When does the ideal gas equation break down?

[LT Judd]

TL;DR Summary

At what pressures and temperatures is ideal gas equation no longer valid?

P1/V1/T1 = P2 V2 /T2 is derived from the ideal gas equation. However it is stated that this equation breaks down at very high pressures and at very low temperatures. Does anyone know what kind of pressures and temperatures we are talking about here?

 

[Vanadium 50]

Depends on how accurate you want it. If you need ppm accuracy it breaks down a lot sooner than if you need percent accuracy.

 

[phyzguy]

I suggest you study the Van der Waals equation. It reduces to the ideal gas equation at low pressures and densities, and the two constants in the equation (usually called a and b) will give you information on how much it deviates from the ideal gas equation.

 

[Chestermiller]

This graph shows the compressibility factor z for a gas as a function of the reduced temperature and the reduced pressure. The reduced temperature is the actual temperature divided by the critical temperature. The reduced pressure is the actual pressure divided by the critical pressure. Deviations of z from 1.0 represent deviations from the ideal gas law.

 

[LT Judd]

Okay, I am just trying to get a gut feel for it, I can see from the above graph that the smaller molecules (N2) do better than the larger molecules (isopentane) ,but not sure about the "reduced pressure" though, at z greater than one ( actual pressure is higher than critical pressure), they wouldn't be gases anyhow would they?. they would be liquids.
Anyhow I did some rough calcs on a 200 bar "quad" of G size cylinders of nitrogen , from some vendors spec sheet. The quoted free volume is about 10% greater than my theory. (P1/V1=P2/V2)
http://aloffshore.com/wp-content/uploads/2017/06/Product-Datasheet-Offshore-Q64.pdf
Just wondering if at 200 bar could the deviation from the ideal gas law be coming into play.

 

[Chestermiller]

Okay, I am just trying to get a gut feel for it, I can see from the above graph that the smaller molecules (N2) do better than the larger molecules (isopentane) ,but not sure about the "reduced pressure" though, at z greater than one ( actual pressure is higher than critical pressure), they wouldn't be gases anyhow would they?. they would be liquids.

According to the Law of Corresponding States, this graph is supposed to apply roughly roughly equally the same for all substances, so there should be no major differences between the compressibility factors for N2 and isopentane.

Anyhow I did some rough calcs on a 200 bar "quad" of G size cylinders of nitrogen , from some vendors spec sheet. The quoted free volume is about 10% greater than my theory. (P1/V1=P2/V2)
http://aloffshore.com/wp-content/uploads/2017/06/Product-Datasheet-Offshore-Q64.pdf
Just wondering if at 200 bar could the deviation from the ideal gas law be coming into play.

The critical pressure of N2 is 34 bars, and its critical temperature is 126 K. So, at room temperature and 200 bars, the reduced pressure of N2 is 5.9 and its reduced temperature is 2.3. Here is a more detailed compressibility plot:

From this graph, you can see that at these conditions, the compressibility factor would be about 1.08. This would be consistent with you vendor information.