to move the charge. A Coulomb is a certain number of electron charges,
6.24 × 10
18 . Voltage has similarities to a molar Gibbs energy (the amount
of free energy it takes to convert 1 mol of a substance from one form
or state to another). Therefore, it should follow that the potential, E, is
proportional to the Gibbs energy of reaction according to:
(ΔG) rec = −nFE
(6.5)
where n is the number of electrons involved in the oxidation/reduction
reaction and F is a proportionality constant called the Faraday constant.
The Faraday constant provides the conversion from the Gibbs energy, which
is a value on a per-mole basis, to voltage, which is on a per-Coulomb
basis. The value of the Faraday constant is then given by:
(6.6)
THE NERNST EQUATION
The Gibbs energy difference can be related to the equilibrium constant,
or equivalently to the ratio of the product, namely the concentration of
the oxidized species, A oxidized , and the reactant, or reduced species, A reduced
(see Chapter 5):
(6.7)
Substituting the relationship between the Gibbs energy and the voltage
(eqn 6.5) yields:
(6.8)
This final equation is called the Nernst equation, named after Walther
Nernst who won the Nobel Prize in Chemistry in 1920. In a sense, it proves
a measure for whether a molecule has an electron, just as the pK A
provides a measure for a proton. The equation can be used to calculate
the potential, given the midpoint potential and the concentrations of the
reactants and products. A useful number to remember is that when the
equilibrium constant is increased 10-fold, the potential changes by:
(6.9)
E E
( .
( )( .
−
= −
×
×
0
8 314
298
1 9 65 1
J/(K mol)
K
0 0
10 0 0592
59 2
4 C mol
J C
mV
1
1
−
−
)
ln( )
.
.
=
=
E E
RT
nF
ln
=
−
0
[A
]
[A
]
oxidized
reduced
−
= −
+
nFE
nFE
RT ln
0
[A
]
[A
]
oxidized
reduced
( )
( )
ln
Δ
Δ
G
G
R T
rec
rec
=
° +
[A
]
[A
oxidized
reduce ed ]
F
.
.
.
=
×
×
=
×
−
−
6 02 10
6 24 10
9 65
23
1
18
1
mol
C
10
4
1
C mol
−
116
PART I
THERMODYNAMICS AND KINETICS
9781405124362_4_006.qxd 4/29/08 14:07 Page 116
6.24 × 10
18 . Voltage has similarities to a molar Gibbs energy (the amount
of free energy it takes to convert 1 mol of a substance from one form
or state to another). Therefore, it should follow that the potential, E, is
proportional to the Gibbs energy of reaction according to:
(ΔG) rec = −nFE
(6.5)
where n is the number of electrons involved in the oxidation/reduction
reaction and F is a proportionality constant called the Faraday constant.
The Faraday constant provides the conversion from the Gibbs energy, which
is a value on a per-mole basis, to voltage, which is on a per-Coulomb
basis. The value of the Faraday constant is then given by:
(6.6)
THE NERNST EQUATION
The Gibbs energy difference can be related to the equilibrium constant,
or equivalently to the ratio of the product, namely the concentration of
the oxidized species, A oxidized , and the reactant, or reduced species, A reduced
(see Chapter 5):
(6.7)
Substituting the relationship between the Gibbs energy and the voltage
(eqn 6.5) yields:
(6.8)
This final equation is called the Nernst equation, named after Walther
Nernst who won the Nobel Prize in Chemistry in 1920. In a sense, it proves
a measure for whether a molecule has an electron, just as the pK A
provides a measure for a proton. The equation can be used to calculate
the potential, given the midpoint potential and the concentrations of the
reactants and products. A useful number to remember is that when the
equilibrium constant is increased 10-fold, the potential changes by:
(6.9)
E E
( .
( )( .
−
= −
×
×
0
8 314
298
1 9 65 1
J/(K mol)
K
0 0
10 0 0592
59 2
4 C mol
J C
mV
1
1
−
−
)
ln( )
.
.
=
=
E E
RT
nF
ln
=
−
0
[A
]
[A
]
oxidized
reduced
−
= −
+
nFE
nFE
RT ln
0
[A
]
[A
]
oxidized
reduced
( )
( )
ln
Δ
Δ
G
G
R T
rec
rec
=
° +
[A
]
[A
oxidized
reduce ed ]
F
.
.
.
=
×
×
=
×
−
−
6 02 10
6 24 10
9 65
23
1
18
1
mol
C
10
4
1
C mol
−
116
PART I
THERMODYNAMICS AND KINETICS
9781405124362_4_006.qxd 4/29/08 14:07 Page 116