A cylinder of oxygen has a gauge pressure of 2000psi and a volume of 16L at 70 degrees F. If the oxygen is used as a constant flow rate of 2 L/minute, measured at 1 atm of pressure, how long will the tank last? Hint: Calculate the mass (grams) of oxygen in the tank and the mass flow rate (number of grams/min) flowing out the tank at 1 atm of pressure.

To determine how long the tank will last, we need to calculate the mass of oxygen in the tank and the mass flow rate of oxygen leaving the tank.

First, let's calculate the mass of oxygen in the tank. We can use the ideal gas law to do this:

PV = nRT

Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)

We need to convert the pressure to atm and the temperature to Kelvin:

Pressure in atm = 2000 psi / 14.7 psi/atm = 136.05 atm
Temperature in K = (70°F - 32) × (5/9) + 273.15 = 294.15 K

Now, we can rearrange the ideal gas law equation to solve for n, the number of moles:

n = PV / RT

n = (136.05 atm) * (16 L) / (0.0821 L·atm/(mol·K)) * (294.15 K)
n = 8.4699 mol

To calculate the mass of oxygen in grams, we need to know the molar mass of oxygen, which is 32 g/mol:

Mass of oxygen = n * molar mass
Mass of oxygen = 8.4699 mol * 32 g/mol
Mass of oxygen = 270.5588 g

Now, let's calculate the mass flow rate of oxygen leaving the tank. We know that the flow rate is 2 L/min at 1 atm of pressure.

Using the ideal gas law again, we can calculate the number of moles of oxygen leaving the tank:

n = PV / RT

n = (1 atm) * (2 L) / (0.0821 L·atm/(mol·K)) * (294.15 K)
n = 0.0605 mol

And finally, the mass flow rate of oxygen in grams per minute is:

Mass flow rate = n * molar mass
Mass flow rate = 0.0605 mol * 32 g/mol
Mass flow rate = 1.936 g/min

Now, to calculate how long the tank will last, we divide the mass of oxygen in the tank by the mass flow rate of oxygen:

Time = Mass of oxygen / Mass flow rate
Time = 270.5588 g / 1.936 g/min
Time ≈ 139.86 min

Therefore, the oxygen tank will last approximately 139.86 minutes when used at a constant flow rate of 2 L/min at 1 atm of pressure.