Page 206 - Handbook of Battery Materials

6.3 The Thermodynamic Situation 175

and its dependence on the pH is described by the Nernst equation (Equation 6.6),
RT a 2
0,S
0
E = E + ln H + (6.6)
2F a H 2
H + /H 2
0
with E = equilibrium potential, E 0,S = standard value of the equilibrium potential
−1
H
H
(when a + and a H 2 are 1 mol L , and a +, a H 2 = activities (i.e., effective
concentrations) of H and H 2 , respectively.
+
Using the definition of the pH value, pH = –log(a +), and the relation between
H
) (Henry’s law),
the gas pressure (p H 2 ) and the concentration of dissolved gas (a H 2
Equation 6.6 can be written:
RT 1
0,S
0
E = E − 2.303 pH + log(p H 2 ) (6.7)
H + /p H 2 F 2
RT
with −2.303 =−0.0592V.
F
+
This is the curve H 2 /H in Figure 6.1 for p H 2 = 1 atm. The standard value of
−1
this equation (proton activity a + = 1mol ; p H 2 =1 atm)
H
0,S
E = 0 (6.8)
H + /pH 2
Equation 6.8 represents by definition the zero point of the electrochemical potential
scale (standard hydrogen electrode, often denoted SHE).
The corresponding relation for oxygen evolution:
1
+
H 2 O → O 2 + 2H + 2e − (6.9)
2
has the equilibrium potential
1/2 2
a
RT a O 2 H +
0,S
0
E = E + ln (6.10)
O 2 O 2
2F a H 2 O
with the standard value
0,S
E = 1.229 V (6.11)
O 2
In Figure 6.1, this is represented by the H 2 O/O 2 , curve.
E 0 is the decomposition voltage of water. Above this value, water is not stable
O 2
but decomposes with formation of oxygen (O 2 ).
+
In Figure 6.1, H 2 O/O 2 and H 2 /H curves are straight lines which have the same
slope of −0.059 V per pH unit.
6.3.2
Oxidation of Lead
Curve A in Figure 6.1 corresponds to the oxidation of lead to its divalent ion,
described by the reaction
Pb ↔ Pb 2+ + 2e − (6.12)