Final answer:
Using the ideal gas law and given data about the compressed air tank, the calculated number of moles of oxygen is 6.53 moles. This does not match any of the provided answer choices, suggesting there might be an error in the question or available answer options.
Step-by-step explanation:
The question asks how much oxygen is contained in moles in a tank of compressed dry air with a given volume, pressure, and temperature. To calculate the number of moles of oxygen in the tank, we need to use the ideal gas law, which is expressed as PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
First, we need to convert the gauge pressure to absolute pressure by adding atmospheric pressure since the ideal gas law requires absolute pressure:
P(abs) = 2200 psi (gauge) + 14.7 psi (atmospheric) = 2214.7 psi
We also need to convert the volume from cubic feet to liters and the pressure from psi to atm:
- 1.76 cubic feet = 49.83 liters
- 1 psi = 0.068046 atm
So, P(abs) in atm is 2214.7 psi × 0.068046 atm/psi = 150.7 atm
Using the ideal gas law, we can find the total number of moles in the tank:
n = (P × V) / (R × T)
n = (150.7 atm × 49.83 L) / (0.0821 Latm/molK × 293 K) = 31.11 moles
Since the air is approximately 21% oxygen by mole, the moles of oxygen are 21% of the total moles:
moles of O2 = 0.21 × 31.11 = 6.53 moles
The closest answer to our calculation is 6.6 moles, which means there seems to be an error in the selection of provided answers, as none of the options (a) 1.32 moles, (b) 2.64 moles, (c) 0.66 moles, (d) 3.96 moles, matches the calculated value of 6.53 moles.