Chemistry: Hot-Air Ballon Oxygen Storage

[GatorAbe]

Homework Statement

Given that 1,206,900 liters of oxygen are required for a round-the-world trip for a hot-air balloon with a crew of three, and given that carbon-fiber wrapped bottles have a maximum pressure of approx 4500 psi, what total volume of pressure vessel would be necessary to bring along adequate compressed air for the flight? If the bottles come in volumes of 12ft^3, how many bottles does this represent? The balloon flies at an altitude of 40,000 feet. Find these values for 40,000 ft and 0 ft (sea level.)

Homework Equations

This question comes across as a standard Chemistry conversion. Air weighs 1.3 grams per liter. 1 psi is equal to .0703 Kg/cm, so 4500 psi equals 316.38 kg/cm.

The Attempt at a Solution

The question seems to be asking me to convert liters to psi, but I can't figure out how to do that, even when I try converting liter to kg/cm.

 

[chemisttree]

Use Boyle's law. P₁V₁ = P₂V₂

For P₁ use 1 atm (what is that in psi?). You know V₁ and P₂ as well. Can you derive V₂?

 

[Blueshift5]

I would approach this problem by first converting all units to a standard measurement. In this case, it would be helpful to convert liters to cubic feet, as that is the unit given for the carbon-fiber wrapped bottles. To do this, we can use the conversion factor of 1 liter = 0.0353 cubic feet.

So, 1,206,900 liters of oxygen would be equal to 42,658.9 cubic feet.

Next, we can use the given information about the maximum pressure of the bottles (4500 psi) to calculate the total volume of pressure vessel needed. Using the ideal gas law (PV=nRT), we can rearrange the equation to solve for volume (V).

V = nRT/P

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

Since we know the pressure (4500 psi) and the temperature (40,000 feet and sea level), we can calculate the volume of pressure vessel needed at each altitude.

For 40,000 feet:
P = 4500 psi = 310.26 atm (using the conversion factor of 1 atm = 14.7 psi)
T = 216.7 K (using the conversion factor of 1 K = -273.15 degrees Celsius)

V = (n)(0.0821 L atm/mol K)(216.7 K)/(310.26 atm)
V = 0.0578n

For 0 feet (sea level):
P = 4500 psi = 310.26 atm
T = 288.2 K (assuming an average sea level temperature of 15 degrees Celsius)

V = (n)(0.0821 L atm/mol K)(288.2 K)/(310.26 atm)
V = 0.0765n

Now, to calculate the number of bottles needed at each altitude, we can divide the total volume of pressure vessel needed by the volume of each bottle (12 ft^3 = 339.8 L).

For 40,000 feet:
Number of bottles = 0.0578n/339.8 L
Number of bottles = 0.00017n

For 0 feet (sea level