Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

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Revised Pages

16.2 Electrochemical Considerations • 667

The voltages in Table 16.1 are for the half-reactions asreduction reactions,with

the electrons on the left-hand side of the chemical equation; for oxidation, the direc-

tion of the reaction is reversed and the sign of the voltage changed.

Consider the generalized reactions involving the oxidation of metal M 1 and the

reduction of metal M 2 as

M 1 →Mn 1 ++ne− −V 10 (16.16a)

Mn 2 ++ne−→M 2 +V^02 (16.16b)

where theV^0 ’s are the standard potentials as taken from the standard emf series. Since

metal M 1 is oxidized, the sign ofV^01 is opposite to the one in Table 16.1. Addition of

Equations 16.16a and 16.16b yields

M 1 +Mn 2 +→Mn 2 ++M 2 (16.17)

and the overall cell potentialV^0 is

V^0 =V^02 −V^01 (16.18)

Electrochemical cell

potential for two

standard half-cells

that are electrically

coupled 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 16.17. When standard

half-cells are coupled together, the metal that lies lower in Table 16.1 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 Msolutions of their ions, at 25◦C). 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 16.17. If

M 1 and M 2 electrodes are pure metals, the cell potential depends on the absolute

temperatureTand the molar ion concentrations [Mn 1 +] and [Mn 2 +] according to the

Nernst equation:

V=

(

V 20 −V^01

)

−

RT

nf

ln

[Mn 1 +]

[Mn 2 +]

(16.19)

Nernst equation—

electrochemical cell

potential for two

half-cells that are

electrically coupled

and for which

solution ion

concentrations are

other than 1M

whereRis the gas constant,nis the number of electrons participating in either of

the half-cell reactions, andfis the Faraday constant, 96,500 C/mol—the magnitude

of charge per mole (6.023× 1023 ) of electrons. At 25◦C (about room temperature),

V=

(

V^02 −V^01

)

−

0. 0592

n

log

[Mn 1 +]

[Mn 2 +]

(16.20)

Simplified form of

Equation 16.19 for

T= 25 ◦C (room

temperature)

to giveVin volts. Again, for reaction spontaneity,Vmust be positive. As expected,

for 1Mconcentrations of both ion types (that is, [Mn 1 +]=[Mn 2 +]=1), Equation 16.19

simplifies to Equation 16.18.