# Vibrational entropy and the partition function

• jbowers9
In summary, the conversation discusses the calculation of the molar entropy of oxygen gas at a specific temperature and pressure, given various parameters such as molecular mass, vibrational and rotational temperatures, and statistical factors. The individual is seeking help with the vibrational entropy calculation and is unsure if they are approaching the problem correctly. They are advised to post their question in the appropriate forum.

## Homework Statement

I'm asked to compute the molar entropy of oxygen gas @ 298.15 K & 1 bar given:
molecular mass of 5.312×10−26 kg, Θvib = 2256 K, Θrot = 2.07 K, σ = 2, and ge1 = 3. I'm currently stuck on the vibrational entropy calculation.

## Homework Equations

[/B]S = NkT ∂/∂T {ln q} + Nk ln (q/N) + Nk
where N is Avogadro's # & k is Boltzman's constant,
so Nk = R.
qvib = e-(Θvib/2T)/(1 - e-(Θvib/T)) where Θvib = hν/k

## The Attempt at a Solution

For the derivative of ln q
I get
∂/∂T {ln q} = Θvib/2T^2{[1+ e-(Θvib/T)]/[1 - e-(Θvib/T)] which @ Θvib = 2256 K is(?) Θvib/2T^2,
so for the first part of the entropy calculation I would have a contribution of
RΘvib/2T.
I can plug in the numbers but I just want to know if I'm headed in the correct direction with this and I will return to confirm other parts of the calculation.

Hey! I'm sorry I can't answer your question, but you're not getting replies probably because it's in the wrong forum. This is more of a thermal physics/thermodynamics question. You should try posting it in the Introductory Physics Homework section.

## 1. What is vibrational entropy?

Vibrational entropy is a measure of the randomness or disorder of the vibrational states of a molecule. It takes into account the different ways in which a molecule can vibrate and the relative frequencies of these vibrations.

## 2. How is vibrational entropy related to the partition function?

The partition function is a mathematical tool used to calculate the thermodynamic properties of a system, including vibrational entropy. It takes into account the energy levels and degeneracies of the different vibrational states of a molecule.

## 3. How does temperature affect vibrational entropy?

As temperature increases, the vibrational states of a molecule become more populated, leading to an increase in the number of ways the molecule can vibrate. This results in an increase in vibrational entropy.

## 4. What role does vibrational entropy play in chemical reactions?

Vibrational entropy can affect the stability and reactivity of molecules, as it contributes to the overall entropy of a system. It can also influence the rate of a chemical reaction by affecting the energy distribution and availability of molecules.

## 5. Can vibrational entropy be measured experimentally?

Yes, vibrational entropy can be measured using techniques such as Raman spectroscopy or infrared spectroscopy. These methods can provide information about the vibrational energy levels and degeneracies of a molecule, which can then be used to calculate the vibrational entropy.