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Why does charging lead acid battery give off hydrogen sulfide gas?

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When a lead-acid battery is discharged, the electrolyte (sulfuric acid) and the active material on the plates of the battery (lead) are consumed to produce water and lead sulfate and current flow. The chemical equation for a lead-acid battery during discharge is: PbO2 Pb 2H2SO4 -->PbSO4 2H2O +Electrical energy. The chemical equation for a lead-acid battery during charge is the reverse with lead, sulfuric acid, and heat being yielded as well as some Hydrogen gas. Ideally, all of the lead sulfate is recombined with the hydrogen from the water to replenish the sulfuric acid. When a lead-acid battery is charged, electrical energy is added to the battery, causing the water and lead sulfate to be recombined to produce electrolyte and the active plate material. During normal charging, hydrogen gas is given off, however if internal damage to the plates or low electrolyte levels exist, internal gassing may create hydrogen sulfide gas. In sealed batteries this would normally not vent to the outside.
 
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What will happen if lead acid battery is charged with ac power?

It will more than likely explode. You charge the battery with a charger that coverts 120V AC to 12V DC.