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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
charge Q has an electrostatic force F exerted on it, this corresponds to an electric field
E E E such that
F QE E E
(8.1-1)
The electric field is a vector that is equal to the electrostatic force per unit charge.
If Q is positive the electric field and the force are in the same direction and if Q is
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 potential ϕ, which is a potential energy per unit charge. The electric field and
the electric potential are related by the equation
E E E −∇ϕ
(8.1-2)
The symbol ∇ stands for the gradient operator, which is a vector derivative operator
that is defined in Eq. (B-43) of Appendix B. The gradient operator is sometimes called
del. The x component of E E E is given by
E E E x −
∂ϕ
∂x
(8.1-3)
and the other components are similar. The SI unit of the electric potential is the volt
(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
charge Q is
V electrostatic Qϕ
(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 called absolute 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 energy U and is
included in the Gibbs energy and in the chemical potential. The chemical potential of
a charged species is given by
µ i µ i,chem + N Av e z i ϕ
(8.1-5)
where N Av is Avogadro’s constant,e is the charge on a proton, and z i is 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 by F and called
Faraday’s constant.
F N Av e 96485 C mol
−1
(8.1-6)
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
charge Q has an electrostatic force F exerted on it, this corresponds to an electric field
E E E such that
F QE E E
(8.1-1)
The electric field is a vector that is equal to the electrostatic force per unit charge.
If Q is positive the electric field and the force are in the same direction and if Q is
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 potential ϕ, which is a potential energy per unit charge. The electric field and
the electric potential are related by the equation
E E E −∇ϕ
(8.1-2)
The symbol ∇ stands for the gradient operator, which is a vector derivative operator
that is defined in Eq. (B-43) of Appendix B. The gradient operator is sometimes called
del. The x component of E E E is given by
E E E x −
∂ϕ
∂x
(8.1-3)
and the other components are similar. The SI unit of the electric potential is the volt
(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
charge Q is
V electrostatic Qϕ
(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 called absolute 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 energy U and is
included in the Gibbs energy and in the chemical potential. The chemical potential of
a charged species is given by
µ i µ i,chem + N Av e z i ϕ
(8.1-5)
where N Av is Avogadro’s constant,e is the charge on a proton, and z i is 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 by F and called
Faraday’s constant.
F N Av e 96485 C mol
−1
(8.1-6)