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

In summary, the conversation discusses the calculation of density for a supercritical fluid, specifically xenon. The density can be determined using the law of corresponding states and the compressibility factor, which is a function of reduced temperature and pressure. The NIST website provides information on the fluid properties of xenon, and a generalized correlation can be used to calculate the compressibility factor. This method gives a result of 200 kg/m3, which is close to the density of 2015 kg/m3 found on the NIST website. The conversation also mentions other methods for calculating the compressibility factor, such as using "a" and "b" values, which may result in a different z value.
  • #1
Laurencet
10
0
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
 
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  • #2
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.)
 
  • #3
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##.
 
  • #4
Thankyou for your answers great to see you came up with the same answer.

mjc123 said:
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.


Chestermiller said:

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
 
  • #5
Google “compressibility factor”
 
  • #7

1. How do I determine the density of a super critical fluid?

The density of a super critical fluid can be calculated using the following formula: density = mass / volume. This means that you need to measure the mass of the fluid and its volume in order to calculate its density.

2. What units should I use when calculating the density of a super critical fluid?

The units used for density are typically grams per cubic centimeter (g/cm3) or kilograms per cubic meter (kg/m3). However, you can use any units as long as they are consistent for both mass and volume.

3. Can I use the ideal gas law to calculate the density of a super critical fluid?

No, the ideal gas law is only applicable to gases at low pressures and high temperatures. Super critical fluids do not behave like ideal gases, so this equation cannot be used to calculate their density.

4. How does temperature and pressure affect the density of a super critical fluid?

In general, as temperature and pressure increase, the density of a super critical fluid decreases. This is because at higher temperatures and pressures, the molecules of the fluid are more spread out and have more space between them, resulting in a lower density.

5. Is there a specific method for measuring the density of a super critical fluid?

Yes, there are several methods for measuring the density of a super critical fluid, including pycnometry, vibrating tube densitometry, and pressure-density correlation methods. Each method has its own advantages and limitations, so it is important to choose the most appropriate method for your specific fluid and conditions.

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