Oxygen therapy uses various devices to provide oxygen to patients having difficulty getting sufficient amounts from air through normal breathing. Among the devices are nasal cannula, which transport oxygen through small plastic tubes from a supply tank to prongs placed in the nostrils. Consider a specific configuration in which the supply tank (volume = 7.00 ft3) was filled to a pressure of 2100.0 psig at a temperature of -30.0°F. The patient is in an environment where the ambient temperature is 40.0°F. When the tank is used, the pressure begins to decrease as oxygen flows at 5.00 L/min through a tube to the cannula where it is discharged into the nostrils.
1) Estimate the original mass of oxygen in the tank using the compressibility-factor equation of state.
2) What is the initial pressure when the temperature is 40.0°F?
3) How long will it take for the gauge on the tank to read 50.0 psig at an atmospheric pressure of 1 atm and the stated discharge?
Please note the unites
Q.1: Given V = 7.00 ft3 = 198.2 L
pressure, P = 2100.0 psig = 142.9 atm
Temperature, T = - 30.0 F = 238.71 K
The compressibility factor equation for oxygen is: Z = PV / nRT ------ (1)
For oxygen, Pr = P / Pc = (142.9 atm / 49.81 atm) = 2.87
Tr = T / Tc = 238.71 K / 154.4 K = 1.546
For the calculated value of Pr and Tr, Z = 0.85
Now from eqn(1)
Z = 0.85 = PV/nRT = 142.9 atm x 198.2 L / (n x 0.0821 L.atm.mol-1.K-1 x 238.71 K)
=> n = 1700.0 mol
=> mass of oxygen = 1700.2 mol x 32.0 g/mol = 54407 g or 54.407 Kg (answer)
Q.2: Given temeperature, T2 = 40.0 F = 277.6 K
According to Gay-Lussac's law,
P1 / P2 = T1/T2
=> 142.9 atm / P2 = 238.71 K / 277.6 K
=> P2 = 166.2 atm or 2442 psig (answer)
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