How do I calculate the density of a super critical fluid?

[Laurencet]

TL;DR Summary

The density of a supercritical fluid

How do I calculate the density of a supercritical fluid? If I have 100 Litres of Xenon at 23°C and 150bar, What will the Xenon in the tank weigh?
The phase diagram is here

https://encyclopedia.airliquide.com/xenon

 

[mjc123]

Look on the NIST website for Xe, under Fluid properties. The answer for your case is 2015 kg/m³.(There is no general equation like PV = nRT to calculate it.)

 

[Chestermiller]

The answer to your question can be determined using the law of corresponding states, based on the compressibility factor z. For xenon, the so-called as centric factor is zero, so the compressibility factor is a function of the reduced temperature and pressure. For xenon, the critical temperature is 289.7 K and 58.4 bars, respectively. So, in this case, the reduced temperature is 296.2/289.7 = 1.02 and the reduced pressure is 150/58.4 = 2.57. From the generalized correlation of compressibility factor as a function of reduced temperature and pressure, this gives a compressibility factor of z = 0.40. Therefore, the number of moles of xenon is $$n=\frac{PV}{zRT}=\frac{(15000000)(0.1)}{(0.40)(8.314)(296.2)}=1523\ moles = 200\ kg$$
So the estimated density is 2000 $kg/m^3$.

 

[Laurencet]

Thankyou for your answers great to see you came up with the same answer.

Look on the NIST website for Xe, under Fluid properties. The answer for your case is 2015 kg/m³.(There is no general equation like PV = nRT to calculate it.)

Do you have a link for where on the NIST website? I searched for XE on the NIST website and came up with 5109 documents... too many to read through.

n=PVzRT=(15000000)(0.1)(0.40)(8.314)(296.2)=1523 moles=200 kgn=PVzRT=(15000000)(0.1)(0.40)(8.314)(296.2)=1523 moles=200 kg​

n=\frac{PV}{zRT}=\frac{(15000000)(0.1)}{(0.40)(8.314)(296.2)}=1523\ moles = 200\ kg So the estimated density is 2000 kg/m3kg/m3kg/m^3.

I came up with 201 kg so very close, is there a good website or paper that explains this, that I can refer to.

Thanks

 

[Chestermiller]

Google “compressibility factor”

 

[mjc123]

https://webbook.nist.gov/cgi/inchi?ID=C7440633&Mask=1Did you try searching for "xenon"? (I know I said "Xe" above, but I meant the element not the letters. I actually found it by googling "xenon density".)

 

[Laurencet]

https://m.tau.ac.il/~tsirel/dump/Static/knowino.org/wiki/Compressibility_factor_(gases).html
I just worked through the above method example calculating "a" "b" and Vm to calculate Z
This gave me a z of 0.389 and a final density of 205.4kg
Further away than the method you used.

Is there more than one way to calculate z? did you do Reduced Temperature / Reduced Pressure?