Page 208 - Handbook of Battery Materials

6.3 The Thermodynamic Situation 177

6.3.3
The Thermodynamic Situation in Lead–Acid Batteries
In the lead–acid battery, sulfuric acid has to be considered as an additional
component of the charge–discharge reactions. Its equilibrium constant influences
the solubility of Pb 2+ and so the potential of the positive and negative electrodes.
Furthermore, basic sulfates exist as intermediate products in the pH range where
Figure 6.1 shows only PbO (cf. corresponding Pourbaix diagrams in Ref. [5], p. 37,
or in Ref. [11]; the latter is cited in Ref. [8]). Table 6.2 shows the various compounds.
The charge–discharge reaction of the negative electrode corresponds to curve A
in Figure 6.1, but the Pb 2+ ion activity is now determined by the solubility of lead
sulfate (PbSO 4 ). Thus Equation 6.12 has to be modified into

+
Pb + H 2 SO 4 → PbSO 4 + 2H + 2e − (6.18)
The dependence of the equilibrium potential on the activities of hydrogen and
sulfuric acid is given by the corresponding Nernst equation:
RT a 2 H +
0,S
0
E = E + ln (6.19)
Pb/PbSO 4 Pb/PbSO 4 2F a +a
H HSO −
4
with the standard value
0,S
E =−0.295 V (6.20)
Pb/PbSO 4
The charge–discharge equation of the positive electrode corresponds to curve B in
Figure 6.1 and the corresponding Equation 6.15. But here also the Pb 2+ activity
is now determined by the solubility of lead sulfate, and Equation 6.15 has to be
modified into:
+
PbSO 4 + 2H 2 O → PbO 2 + H 2 SO 4 + 2H + 2e − (6.21)
with the corresponding Nernst equation
a 2 a
RT H + HSO −
0
0,S
4
E = E + ln (6.22)
PbO 2 /PbSO 4 PbO 2 /PbSO 4 2F a 2
H 2 O
and the standard value
E 0,S = 1.636 V (6.23)
PbO 2 /PbSO 4
Note: Here the calculations of the standard potentials are referred to the dissociation
of H 2 SO 4 ,intoH + and HSO 4 which fairly, closely corresponds to the actual
situation. Sometimes such calculations are based on the assumption of completely
dissociated sulfuric acid,
H 2 SO 4 → 2H +SO 2− (6.24)
+
4
This causes different standard values, but the results are identical (cf., e.g., Ref.
[12]).
Figure 6.2 illustrates the resulting situation. Due to the strong acidic solution
in the battery, it corresponds to Figure 6.1 for small pH values, but here the