What weight of lead sulfate is produced during discharge of a lead storage battery over a 3.0 hour period at an average current of 0.50 A? [Hint: Consider both electrode processes.]

Question

Quizplus · Accepted Answer

First, we need to write the half-reactions for the discharge of the lead-acid battery:

Pb(s) + HSO4- (aq) → PbSO4(s) + H+(aq) + 2e- (at the anode)

PbO2(s) + 3H+(aq) + HSO4- (aq) + 2e-  → PbSO4(s) + 2H2O(l) (at the cathode)

The balanced overall reaction is:

Pb(s) + PbO2(s) + 2H2SO4(aq) → 2PbSO4(s) + 2H2O(l)

We can use Faraday's laws of electrolysis to calculate the amount of lead sulfate produced during the discharge. We know that 1 Faraday of electricity (96,485 C) will produce 1 mole of electrons, which corresponds to the transfer of 1 mole of electrons in a redox reaction.

The total charge passed during the 3.0 hour discharge is:

Q = It = (0.50 A)(3.0 h)(3600 s/h) = 5400 C

Using the balanced overall reaction, 2 mol of electrons are transferred per mole of PbSO4 produced. Therefore, the number of moles of PbSO4 produced is:

mol PbSO4 = (2 mol e- / 1 mol PbSO4) x (1 F / 96,485 C) x (5400 C) = 0.111 mol

The molar mass of PbSO4 is 303.26 g/mol, so the mass of PbSO4 produced is:

mass PbSO4 = (0.111 mol) x (303.26 g/mol) = 33.7 g

However, this calculation assumes that 100% of the discharged active materials (Pb and PbO2) are converted to PbSO4. This is not the case in practice, due to factors such as incomplete reactions, side reactions, and formation of other products. Typically, the actual amount of PbSO4 produced is around 50-70% of the theoretical amount.

Therefore, the most reasonable answer is B) 17 g, which corresponds to around 50% yield.

What Weight of Lead Sulfate Is Produced During Discharge of a Lead