A typical scuba tank, when fully charged, contains 11 L of air at 206 atm. Assum

Question

A typical scuba tank, when fully charged, contains 11 L of air at 206 atm. Assume an "empty" tank contains air at 34 atm and is connected to an air compressor at sea level. The air compressor intakes air from the atmosphere, compresses it to high pressure, and then inputs this high-pressure air into the scuba tank.

Part A

If the (average) flow rate of air from the atmosphere into the intake port of the air compressor is 260 L/min how long will it take to fully charge the scuba tank? Assume the tank remains at the same temperature as the surrounding air during the filling process.

Express your answer using two significant figures.

Explanation / Answer

Assuming an ideal gas,
n = pV/(RT)

initial moles of air in tank:
(ni) = (34 atm)(11 L)/(RT)
(ni) = (374 atm-L)/(RT)

final moles of air in tank:
(nf) = (206 atm)(11 L)/(RT)
(nf) = (2266 atm-L)/(RT)

mole rate of change:
n/t = (1 atm)(260 L/min)/(RT)
n/t = (260 atm-L/min)/(RT)

(nf) = (ni) + (n/t)(t)
(2266 atm-L)/(RT) = (374 atm-L)/(RT) + (260 atm-L/min)(t)/(RT)
2266 atm-L = 374 atm-L + (260 atm-L/min)(t)
t = 7.276 min.

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