# Physics hep A standard cylinder of oxygen used in a hospital has gauge pressure = 2000 (13,800 ) and volume =?

A standard cylinder of oxygen used in a hospital has gauge pressure = 2000 psi (13,800kPa ) and volume = 14L (0.014m^3 ) at T= 295K . How long will the cylinder last if the flow rate, measured at atmospheric pressure, is constant at 3.0L/min ?

Relevance

Assuming the temperature stays constant, then

pV/n = RT

The absolute pressure is 13,800kPa + 101kPa = 13,901kPa

1.39e7Pa * 0.014m³ / n = 8.314J/ºK/mol * 295ºK = 2453 J/mol

n = 1.39e7Pa * 0.014m³ / 2453 J/mol = 79.35 mol

The flow stops when the pressure in the tank = 1 atm = 101325 Pa:

n = 101325Pa * 0.014m³ / 2453J/mol = 0.58 mol

Therefore 79.35 - 0.58 = 78.77 mol of oxygen leaves the tank.

Assuming the environment outside the tank to be near STP, then there are 22.4 L/mol, if I recall my dusty chemistry. That means there are 78.77mol * 22.4L/mol = 1764 L of oxygen that leave the tank. At 3L/min, the tank will last for t = 1764/3 min = 588 min = 9 hr 48 min.

• You cannot assume STP outside the tank because this would mean your hospital is at T=32 degrees F. I haven't been inside too many hospitals but I imagine this is unlikely the case.

Once you calculate mols oxygen that leave the tank (78.77 mols), use ideal gas law to predict volume of gas (at P=1.01 x 10^5 Pa and T=295 K). Then divide that volume (in Liters) by the volumetric flow rate (Liters/minute) to determine time.

• PV = nRT n and R could be disregarded on account which you're coping with the comparable gas. anticipate T emperature is continuous and does not exchange. confirm you utilize absolute rigidity and discover out how plenty the 17 L container is conserving at 2000 psi. Divide by using 2.8 L/min and by using 60 to get hours. 2000/14.7 x 17/(2.8 x 60)