When does the ideal gas equation break down?

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Discussion Overview

The discussion revolves around the limitations of the ideal gas equation, particularly under conditions of high pressure and low temperature. Participants explore when the ideal gas law may no longer provide accurate predictions, referencing alternative equations and empirical data.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant notes that the ideal gas equation breaks down at very high pressures and low temperatures, seeking clarification on the specific ranges of these conditions.
  • Another participant suggests that the accuracy required influences when the ideal gas law becomes inadequate, indicating that higher precision demands may reveal deviations sooner.
  • A suggestion is made to study the Van der Waals equation, which accounts for molecular size and interactions, and reduces to the ideal gas equation under certain conditions.
  • A participant shares a graph of the compressibility factor (z) as a function of reduced temperature and pressure, explaining that deviations from 1.0 indicate deviations from ideal gas behavior.
  • One participant expresses uncertainty about the implications of reduced pressure, questioning whether gases at pressures above their critical pressure would exist as liquids.
  • Another participant provides calculations related to nitrogen gas in high-pressure cylinders, noting a discrepancy between theoretical and vendor-specified free volume, and wonders if this deviation could be attributed to the limitations of the ideal gas law.
  • Further details are provided regarding the critical pressure and temperature of nitrogen, with calculations showing that at 200 bars and room temperature, the reduced pressure and temperature suggest a compressibility factor of about 1.08, which aligns with vendor information.

Areas of Agreement / Disagreement

Participants express various viewpoints on the breakdown of the ideal gas law, with no consensus reached on the specific conditions or implications of deviations. Multiple competing views remain regarding the interpretation of compressibility factors and the applicability of alternative equations.

Contextual Notes

Participants reference specific conditions and calculations that may depend on definitions and assumptions related to gas behavior, critical points, and the accuracy of measurements. The discussion includes unresolved mathematical steps and interpretations of empirical data.

LT Judd
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TL;DR
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?
 
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Depends on how accurate you want it. If you need ppm accuracy it breaks down a lot sooner than if you need percent accuracy.
 
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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.
 
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1596075994760.png

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.
 
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.
 

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LT Judd said:
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:
1596372939239.png

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.
 

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