Question

During the charging and discharging of a lead-acid battery (a $\text{Pb}$ anode, a grid of $\text{Pb}$ packed with $\text{PbO}_2$ as cathode, and an aqueous solution of $\text{H}_2\text{SO}_4$ as an electrolyte), which of the following redox reactions does NOT occur?

• A. $\text{Pb}^{4+} + 4\text{e}^- \rightarrow \text{Pb}$
• B. $\text{Pb}^{2+} \rightarrow \text{Pb}^{4+} + 2\text{e}^-$
• C. $\text{Pb} \rightarrow \text{Pb}^{2+} + 2\text{e}^-$
• D. $2\text{Pb}^{2+} \rightarrow \text{Pb}^{4+} + \text{Pb}$

Hint:

In both charging and discharging of a lead-acid battery, the stable end-product of both electrode reactions is always solid insoluble $\text{PbSO}_4$ (where lead is in the $+2$ state).
Therefore, only 2-electron transfer steps involving $\text{Pb}^{0} \leftrightarrow \text{Pb}^{2+}$ and $\text{Pb}^{2+} \leftrightarrow \text{Pb}^{4+}$ occur.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
A lead-acid storage battery is a secondary cell, meaning its chemical reactions are completely reversible. It operates on a specific set of redox processes involving solid Lead (\( \text{Pb} \), oxidation state $0$), Lead dioxide (\( \text{PbO}_2 \), oxidation state $+4$), and Lead(II) sulfate (\( \text{PbSO}_4 \), oxidation state $+2$).
Step 2: Detailed Explanation:
Let us review the chemical half-reactions that take place during operation:
During Discharging (Acting as a Galvanic Cell):
- At the Anode (Oxidation): Elemental lead loses electrons to form \( \text{Pb}^{2+} \) ions.
\[ \text{Pb(s)} \rightarrow \text{Pb}^{2+}\text{(aq)} + 2\text{e}^- \quad \text{[Matches option C]} \]
- At the Cathode (Reduction): \( \text{PbO}_2 \) where lead is in the \( \text{Pb}^{4+} \) state accepts electrons to form \( \text{Pb}^{2+} \) ions.
\[ \text{PbO}_2\text{(s)} + 4\text{H}^+\text{(aq)} + 2\text{e}^- \rightarrow \text{Pb}^{2+}\text{(aq)} + 2\text{H}_2\text{O(l)} \]
Net Discharging Reaction: \( \text{Pb} + \text{PbO}_2 + 2\text{H}_2\text{SO}_4 \rightarrow 2\text{PbSO}_4 + 2\text{H}_2\text{O} \)
During Charging (Acting as an Electrolytic Cell):
The charging mechanism reverses the discharging process by supplying external electrical energy:
- At the Anode: \( \text{Pb}^{2+} \) is oxidized back up to \( \text{Pb}^{4+} \).
\[ \text{Pb}^{2+} \rightarrow \text{Pb}^{4+} + 2\text{e}^- \quad \text{[Matches option B]} \]
- At the Cathode: \( \text{Pb}^{2+} \) is reduced back down to elemental \( \text{Pb} \).
\[ \text{Pb}^{2+} + 2\text{e}^- \rightarrow \text{Pb} \]
Combining these charging steps yields a disproportionation/comproportionation relationship where \( \text{Pb}^{2+} \) splits simultaneously into both configurations:
\[ 2\text{Pb}^{2+} \rightarrow \text{Pb}^{4+} + \text{Pb} \quad \text{[Matches option D]} \]
Analyzing option (A): The direct four-electron reduction of \( \text{Pb}^{4+} \) directly to elemental \( \text{Pb} \) (\( \text{Pb}^{4+} + 4\text{e}^- \rightarrow \text{Pb} \)) does not occur at any stage during the life cycle of a lead-acid battery. Instead, all transitions pass through the stable \( \text{Pb}^{2+} \) intermediate.
Step 3: Final Answer:
The reaction that does NOT occur is \( \text{Pb}^{4+} + 4\text{e}^- \rightarrow \text{Pb} \).