Page 102 - Corrosion Engineering Principles and Practice

76 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 77

be considered, that is, two solid species (Al and Al O ·H O) and two
2
2
3
3+
ionic species (Al and AlO ). The first equilibrium to consider
−
2
examines the possible presence of either Al or AlO expressed in
−
3+
2
Eq. (4.42).
Al 3+ + 2H O  AlO 2 − + 4H (4.42)
+
2
Since there is no change in valence of the aluminum present in the
two ionic species considered, the associated equilibrium is independent
of the potential and the expression of that equilibrium can be derived in
Eq. (4.43) for standard conditions.
RT ln K eq = RT ln Q = −∆ G reaction (4.43)
0
where Q is expressed in Eq. (4.44).
a × a 4
Q = AlO 2 − H + (4.44)
a + × a 2
Al 3 H O
2
Assuming that the activity of H O is unity and that the activities
2
of the two ionic species are equal, one can obtain a simpler expression
+
of the equilibrium in Eq. (4.43) based purely on the activity of H ,
Eq. (4.45) and its logarithmic form, Eq. (4.46).
RT ln [H ] = −∆ G 0 reaction (4.45)
+
4
0
log 10 [H ] = − pH = 4 × −G reaction RT (4.46)
+
2.303 ×
0
and if G is expressed in joules and the temperature is 25°C or 298 K
Eq. (4.46) is even further simplified in Eq. (4.47).
pH = 4.38 × 10 −5 × G 0 reaction (4.47)
By using the standard thermodynamic data from the literature [3],
it is possible to calculate that the free energy of reaction in
3+
−1
Eq. (4.42) is in fact equal to 120.44 kJ mol when both [Al ] and [AlO ]
−
2
are equal. Equation (4.47) then becomes Eq. (4.48).
pH = 4.38 × 10 −5 × 120,440 = 5.27 (4.48)
This is represented, in the E-pH diagram shown in Fig. 4.11, by
3+
a dotted vertical line separating the dominant presence of Al at
low pH from the dominant presence of AlO at the higher end of
−
2
the pH scale.
The next phase for constructing the aluminum E-pH diagram is
to consider all possible reactions between the four chemical species
containing aluminum retained for this exercise, that is, Al, Al O ·H O,
2
2
3
Al , and AlO . These reactions are summarized in Table 4.12. A
3+
−
2
computer program that would compare all possible interactions and
rank the chemical species involved in terms of their thermodynamic