A lead storage battery consists of a lead anode and a grid of lead packed with lead dioxide as the cathode. The electrolyte taken is 39% H₂SO₄ by mass having a density of 1.294 g mL^-1. The battery holds 3.5 L of the acid. During the discharge of the battery, the density of H₂SO₄ falls from 1.294 g mL^-1 to 1.139 g mL^-1 which is 20% by H₂SO₄ mass.

Which reaction occurs at the anode during charging?

\(PbSO_4\text{  +  }2H_2O\text{  -----------→  } 2PbO_2\text{  +  }4H^+\text{  +  }SO_4^{2−}\text{  +  }2e^−\)

The correct answer is option 4. \(PbSO_4\text{  +  }2H_2O \longrightarrow 2PbO_2\text{  +  }4H^+\text{  +  }SO_4^{2−}\text{  +  }2e^−\)

In a lead-acid battery, the charging process involves converting the chemical reactions that occurred during discharging back to their original state.

At the anode during charging, lead sulfate \((PbSO_4)\) forms on the plates when the battery is discharged. During the charging process, this lead sulfate needs to be converted back into lead dioxide \((PbO_2)\) and lead \((Pb)\).

The reaction at the anode during charging involves the reduction of lead sulfate \((PbSO_4)\) and water \((H_2O)\). Here's a breakdown of the reaction:

Lead sulfate \((PbSO_4)\) reacts with water \((H_2O)\) to form lead dioxide \((PbO_2)\), hydrogen ions \((H^+)\), sulfate ions \((SO4^2-)\), and electrons \((e^-)\).
\[ PbSO_4 + 2H_2O \rightarrow 2PbO_2 + 4H^+ + SO_4^{2-} + 2e^− \]

So, during charging, lead sulfate is converted into lead dioxide at the anode, which is a crucial step in replenishing the battery's charge.