Question

Scuba Tanks: A popular scuba tank is the “aluminum 80,” so named because it can deliver 80 cubic feet of air at “normal” temperature (72°F) and pressure (1.00 atm, 14.7 psi) when filled with air at a pressure of 3000 psi. A particular aluminum 80 tank has a mass of 15 kg when empty. What is its mass when filled with air at 3000 psi?

Answer 1

V = 80 ft3 of T = 72F, P = 1 atm air at P = 3000 psi

m = 15 kg of empty

find mass when filled with air...

Apply Ideal Gas Law,

PV = nRT

where

P = absolute pressure

V = total volume of gas

n = moles of gas

T = absolute Temperature

R = ideal gas constant

PV = nRT

n = PV/(RT)

P = 3000 psi = 3000/14.7 = 204.081 atm

V = 80ft3 = 2265.35 Liters

T = 72F = 22°C = 22.2+273.15 K = 295.35 K

n = (1)(2265.35)/(0.082*295.35)

n = 93.537 mol of air

mass = mol*MW = 93.537*29 = 2712.573 g = 2.71 kg

Total mass = 15 + 2.71 = 17.71 kg of tank + air