Page 80 - Corrosion Engineering Principles and Practice

58 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 59

There is also a parasitic reaction at the aluminum anode that has
to be considered because it has serious safety implications, that is,
the production of hydrogen gas from the reduction of water
described in Eq. (4.17):

2H O + 2e − → H + 2OH − (4.17)
2
2
There is however only one reaction on the cathode, that is, the
reduction of oxygen shown in Eq. (4.18):

O + 2H O + 4e − → 4OH (4.18)
−
2
2
The overall cell voltage can be calculated from thermodynamic
data by computing Gibbs free energy for the individual species
involved in the global reaction described in Eq. (4.19) using the
coefficients expressed in that equation:

−
4Al + 4OH + 3O → 4AlO 2 − + 2H O (4.19)
2
2
4.4.2 Detailed Calculations
Calculate G for each species. The free energy of a substance, for
0
which heat capacity data are available, can be calculated as a function
of temperature using Eq. (4.20):

T2 2 C 0 T 2
G 0 = G 0 − S 0 − T 2 ∫ p dT + C dT (4.20)
∫
0
(T )
(T )
2
1
(T ) 1  T − T  T p
  2 1   T1 T 1
For pure substances (i.e., solids, liquids, and gases) the heat
capacity C is often expressed, as in Table 4.3, as a function of the
0
p
absolute temperature:
C = A BT CT (4.21)
+
0
+
2 −
p
For ionic substances, one has to use another method, such as
proposed by Criss and Cobble in 1964 [1], to obtain the heat capacity,
provided the temperature does not rise above 200°C. The expression
of the ionic capacity in equation (Eq. 4.22) makes use of absolute
entropy values and the parameters a and b contained in Table 4.3.
.
 298 16 (4.22)
0
C = ( . a bS 0 ( 298 K) )( T − 298 16)/ln   T T 2  
.
4 186 +
p
2
By combining Eqs. (4.21) or (4.22) with Eq. (4.20) one can obtain
the free energy in Eq. (4.23) at any given temperature by using the
fundamental data contained in Table 4.3 and Table 4.4:
T
G 0 T ( ) = G 0 (298 K) + ( C − S 0 (298 K) ⋅ ) ( T − 298 16)− T ln    298 16. 2    ⋅C (4.23)
⋅
−
0
.
0
p
2
p
2