Write a balanced equation for the overall cell reaction when a lead storage battery is being charged. Refer to Section 19.10.

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1. Identify the half-reactions involved in a lead storage battery. During charging, the reactions are reversed compared to discharging. The discharging reactions are: \( \text{Pb} + \text{PbO}_2 + 2\text{H}_2\text{SO}_4 \rightarrow 2\text{PbSO}_4 + 2\text{H}_2\text{O} \).
2. Reverse the discharging reactions to represent the charging process. The half-reactions for charging are: \( \text{PbSO}_4 + 2\text{e}^- + 2\text{H}^+ \rightarrow \text{Pb} + \text{H}_2\text{SO}_4 \) and \( \text{PbSO}_4 + 2\text{H}_2\text{O} \rightarrow \text{PbO}_2 + 4\text{H}^+ + 2\text{e}^- + \text{SO}_4^{2-} \).
3. Balance the electrons in the half-reactions. Ensure that the number of electrons lost in the oxidation half-reaction equals the number of electrons gained in the reduction half-reaction.
4. Combine the balanced half-reactions to form the overall balanced equation for the charging process. This involves adding the two half-reactions together and canceling out the electrons and any other species that appear on both sides of the equation.
5. Verify that the final equation is balanced in terms of both mass and charge. Check that the number of each type of atom and the total charge are the same on both sides of the equation.