A voltaic cell can be built using the reaction between Al metal and O2 from the air. If the Al anode of this cell consists of 65 g of aluminum, how many hours can the cell produce 1.5 A of electricity, assuming an unlimited supply of O2?
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To find the number of hours the cell can produce 1.5 A of electricity, we need to calculate the total charge produced by the reaction and then divide it by the current.
First, let's determine the moles of Al used in the reaction. We can use the molar mass of aluminum (26.98 g/mol) to convert the mass of aluminum to moles.
65 g Al × (1 mol Al / 26.98 g Al) = 2.41 mol Al
According to the reaction, 4 moles of electrons are produced for every mole of Al reacted. Thus, the total charge produced can be calculated using Faraday's constant:
Total charge = moles of electrons × Faraday's constant
moles of electrons = 2.41 mol Al × (4 mol e- / 1 mol Al) = 9.64 mol e-
Faraday's constant (F) = 96,485 C/mol e-
Total charge = 9.64 mol e- × 96,485 C/mol e- = 932,354 C
Now, we can calculate the time it takes to produce 1.5 A of electricity by dividing the total charge by the current:
Time = Total charge / Current
Time = 932,354 C / 1.5 A ≈ 621,569 seconds
Finally, to convert the time to hours, divide the value by 3600 (the number of seconds in an hour):
Time in hours ≈ 621,569 seconds / 3600 s/h ≈ 172.65 hours
Therefore, the cell can produce 1.5 A of electricity for approximately 172.65 hours.