Physical Chemistry Third Edition

352 8 The Thermodynamics of Electrochemical Systems

8.1 The Chemical Potential and the Electric Potential

Our discussion of the chemical potential in the preceding three chapters is incomplete

in the case of charged particles in an electric field. If a stationary particle with electric

chargeQhas anelectrostatic forceFexerted on it, this corresponds to an electric field

EEEsuch that

FQEEE (8.1-1)

The electric field is a vector that is equal to the electrostatic force per unit charge.

IfQis positive the electric field and the force are in the same direction and ifQis

negative the field and the force are in opposite directions. Since a velocity-independent

force can be derived from a potential energy, the electric field can be derived from the

electric potentialφ, which is a potential energy per unit charge. The electric field and

the electric potential are related by the equation

EEE−∇φ (8.1-2)

The symbol∇stands for thegradient operator, which is a vector derivative operator

that is defined in Eq. (B-43) of Appendix B. The gradient operator is sometimes called

del. Thexcomponent ofEEEis given by

EEEx−

∂φ

∂x

(8.1-3)

and the other components are similar. The SI unit of the electric potential is thevolt

(V), equivalent to newtons per coulomb. The SI unit of the electric field is volts per

meter (V m−^1 ). The electrostatic contribution to the potential energy of a particle of

chargeQis

VelectrostaticQφ (8.1-4)

A constant can be added to the electric potential without any physical effect, as is the

case with any potential energy. The electric potential is generally due to the presence

of electric charges. It is customary to assign the value of the electric potential to vanish

at a location that is infinitely distant from all charges. Electric potentials relative to this

zero are calledabsolute potentials.

The volt is named for Alessandro
Guiseppi Antonio Anastasio Volta,
1745–1827, the Italian chemist
who invented the first practical
electrochemical cell around 1799. He
was made a count by Napoleon in 1801.

Faraday’s constant is named for
Michael Faraday, 1791–1867, a great
English physicist and chemist who
discovered the laws of electrolysis, who
was the first to isolate metallic sodium
and potassium, and who invented the
first electric generator.

The electrostatic potential energy is part of the thermodynamic energyUand is

included in the Gibbs energy and in the chemical potential. The chemical potential of

a charged species is given by

μiμi,chem+NAveziφ (8.1-5)

whereNAvis Avogadro’s constant,eis the charge on a proton, andziis the valence of

the ion (the number of proton charges on the ion). The valence is positive for a cation

and negative for an anion. The charge on a mole of protons is denoted byFand called

Faraday’s constant.

FNAve96485 C mol−^1 (8.1-6)