How long will current flow is a Pb storeage battery uses 500g of Pb to deliver 1.50 amps?

Question

How long will current flow is a Pb storeage battery uses 500g of Pb to deliver 1.50 amps?

What equations or what not do I need to know to work this problem, please help! PS: the answer is 86.2 hours.

Answer 1

Somehow, you have to relate that to the mass of lead, right?  Well, the lead in the battery is how the charge gets produced, so the amount of total charge is related to the amount of total lead.

First, it's 1.5 Amps.  How much charge is this?  An amp is 1 coulomb/sec, and a coulomb is 6.2 E 18 charges.  So that's your charge rate per second.  When that adds up to all the lead you have, you're done.

How much lead?  500 g.  To relate that to charges, you need how many atoms of lead you have since the atoms produce the charge.  Lead is heavy, 207 g/mole.  So you have 500/207 moles of lead.  A mole is 6 E 23 atoms.  

Now you know how many charges per second, and how many atoms (which produce charges) you have total.  If you divide, you'll get the duration in seconds.

So just turn the crank:  500/207*6E23 = 1.45 E 24 atoms.  Divide by 6.2E18*1.5, or 9.3 E18  and you get 1.56 E 5 seconds, or 43.3 hours  (rounding along the way) That's if each lead atom gives you an electron.  But in electrochemistry, an atom can give you one, two, three... electrons.   NOW - check your battery equation, there's the trick.. each lead atom in a battery provides TWO electrons.  Therefore twice the current per atom as was assumed, and twice the length of time discharging at a constant rate.  So muliply this by two, and get 86.6 hours.