How to Calculate the Molar Entropy of H2O(g) at 25°C and 1 bar?

[physicisttobe]

Homework Statement

molar Entropy

Relevant Equations

...

Hi everyone!

It's about the following task:
Calculate the molar entropy of H2O(g) at 25°C and 1 bar.
θrot = 40.1, 20.9K, 13.4K
θvib=5360K, 5160K, 2290K
g0,el = 1

Note for translational part: ln(x!) = x lnx - x

Can you explain me how to calculate this problem?

 

[DrClaude]

Relevant Equations: ...

You can do better than this.

 

[physicisttobe]

I mean I have to calculate the difference right?
I only know this formula: ∆𝑆 = +𝑁𝑘 ln(1/2 ) = −𝑁𝑘 ln(2)
I struggled the whole day with this task, I hope I can solve it with your help

 

[physicisttobe]

I also know this equation: S = -nR (xA lnxA + xB lnxB)
The allegations above do not apply to those equations.

 

[DrClaude]

If you have such a question, you must have seen more equations than this. Assuming that this is a statistical physics course, you must have seen the link between entropy and the partition function.

 

[physicisttobe]

But which equation do you mean? In statistical physics course we didn‘t calculate the molar entropy which is why I have struggles finding the right equation.
But in general you calculate molar quantities with this Sm = ∆S/n

 

[DrClaude]

Are you using a textbook? If yes, which one?

Some resources:
https://chem.libretexts.org/Bookshe..._of_State_Functions_to_the_Partition_Function
https://homepages.rpi.edu/~meuniv/TSM/lecture12.html

Calculate the molar entropy of H2O(g) at 25°C and 1 bar.
θrot = 40.1, 20.9K, 13.4K
θvib=5360K, 5160K, 2290K
g0,el = 1

Do you understand why θ_rot, θ_vib, and g₀ are given?

 

[physicisttobe]

Unfortunately not, our prof. didn't recommend any textbook. I was searching for a good textbook but I couldn't find helpful books, more specifically I couldn't find a textbook which includes exactly the topics we are discussing. Therefore, I had difficulties solving problems. Furthermore, we didn't calculate any problems yet. I hope, we will do some tasks with our prof. in the future but I don't want to wait. I want to practice now in order to understand the further lectures we are discussing in class.
Back to your question: No sorry, I don't understand why those quantities are given.

 

[physicisttobe]

@DrClaude which equation should I use for this? Should I use the boltzmann equation S = kB lnW ?

 

[DrClaude]

@DrClaude which equation should I use for this? Should I use the boltzmann equation S = kB lnW ?

I don't know which equation you should start from since I don't know what is to be taken for granted in your course. My starting point would have been to start from entropy as a function of the partition function.