to move the charge. A Coulomb is a certain number of electron charges,
6.24 × 1018. 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, Aoxidized, and the reactant, or reduced species, Areduced
(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 pKA
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)
EE
(.
()(.
−=−
×
×
0 8 314^298
1965 1
J/(K mol) K
00
4 10 0 0592 59 2
Cmol
− 1 JC−^1 mV
)
ln( )==..
EE
RT
nF
=−^0 ln
[A ]
[A ]
oxidized
reduced
−=− +nFE nFE^0 RTln
[A ]
[A ]
oxidized
reduced
() ()ΔΔGGRTrec=°+rec ln
[A ]
[A
oxidized
reduceed]
F
.
.
=.
×
×
=×
−
−
602 10
624 10
965
23 1
18 1
mol
C
1041 Cmol−
116 PARTI THERMODYNAMICS AND KINETICS
