An emphysema patient is breathing pure O2 through a face mask. The cylinder of O2 contains 0.20 ft3 of O2 gas at a pressure of 2200 lb/in2.
(a) What volume would the oxygen occupy at atmospheric pressure (and the same temperature)?
ft3
(b) If the patient takes in 8.0 L/min of O2 at atmospheric pressure, how long will the cylinder last?
2.55
5
To answer these questions, we need to use the ideal gas law, which states that:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
For part (a), we need to find the volume the oxygen would occupy at atmospheric pressure. The pressure in the cylinder is given as 2200 lb/in². Let's convert this to the SI unit of pressure, which is Pascal (Pa):
1 lb/in² = 6894.76 Pa
So, the pressure in the cylinder is:
2200 lb/in² * 6894.76 Pa/lb/in² = 1.517 x 10^7 Pa
To find the volume at atmospheric pressure, we need to assume the temperature is constant. Therefore, we can rearrange the ideal gas law equation to solve for the volume:
V1 = (P2 × V2) / P1
Where:
V1 = initial volume (volume in the cylinder)
P1 = initial pressure (pressure in the cylinder)
V2 = final volume (volume at atmospheric pressure)
P2 = final pressure (atmospheric pressure)
Given:
P1 = 1.517 x 10^7 Pa
P2 = atmospheric pressure (which is around 101325 Pa)
Now, we can substitute the values into the equation to find V2:
V2 = (P2 × V1) / P1
V2 = (101325 Pa × 0.20 ft³) / (1.517 x 10^7 Pa)
Convert 0.20 ft³ to the SI unit of volume, which is cubic meters:
1 ft³ = 0.02832 m³
0.20 ft³ = 0.20 ft³ × 0.02832 m³/ft³ = 0.005664 m³
V2 = (101325 Pa × 0.005664 m³) / (1.517 x 10^7 Pa)
Calculate V2 to get the volume at atmospheric pressure.