Page 73 - Corrosion Engineering Principles and Practice

54 C h a p t e r 4 C o r r o s i o n T h e r m o d y n a m i c s 55

4.3 Nernst Equation
The Nernst equation was named after the German chemist Walther
Nernst who established very useful relations between the energy and
the potential of a cell to the concentrations of participating ions and
other chemical species. Equation (4.8) can be derived from the equation
linking free energy changes to the reaction quotient (Q ):
reaction
∆G = ∆G + RT ln Q reaction (4.8)
0
where Q reaction is defined in Eq. (4.10) for a generalized equation of
the form:
aA bB + ... → mM + nN + ... (4.9)
+

The capital letters A, B, M, and N in Eq. (4.9) represent, respectively,
the reactants and products of a given reaction while the small letters
represent the coefficients required to balance the reaction.
m
n
Q reaction = a ⋅ a ⋅⋅⋅ (4.10)
N
M
a ⋅⋅⋅
b
a ⋅
a
B
A
At equilibrium, ∆G = 0 and Q reaction corresponds to the equilibrium
constant (K ) described earlier in Eq. (4.7).
eq
In the case of an electrochemical reaction, substitution of the
0
relationships ∆G = −nFE and ∆G = −nFE into the expression of a
0
reaction free energy and division of both sides by −nF gives the
Nernst expression for an electrode reaction described in Eq. (4.11):
E = E − RT ln Q (4.11)
0
nF reaction
Combining constants at 25°C (298.15 K) gives the simpler form of
the Nernst equation for an electrode reaction at this temperature:
.
E = E − 0 059 log Q (4.12)
0
n 10 reaction
In Eq. (4.12), the electrode potential (E) would be the actual
potential difference across a cell containing this electrode as a half-
cell and a standard hydrogen electrode as the other half-cell.
Alternatively, the relationship in Eq. (4.3) can be used to combine two
Nernst equations corresponding to two half-cell reactions into the
Nernst equation for a cell reaction:
E cell = E ( 0 cathode − E anode ) − . 0 059 log 10 Q reaction (4.13)
0
n
i
Some of the species that take part in these electrode reactions are
pure solid compounds and pure liquid compounds. In dilute aqueous
solutions, water can be treated as a pure liquid. For pure solid
compounds or pure liquid compounds, activities are constant and
their values are considered to be unity. The activities of gases are
usually taken as their partial pressures and the activities (a ) of solutes
i