Why Does the Ideal Gas Law Fail at the Critical Point of Carbon Tetrachloride?

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SUMMARY

The Ideal Gas Law fails to accurately predict the pressure of carbon tetrachloride (CCl4) at its critical point, where T_c is 283.15 K and density_c is 0.5576 g/cm³. Calculations using the Ideal Gas Law yield a pressure of only 125.6 mmHg, significantly lower than the literature value of 34181 mmHg. This discrepancy highlights the limitations of the Ideal Gas Law under conditions near the critical point, where intermolecular forces become significant and the assumptions of ideal behavior no longer hold.

PREREQUISITES
  • Understanding of the Ideal Gas Law and its assumptions
  • Knowledge of critical points in thermodynamics
  • Familiarity with units of pressure (mmHg, Pa)
  • Basic concepts of density and molar mass calculations
NEXT STEPS
  • Research the limitations of the Ideal Gas Law near critical points
  • Explore the Van der Waals equation for real gas behavior
  • Study the properties of carbon tetrachloride and its phase diagram
  • Learn about intermolecular forces and their effects on gas behavior
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Chemists, physicists, and engineering students interested in thermodynamics and gas behavior, particularly those studying real gases and critical phenomena.

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[SOLVED] ideal gas law numerically

If I calculate the pressure of water vapor at stp (in mmHg),
P= 1000*7.502e-3*R*(0+273)*.804/18;
where the 7.502e-3 factor converts from Pa to mmHg, 1000 is because my density (.804) is in grams/cm^3, 18 is the molar mass of water, etc etc. and this comes out to be 760mm (1atm), as expected. Now, here's the problem. I've got carbon tetrachloride at it's critical point. Literature shows its T_c = 283.15, density_c=.5576, and pressure_c = 34181 mmHg. However, if I just do
P= 1000*7.502e-3*R*(283.15+273)*.5576/154.01;
I get 125.6 mmHg, not 34181 mmHg. Where did I go wrong? Is it just that the dieal gas law fails, because I've also tried data points that aren't near the critical region and at room temp and neither work..
 
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Is your density in g/cm^3 or g/L ?
 

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