Finding the compressibility factor (Z)

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Discussion Overview

The discussion revolves around determining the compressibility factor (Z) for hydrogen gas under specific conditions of pressure and temperature. Participants explore the implications of using Z in the context of the ideal gas law and its relevance in non-ideal gas behavior, particularly for hydrogen at high temperatures and pressures.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks clarification on how to use the reduced pressure (Pr) and reduced temperature (Tr) to find Z, expressing confusion about the formulas involved.
  • Another participant asserts that the problem is not simply an ideal gas question, emphasizing that Z accounts for deviations from ideal gas behavior due to the high temperature and pressure conditions.
  • A later reply challenges the accuracy of the initial calculations for Tr, pointing out discrepancies in the temperature conversion and suggesting that the value should be significantly different.
  • One participant later corrects their earlier mistake regarding the temperature, providing a revised calculation for Tr and suggesting a value for Z based on a chart found in their textbook.
  • There is discussion about the potential methods to approximate Z, including the possibility of using the Van der Waals equation or the Virial theorem, though no consensus is reached on the best approach.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the problem, with some asserting it is not an ideal gas scenario while others initially consider it as such. There is no consensus on the best method to calculate Z or the accuracy of the values presented.

Contextual Notes

Participants highlight limitations in their calculations, including potential errors in temperature conversion and the need for more significant figures in pressure calculations. The discussion also reflects uncertainty regarding the appropriate equations or methods to use for non-ideal gas behavior.

awyea
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Homework Statement


Determine the volume, in m^3, occupied by 20 kg of hydrogen (H2) at 1170 kPa, 2220°C.

Homework Equations



Z=pv/rt, Pr=P/Pc, Tr=T/Tc, and for hydrogen M = 2.016 (kg/kmol) Tc = 33.2 (K) Pc = 13.0 bar Zc=pc*vc/(RTc)


The Attempt at a Solution


I know if I find Z then the problem is a done deal. I'm just confused about how to use Pr,Tr, and the table to find Z. I found Pr=.9 and Tr=1.59 but is there a formula for Z?

Thanks in advance for the help (I'm not a fan of Thermo so far and my Profs at my old college spoiled me with great teaching)
 
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Isn't it just an ideal gas question?
 
Sadly no, Z is the factor that relates PV/RT of Hydrogen to the PV/RT of and ideal gas. Hydrogen in this problem, because of the high temperatures and pressure, is not an ideal gas.
 
awyea said:

Homework Statement


Determine the volume, in m^3, occupied by 20 kg of hydrogen (H2) at 1170 kPa, 2220°C.

Homework Equations



Z=pv/rt, Pr=P/Pc, Tr=T/Tc, and for hydrogen M = 2.016 (kg/kmol) Tc = 33.2 (K) Pc = 13.0 bar Zc=pc*vc/(RTc)


The Attempt at a Solution


I know if I find Z then the problem is a done deal. I'm just confused about how to use Pr,Tr, and the table to find Z. I found Pr=.9 and Tr=1.59 but is there a formula for Z?

Thanks in advance for the help (I'm not a fan of Thermo so far and my Profs at my old college spoiled me with great teaching)

Something is sadly amiss. You have said that you found Tr = 1.59, after also saying that T = 2220+273 K and Tc = 33.2K. But when I calculate using the equation that you have supplied

Tr = T/Tc

I get Tr = 2493/33.2 , which is roughly 78, not 1.59! Your value for pr seems about right, although you will need to carry at least 1 more significant figure, and preferably 2 more to get a result with any precision.

The other point is that I am not seeing an equation for whichever approach you are using to approximate the ideal gas equation, if that is not good enough. Van der Waals equation? Virial theorem calculation? or what?
 
Ok, I feel really bad about this, the T value is -220 °C, which makes the Tr come out to 53.0K/33.2k=1.59. Pr=.900 with the correct number of sig. figs. After reading the question twice more, looking for something about how to approximate Z, i finally found the attached chart hiding in the back of the book. This makes it look like Z should be .95, although it seems like a very inaccurate way to find it. If this is true, v=(8.314m3Pa/(k*mol)*53K*.95/(11.7x10^3 Pa)=.0358m3/mol
Using dimensional analysis, .0358m3/mol / .00202 kg/mol * 20kg = 354 m3, and it looks like I could have done this problem without wasting everyone's time. Sorry about that.
 

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