# Entropy and the partition function for nitrogen

• jbowers9
In summary: Anyway, thanks for the pointer.In summary, the translational entropy for nitrogen gas is 207.8 j/kgmol. The tabulated value is 150.4, but the discrepancy may involve a factor of .01 or .001.
jbowers9

## 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:
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.

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.

## 1. What is entropy and how does it relate to the partition function for nitrogen?

Entropy is a measure of the disorder or randomness in a system. It is related to the partition function for nitrogen by the equation S = kB ln(Q), where S is entropy, kB is the Boltzmann constant, and Q is the partition function. This equation shows that entropy is directly proportional to the natural logarithm of the partition function.

## 2. How is the partition function for nitrogen calculated?

The partition function for nitrogen is calculated by summing all possible energy states of the molecule, weighted by their respective probabilities. This includes translational, rotational, vibrational, and electronic energy states. The partition function is an important quantity in statistical mechanics, as it is used to calculate thermodynamic properties of a system.

## 3. What is the significance of the partition function for nitrogen in thermodynamics?

The partition function for nitrogen is a key quantity in calculating thermodynamic properties such as internal energy, entropy, and free energy. It provides a way to connect the microscopic behavior of individual molecules to the macroscopic behavior of a system. It also allows for the determination of equilibrium constants and reaction rates.

## 4. How does temperature affect the partition function for nitrogen?

Temperature has a significant effect on the partition function for nitrogen, as it is directly related to the Boltzmann factor in the equation Q = Σe-E/kBT. As temperature increases, the Boltzmann factor decreases, leading to a larger contribution from higher energy states and a larger partition function. This ultimately results in an increase in entropy and other thermodynamic properties.

## 5. Can the partition function for nitrogen be used to predict the behavior of other molecules?

Yes, the partition function can be used to predict the behavior of any molecule, as it is a fundamental quantity in statistical mechanics. However, the exact calculations may differ depending on the specific properties of the molecule, such as its molecular weight and energy levels. Additionally, the partition function is most accurate for gases in thermal equilibrium, but can still provide useful insights for other systems.

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