Thermodynamics and Chemistry

CHAPTER 14 GALVANIC CELLS

14.2 ELECTRICPOTENTIALS IN THECELL 456

one side of the interface and an excess negative charge of equal magnitude on the other side.
The electrical double layer creates the contact potential.
To understand why a stable equilibrium state of two metals in contact includes a con-
tact potential, we can consider the chemical potential of the free electrons. The concept of
chemical potential (i.e., partial molar Gibbs energy) applies to the free electrons in a metal
just as it does to other species. The dependence of the chemical potentialíeof free elec-
trons in metal phaseíon the electric potentialíof the phase is given by the relation of
Eq.10.1.6on page 287 , with the charge numberziset equal to 1 :

íe./Díe.0/Fí (14.2.2)

Hereíe.0/is the electron chemical potential in a phase with the same intensive properties
as phaseíbut at zero electric potential.íe.0/depends only on the temperature and the
composition of phaseí. (The dependence on pressure is so small for a solid that we will
ignore it.)
Consider two or more electron conductors that are so arranged that electrons can freely
transfer among them. There is the usual condition for transfer equilibrium in these phases:
the chemical potential (in this casee) is the same in each phase. Thus, electron transfer
equilibrium between phasesíandìrequiresíeandìeto be equal. We equateíeandìe,
substitute from Eq.14.2.2to obtainíe.0/FíDìe.0/Fì, and rearrange to

ìíD

ìe.0/íe.0/

F

(14.2.3)

(phases in electron

transfer equilibrium)

The quantities on the right side of Eq.14.2.3are functions only of the temperature and the
compositions of phasesíandì. If the phases have the same temperature and composition
and are in electron transfer equilibrium,íandìare equal.
For an equilibrium state of metalsíandìin contact, Eq.14.2.3shows that the contact
potentialìídepends only on the temperature and the compositions of the two metals.^3

Equation14.2.3explains why a galvanic cell must have at least one electrical conductor

that is not an electron conductor. If electrons were free to pass from one terminal

through the system to the other terminal of the same temperature and composition,

then in a zero-current equilibrium stateewould be the same in both terminals. In

that case there would be no potential difference between the terminals, and the system

would not be a galvanic cell.

Metal–electrolyte interfaces

An electrode reaction of a galvanic cell takes place at the interface between a metal electron
conductor and an electrolyte solution. In an equilibrium state of the cell, the electrode
reaction is at equilibrium. The condition for this equilibrium is

P

iiiD^0 , where the
sum is over the reactants and products of the electrode reaction, including the electrons.
The chemical potentials of the ions and electrons in the electrode reaction are functions of

(^3) The temperature dependence of a contact potential between two different metals is the basis of the operation
of a thermocouple or thermopile to measure temperature (Sec.2.3.5).