Cylindrical Canister Mole Problem

[ryaneye]

Homework Statement

An empty cylindrical canister 1.50 m long and 94.0 cm in diameter is to be filled with pure oxygen at 30.0 C to store in a space station. To hold as much gas as possible, the absolute pressure of the oxygen will be 21.5 atm . The molar mass of oxygen is 32.0 g/mol .

Homework Equations

How many moles of oxygen does this canister hold?
For someone lifting this canister, by how many kilograms does this gas increase the mass to be lifted?

The Attempt at a Solution

 

[jbsteele]

1. How many moles of oxygen does this canister hold?PV = nRTn = PV/RT n = (21.5 atm)(1.50 m^3)/(8.314 J/mol K)(303.5K) n = 30.2 moles of oxygen2. For someone lifting this canister, by how many kilograms does this gas increase the mass to be lifted?m = nM m = (30.2 moles)(32.0 g/mol) m = 964.4 g m = 0.9644 kg

 

[baba89]

To calculate the volume of the canister, we use the formula for the volume of a cylinder: V = πr^2h, where r is the radius (47.0 cm) and h is the height (1.50 m). This gives us a volume of 3.48 x 10^4 cm^3 or 3.48 x 10^-2 m^3.
To calculate the number of moles of oxygen, we use the ideal gas law: PV = nRT, where P is the absolute pressure (21.5 atm), V is the volume (3.48 x 10^-2 m^3), n is the number of moles (unknown), R is the gas constant (0.08206 L·atm/mol·K), and T is the temperature in Kelvin (273.15 + 30 = 303.15 K). Rearranging the equation, we get n = PV/RT = (21.5)(3.48 x 10^-2)/(0.08206)(303.15) = 2.92 moles of oxygen.
To calculate the mass of the oxygen, we use the molar mass of oxygen (32.0 g/mol) and the number of moles we calculated earlier (2.92 moles). This gives us a mass of 93.4 g.
To convert this mass to kilograms, we divide by 1000, giving us a mass of 0.0934 kg.
Therefore, the gas increases the mass of the canister by 0.0934 kg. This may seem like a small amount, but in the weightless environment of a space station, every gram counts. It is important to carefully consider the weight of all objects brought on board, including gas canisters, to ensure the safety and efficiency of the space station.