A fully charged lead–acid battery consists of one electrochemical cell that contains the following half-reactions under standard conditions:
PbO₂(s) + SO₄²⁻(aq) + 4 H⁺(aq) + 2 e⁻ → PbSO₄(s) + 2 H₂O(l) E° = +1.69 V
PbSO₄(s) + 2 e⁻ → Pb(s) + SO₄²⁻(aq) E° = –0.36 V
The internal resistance of the cell is 0.15 Ω. While delivering current to a portable device, the cell operates at a constant current of 5.0 A.
(a) Write the balanced overall reaction that occurs during discharge of the cell and calculate its standard potential, E°_cell.
(b) At the 5.0 A discharge current, determine the instantaneous terminal voltage of the cell (the potential difference measured across the external terminals) assuming standard-state concentrations are maintained.
(c) When the battery is recharged, identify which of the two given half-reactions is reversed at each electrode. Explain how this reversal affects the sign designation (anode vs. cathode) compared with the discharge process.
(d) Calculate the minimum external potential that must be applied to recharge the cell at the same 5.0 A current if the internal resistance remains 0.15 Ω and concentration polarization is negligible.