The cell reaction of lead storage battery when it is discharged is give below:
At anode: Pb(s) + SO42–(aq) → PbSO4 (s) + 2e–
At cathode: PbO2(s)+ SO42–(aq)+4H+(aq) +2e–→PbSO4(s)+2H2O (l)
Pb(s)+PbO2(s)+2H2SO4(aq)→ 2PbSO4(s) + 2H2O(l)
The density is high when the concentration of H2SO4 is high, but during discharge this sulphuric acid gets consumed and becomes diluted with water. So, density decreases as the product water form dilute the H2SO4 concentration during the discharge of the battery.
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