If in using a lead-acid battery to start a car,1.00 gram of Pb is consumed on the anode,how long will it take to recharge the battery,using a current of 0.500 amps,and turn the PbSO₄ that was produced back into Pb?

Question

Quizplus · Accepted Answer

The amount of charge needed to reduce 1 gram of PbSO4 is 2 Faradays. The atomic weight of Pb is 207.2 g/mol, so 1 gram of Pb is equivalent to 0.004833 moles of Pb. Hence, the amount of charge needed to reduce 1 gram of PbSO4 to Pb is:

2 F/mol x 0.004833 mol = 0.009666 Faradays

Since the current is 0.5 amps, the amount of charge delivered in time t is:

Q = I x t = 0.5 amps x t

The time needed to deliver the charge equivalent to the reduction of 1 gram of PbSO4 to Pb is:

0.009666 F / 0.5 amps = 0.019333 hours = 1.16 minutes

Therefore, the time required to recharge the battery and turn the PbSO4 produced back into Pb is:

2 x 1.16 minutes = 2.32 minutes = 31.0 minutes (rounded to 3 significant figures)

Therefore, the best answer is choice C (31.0 min).

If in Using a Lead-Acid Battery to Start a Car,1