Let's begin by writing the balanced reaction for the complete combustion of propane:
C3H8+5O2⟶3CO2+4H2OThis equation tells us that 1 mole of propane
(C3H8) requires 5 moles of oxygen
(O2) for complete combustion.
First, we need to determine how many moles of propane are present in 44 g :
Molar mass of
C3H8=3×12+8×1=44g∕molSo,
Number of moles of
C3H8=‌=1‌molSince 1 mole of propane requires 5 moles of oxygen:
Number of moles of
O2 required
=1×5=5‌molNext, we determine the amount of oxygen produced via the electrolysis of water. During electrolysis, the following reaction occurs:
2H2O⟶2H2+O2 This equation shows that 1 mole of
O2 is produced for every 2 moles of
H2O electrolyzed. According to Faraday's laws of electrolysis:
Q=I×t where:
Q= Total electric charge (Coulombs)
I= Current (Amperes)
t= Time (seconds)
According to Faraday's first law, the amount of substance produced at an electrode is directly proportional to the quantity of electricity passed through the electrolyte:
n=‌ where:
n= Number of moles of gas
z= Number of electrons transferred (for
\ mathrm
{0}−2,z=4 because
2H2O⟶4e−+O2 )
F= Faraday's constant
(96500C∕mol) The total charge
Q required to produce 5 moles of oxygen gas is:
Q=n×z×F=5×4×96500c=1930000cNext, we determine the time required to pass this charge using a current of 200 A :
t=‌=‌ s=9650 sConvert this time into hours:
t=‌| 9650 s |
| 3600 s∕‌ hour ‌ |
≈2.68‌ hours ‌Therefore, the correct answer is Option A: 2.68 hours.