How Much Nitrogen Gas Escapes from a Compressed Cylinder?

[MathewsMD]

i) Commercially, nitrogen is sold as compressed gas in cylinders. If a cylinder of volume 116 L is filled with N₂ to a pressure of 1.38 x 10⁴ kPa at 298.15K, what mass of N₂ does the cylinder contain? Assume ideal gas behaviour. Answer: Mass N2 = 18104 g = 18.1 kg

ii) Now, regarding part i), if the tap were opened and the gas allowed to escape, how many litres of N₂ gas at 100 kPa and 298.15K would come out of the cylinder. Answer: Volume at 100 kPa = 16008 L. But, 116 L remains in the container, so Vol gas escaped = 16008 – 116 = 15892 L = 1.59 x 10⁴ L

For part ii), the answer was found by finding the total volume that could be contained in the environment using pV = nRT, and then subtracting 116 L from that total since that much is still remaining.

Now, my question is: Is it possible to find the actual amounts (in moles) of N₂ in the cylinder and outside, respectively? I am wondering this b/c the actual pressure in the environment would no longer be exactly 100 kPa since 116 L was removed in terms of nitrogen gas, and now the pressure is not exactly 100 kPa nor is the amount what we originally stated when using pV = nRT.
With the pressures and amounts of nitrogen gas now unknown in the cylinder and environment due to the subtraction of 116 L, is there any way to actual find these variables?
Was there an error in my logic?

Thanks!

 

[Simon Bridge]

For part ii), the answer was found by finding the total volume that could be contained in the environment using pV = nRT, and then subtracting 116 L from that total since that much is still remaining.

In part II - gas escapes until the pressures inside and outside are equal...

Is it possible to find the actual amounts (in moles) of N2 in the cylinder and outside, respectively?

Yes and no.
IRL - the atmosphere is very complicated and perfect measurement is not possible anyway.
In terms of the question though - for practical purposes we can.

I am wondering this b/c the actual pressure in the environment would no longer be exactly 100 kPa since 116 L was removed in terms of nitrogen gas, and now the pressure is not exactly 100 kPa nor is the amount what we originally stated when using pV = nRT.

Even idealizing things, the pressure change is so small you are making a much bigger approximation just by assuming nitrogen behaves as an ideal gas.

With the pressures and amounts of nitrogen gas now unknown in the cylinder and environment due to the subtraction of 116 L, is there any way to actual find these variables?

Yes.

Staying with an idealized situation - think about putting the cylinder of ideal gas at pressure P1 in a big room filled with ideal gas at pressure P2<P1, both gases initially at the same temperature and V2>>V1 ... what you are looking for is the equilibrium pressure.

This is a specific case of gas flowing between two chambers initially at different pressures.
To avoid making any approximations in this model, we'd probably need to know more detail about how the gas is mixed.

If the whole gas ends up at the same temperature as it started, then the equilibrium pressure is just that for the whole occupying the combined volume.

The entire atmosphere would be a very big complicated room indeed.

 

[Chestermiller]

If the final pressure is 100 kPa (such that the final pressure within the cylinder is equal to the external atmospheric pressure), you can calculate the number of moles remaining within the cylinder. You know the initial number of moles in the cylinder, so you know the number of moles that came out of the cylinder. You can then find the volume occupied by this number of moles at the final temperature and pressure.

Chet