# Application of the ideal gas law

• I
Hi,

I want to calculate the amount of liquid nitrogen (at boiling temp.) needed to build a pressure of 10.1 bar in a vessel of volume 66 m3. The liquid will be poured slowly into the vessel, boil off and fill the volume with gas at the specified pressure. I make the assumption that the process is isothermal (T = 300 K); is this a valid assumption? If so, the ideal gas law gives that the needed amount of N2 is n ≈ 27000 moles.

Given that the molar mass is m = 14.0067 g/mol, we get a total mass of M = 378 kg. The density of liquid nitrogen at boiling temp. is 0.808 kg/l, so this gives the needed amount 468 liters.

Is this reasonable, or are there any major flaws in the calculation?

Thanks

The assumption might be valid for a homework problem. It's hard (not impossible) to imagine a physical situation where there was sufficient heat to boil the LN2 and not also heat the gas. There is also a major flaw - check your molar mass.

Chestermiller
Mentor
Hi,

I want to calculate the amount of liquid nitrogen (at boiling temp.) needed to build a pressure of 10.1 bar in a vessel of volume 66 m3. The liquid will be poured slowly into the vessel, boil off and fill the volume with gas at the specified pressure. I make the assumption that the process is isothermal (T = 300 K); is this a valid assumption? If so, the ideal gas law gives that the needed amount of N2 is n ≈ 27000 moles.

Given that the molar mass is m = 14.0067 g/mol, we get a total mass of M = 378 kg. The density of liquid nitrogen at boiling temp. is 0.808 kg/l, so this gives the needed amount 468 liters.

Is this reasonable, or are there any major flaws in the calculation?

Thanks
Isn't the molar mass of N2 28 g/mole?