Nitrogen gas density calculation

[vtmike]

Hi,

I have a tank with internal volume 2.01 L filled with N2 gas at 308K. The pressure inside the tank is 340.23 atm. I am trying to find the density of gas inside the tank. This is required becase the tool inside this chamber cannot operate above densities of .036 lb/in^3.
P = 340.23 atm ; T = 308K ; V = 2.01 L ; R = .0821 L.atm/Mol.K

This is how far I got,
1) Using Ideal gas equation,
PV = nRT
n = 27.04 moles
Thus, density = 376.67 g/L = .013 lb/in^3

2) Using Van Der Waals correction,
P = (nRT/(V-nb)) - ((n^2)*a/V^2)
For Nitrogen (N2), a = 1.37 L^2-atm/mol^2 ; b = .0387 L/mol
n = 49.97
Thus, density = 696 g/L = .025 lb/in^3

Now when I toook the pressure down to 204.13 atm, I expected the density to go down but the density infact increased which did not make any sense to me.

When, P = 204.13 atm ==> Density = .026 lb/in^3 From van Der Waals Equation.
On the other hand, when P = 204.13 atm ===> Density = .008 lb/in^3 using Ideal Gas Equation.

Can anyone explain how the density is going up using Van Der Waals equation when the pressure is reduced?

Thanks,
Mike

 

[BigInch]

I'm not saying its not a good idea to try to calculate it yourself, and assuming your math is correct; perhaps a pretty good stretch, have you ever heard of NIST gas property calculator website?

You might try other EOS methods; BWR maybe.

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[25362]

Using your figures for a, b, R, T, and P, I get n ~ 23.02 not 49.97.

Bringing the pressure down to 204.13 atm, I get n ~ 16.

Therefore kindly check your calculations and report back. Thanks.

 

[katmar]

I agree with 25362's result of n=23.02 using van der Waal. Using the NIST data I get n=22.74 and Uconeer (based on the Peng-Robinson EOS) gives n=23.82. All of these give densities safely below your tool's limit.

Uconeer is a free units conversion program available from the link in my signature below.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[vtmike]

Thanks for the replies everyone.

25362 & katmar you are both right. Apparently it was a simple algebric error in my calculations. n is approximately 23 using Van Der Waals correction to ideal.

Thanks,
Mike