Entropy and the partition function for nitrogen

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SUMMARY

The discussion focuses on calculating the translational entropy for nitrogen (N2) using the formula Strans = R ln[(2ΠmkT/h2)3/2*V*e5/2/Na]. The user calculated a value of 207.8 J/Kmol, significantly higher than the tabulated value of 150.4 J/Kmol. Key factors contributing to the discrepancy include incorrect unit conversions, particularly the volume from liters to SI units, and potential errors in the mass value used for nitrogen. The user utilized Excel for calculations and identified that the discrepancy may involve a factor of 0.01 or 0.001 in the power expression.

PREREQUISITES
  • Understanding of the ideal gas law and its application in thermodynamics
  • Familiarity with the concept of translational entropy
  • Proficiency in using Excel for scientific calculations
  • Knowledge of SI unit conversions, particularly for volume
NEXT STEPS
  • Review the derivation of the translational entropy formula Strans = R ln[(2ΠmkT/h2)3/2*V*e5/2/Na]
  • Learn about unit conversions in thermodynamics, especially converting liters to cubic meters
  • Explore the significance of constants such as Planck's constant (h) and Boltzmann's constant (kB) in entropy calculations
  • Investigate common pitfalls in entropy calculations and how to avoid them
USEFUL FOR

Students studying thermodynamics, researchers in physical chemistry, and anyone involved in calculating entropy for gases, particularly nitrogen.

jbowers9
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Homework Statement



I'm attempting to calculate the translational entropy for N2 and I get a value of 207.8 J/Kmol. The tabulated value is given as 150.4 and I am stumped as to why the decrepancy.
T = 298.15 K and P = 0.99 atm and V = 24.8 L
R = 8.314 J/Kmol[/B]

Homework Equations


Strans = R ln[(2ΠmkT/h2)3/2*V*e5/2/Na][/B]

The Attempt at a Solution


I plugged in all the correct(?) values and cannot figure out what I'm doing wrong.
[/B]
 
Last edited:
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What value did you use for the mass?
 
28 amu =
4.65E-26 kg
 
My calculated value is off by 30% which is huge. I rechecked the constants I used and the units :
h = 6.63E-34 m2kg/s
k
B = 1.38E-23 JK-1
NA
= 6.02E+23
T
= 298.15 K
V
= 24.79 L
I really am stumped. I'm using Excel to do the calculation and I've checked it several times and
ln[(2ΠmkT/h2)3/2*Ve5/2/Na] calculates to 25 when it "should" be about 18 and change.
I don't know where to go with this. All the other entropy contributions to the entropy from the total partition function were right on the mark except this one. HELP!
 
jbowers9 said:
My calculated value is off by 30% which is huge. I rechecked the constants I used and the units :
h = 6.63E-34 m2kg/s
k
B = 1.38E-23 JK-1
NA
= 6.02E+23
T
= 298.15 K
V
= 24.79 L
I really am stumped. I'm using Excel to do the calculation and I've checked it several times and
ln[(2ΠmkT/h2)3/2*Ve5/2/Na] calculates to 25 when it "should" be about 18 and change.
I don't know where to go with this. All the other entropy contributions to the entropy from the total partition function were right on the mark except this one. HELP!

I've also found, thanks to Excel, that the descrepancy involes either a factor of .01 inside the power expression
(2ΠmkT/h2)3/2 or .001 times the expression [(2ΠmkT/h2)3/2*Ve5/2/Na] but I still don't know what it could be.
 
Be sure to convert liters to SI units.
 
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Likes   Reactions: DrClaude
Wow. Thanks a pile dude(?). What an embarassing oversite on my part! (Homer Simpson Duh!) All this time, I'm in my 50's, and I'm thinking liter is, or absentmindedly thinking it is, the SI unit for volume. It's all about the units, man.
 

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