How Does Filling a Canister with Oxygen Affect Its Weight?

[Luongo]

An empty cylindrical canister 1.60m long and 89.0cm in diameter is to be filled with pure oxygen at 27.0 C to store in a space station. To hold as much gas as possible, the absolute pressure of the oxygen will be 21.3atm . The molar mass of oxygen is 32.0g/mol. 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?

So what i did was got the volume of cylinder using V = pi r^2 h
im (m^3) i multiplied by 1000 to get it in litres. 3981L
then i just plugged in n= 3981L (21.3atm) / .08206 (300K)
what am i doing wrong? shudnt i get the moles in the canister 3445 moles.

Homework Statement

Homework Equations

The Attempt at a Solution

 

[Redbelly98]

So what i did was got the volume of cylinder using V = pi r^2 h
im (m^3) i multiplied by 1000 to get it in litres. 3981L
then i just plugged in n= 3981L (21.3atm) / .08206 (300K)
what am i doing wrong? shudnt i get the moles in the canister 3445 moles.

Your answer looks good to me, but if you are graded on significant figures you'll want to consider that.

 

[tomcue]

Your approach is correct. However, when converting the volume to liters, you forgot to account for the conversion from cubic meters to liters. The correct volume should be 3.981 m^3, which when converted to liters becomes 3,981,000 L. Also, the temperature should be in Kelvin, so it should be 300K instead of 27°C.

Using the ideal gas law, we can calculate the number of moles of oxygen in the canister:

n = PV/RT = (21.3 atm) (3.981 m^3) / (0.08206 L atm/mol K) (300K) = 3445 moles

To calculate the increase in mass, we can use the molar mass of oxygen to convert moles to grams, and then kilograms:

m = nM = (3445 mol) (32.0 g/mol) = 110240 g = 110.24 kg

Therefore, the gas will increase the mass to be lifted by 110.24 kg.