Page 100 - Corrosion Engineering Principles and Practice

74 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 75

4.8.1 E-pH Diagram of Water
The following example illustrates how the stability or predominance
diagram of water can be constructed from its basic thermodynamic
information. Equation (4.33) describes the equilibrium between
hydrogen ions and hydrogen gas in an aqueous environment:

+
−
2H + 2e  H (g) (4.33)
2
Adding sufficient OH to both sides of reaction in Eq. (4.33) results in
−
Eq. (4.34) in neutral or alkaline solutions:
+
−
−
2H O 2e  H (g) + 2OH (4.34)
2
2
At higher pH than neutral, Eq. (4.34) is a more appropriate
representation. However, since the concentrations of H and OH
+
−
ions are related by the dissociation constant of water expressed in
Eq. (4.35), Eq. (4.33) and (4.34) basically represent the same reaction
for which the thermodynamic behavior can be expressed by Nernst
equation.
+
−
]
H O  H + OH with K eq = [H [OH ] = 10 − 14 at 25 C (4.35)
−
+
°
2
[H O]
2
RT [H ] 2
+
E + = E 0 + + ln (4.36)
H /H 2 H /H 2 nF p
H 2
that becomes Eq. (4.37) at 25°C and the partial pressure of hydrogen
(p ) of value unity.
H 2
E + = E 0 + − 0.059 pH (4.37)
H /H 2 H /H 2
Equation (4.33) and its alkaline or basic form, Eq. (4.34), delineate
the stability of water in a reducing environment and are represented
in a graphical form by the sloping line (a) on the Pourbaix diagram in
Fig. 4.10. Below the equilibrium reaction shown as line (a) in this
figure, the decomposition of H O into hydrogen is favored while
2
water is thermodynamically stable above the same line (a). As
potential becomes more positive or noble, water can be decomposed
into its other constituent, oxygen, as illustrated in Eqs. (4.38) and
(4.39) for respectively the acidic form and neutral or basic form of the
same process.
O + 4H + 4e −  2 H O (4.38)
+
2
2
O + 2H O 4e −  4OH (4.39)
−
+
2 2
And again these equations are equivalent and only reflect the pH
condition of the environment. The corresponding Nernst expression