
Because metal M 1 is oxidized, the sign of V1
0 is opposite to that as it appears in
Table 17.1. Addition of Equations 17.16a and 17.16b yields
and the overall cell potential V 0 is
M 1 ¡ M n
1 ne V1
0
2 ne ¡ M 2 V2
0
M n
M 1 M n
2 ¡ M 1 n M 2
¢V 0 V 0 2 V 0 1
(17.17)
(17.18)
For this reaction to occur spontaneously, V 0 must be positive; if it is negative,
the spontaneous cell direction is just the reverse of Equation 17.17. When standard
half-cells are coupled together, the metal that lies lower in Table 17.1 will experience
oxidation (i.e., corrosion), whereas the higher one will be reduced.
Influence of Concentration and Temperature
on Cell Potential
The emf series applies to highly idealized electrochemical cells (i.e., pure metals in
1 M solutions of their ions, at 25ºC). Altering temperature or solution concentration
or using alloy electrodes instead of pure metals will change the cell potential,
and, in some cases, the spontaneous reaction direction may be reversed.
Consider again the electrochemical reaction described by Equation 17.17. If M 1
and M 2 electrodes are pure metals, the cell potential depends on the absolute temperature
T and the molar ion concentrations [M n
1 ] and [M n
2 ] according to the
Nernst equation:
¢V 1V2 0 V1 0 2 RT
nf ln [M n
(17.19)
where R is the gas constant, n is the number of electrons participating in either of the
half-cell reactions, and f is the Faraday constant, 96,500 C/mol—the magnitude of
charge per mole (6.022 10 23 ) of electrons. At 25ºC (about room temperature),
¢V 1V 0 2 V 1 0 2 0.0592
n
1 ]
[M n
2 ]
log 3Mn 1 4
3M n
2 4
(17.20)
to give V in volts.Again, for reaction spontaneity, V must be positive.As expected,
for 1 M concentrations of both ion types (that is, [M n
1 ] [M n
2 ] 12, Equation
17.19 simplifies to Equation 17.18.
Concept Check 17.2
Modify Equation 17.19 for the case in which metals M 1 and M 2 are alloys.
[The answer may be found at www.wiley.com/college/callister (Student Companion Site).]