Physical Chemistry Third Edition

8.1 The Chemical Potential and the Electric Potential 353

Equation (8.1-5) can be written

μiμi,chem+ziFφ (8.1-7)

We callμi,chemthechemical part of the chemical potential. It is assumed to be inde-

pendent of the electric potential and depends only on temperature, pressure, and the

composition of the system. The chemical potential including the electric potential term

is the true chemical potential that obeys the fundamental fact of phase equilibrium.

Some electrochemists use the termelectrochemical potentialfor the chemical potential

in Eq. (8.1-7) and refer to the chemical part of the chemical potential as the “chemical

potential.” We will use the term “chemical potential” for the true chemical potential

and the term “chemical part of the chemical potential” forμi,chem.

The chemical potential of a single charged species cannot be measured, since charged

particles cannot easily be added to a system without adding ions of the opposite charge

at the same time. Consider an electrolyte solute with the formula Mν+Xν−and with ion

valencesz+andz−. The cation is represented by Mz+and the anion is represented by

Xz−. We use a subscript+to indicate the cation, a subscript−to indicate the anion,

and a subscriptito denote the neutral compound. We use the analogue of Eq. (7.4-3)

to write the chemical potential of the neutral electrolyte solute:

μiν+μ++ν−μ−ν+μ+,chem+ν−μ−,chem+(ν+z++ν−z−)Fφ

(8.1-8)

For example, Eq. (8.1-8) for Na 2 SO 4 is

μ(Na 2 SO 4 ) 2 μchem(Na+)+μchem(SO^24 −)+(2)(+1)+(1)(−2)Fφ

 2 μchem(Na+)+μchem(SO^24 −)

Electrical neutrality implies thatν+z++ν−z−0 for any neutral electrolyte, so the

term proportional toφin Eq. (8.1-8) cancels, as it does for any neutral electrolyte

solute.

μiν+μ+,chem+ν−μ−,chemμi,chem (8.1-9)

Position

i,chem

ziF

i

Figure 8.1 The Equilibrium Che-

mical Potential, The Chemical Part

of the Chemical Potential, and

the Electric Potential at the Inter-

face between two Metallic Phases

(Schematic).

Exercise 8.1

a.Show that the electrochemical potential of aqueous CaCl 2 has no dependence on the electric

potential.

b.Show that the electrochemical potential of aqueous Na 3 PO 4 has no dependence on the electric

potential.

Electrons have a chemical potential like any other species:

μ(e−)μchem(e−)−Fφ (8.1-10)

A conducting phase such as a metal contains mobile electrons. If two conducting phases

are placed in contact and allowed to come to equilibrium, the chemical potential of the

electron will have the same value in both phases. The chemical part of the electron’s

chemical potential can have different values in the two materials if the electric potential

φhas different values, as depicted in Figure 8.1.