Entropy and the partition function for nitrogen

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Homework Help Overview

The discussion revolves around calculating the translational entropy for nitrogen (N2) using the partition function. The original poster reports a calculated value of 207.8 J/Kmol, which significantly differs from the tabulated value of 150.4 J/Kmol, leading to confusion regarding the source of the discrepancy.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the values used for constants and the mass of nitrogen, with one participant expressing uncertainty about the calculation process and the resulting entropy value. There are inquiries about unit conversions and potential errors in the calculations.

Discussion Status

The discussion is ongoing, with participants providing insights into potential issues with unit conversions and constants. One participant acknowledges a mistake regarding the SI unit for volume, indicating a productive direction in the conversation.

Contextual Notes

There is mention of specific values for constants and conditions (temperature, pressure, volume) used in the calculations. The original poster notes a significant percentage difference in their calculated value, suggesting that the problem may involve unit conversion errors or miscalculations in the formula.

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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