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

## Summary:

The density of a supercritical fluid

## Main Question or Discussion Point

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
Mentor
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 $kg/m^3$.

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
Mentor