Question

When a lead acid car battery is recharged by the alternator, it acts essentially as an electrolytic cell in which solid lead(II) sulfate PbSO4 is reduced to lead at the cathode and oxidized to solid lead(II) oxide PbO at the anode. Suppose a current of 96.0A is fed into a car battery for 37.0 seconds. Calculate the mass of lead deposited on the cathode of the battery. Round your answer to 3 significant digits. Also, be sure your answer contains a unit symbol.

Answer 1

Answer:

3.81 g Pb

Explanation:

When a lead acid car battery is recharged, the following half-reactions take place:

Cathode: PbSO₄(s) + H⁺ (aq) + 2e⁻ → Pb(s) + HSO₄⁻(aq)  

Anode: PbSO₄(s) + 2 H₂O(l) → PbO₂(s) + HSO₄⁻(aq) + 3H⁺ (aq) + 2e⁻

We can establish the following relations:

• 1 A = 1 c/s
• 1 mole of Pb(s) is deposited when 2 moles of e⁻ circulate.
• The molar mass of Pb is 207.2 g/mol
• 1 mol of e⁻ has a charge of 96468 c (Faraday's constant)

Suppose a current of 96.0A is fed into a car battery for 37.0 seconds. The mass of lead deposited is:

$37.0s.\frac{96.0c}{s} .\frac{1mole^{-} }{96468c} .\frac{1molPb}{2mole^{-} } .\frac{207.2gPb}{1molPb} =3.81gPb$