Chemistry Full Excitation of Molecular Vibration Modes

[VincentLaw]

Homework Statement

Given the relationship Cp/R as a function of Temperature, approximate the number of fully excited vibration modes at a given temperature for a given molecule.

2. The attempt at a solution
I have looked through several textbooks and many web sites, but I can't find this type of problem discussed anywhere. vaguely similar problems I have found only assume given excitation states. It seems like a relatively obscure problem, but I assume there is a generic solution process.

 

[AGNuke]

I assume you are talking about degree of freedom, the total ways in which the molecule can exhibit motion, seeing you mentioned C_p/R.

Anyway, can you give a sample molecule on which you would like to attempt this question on?

 

[JohnRC]

Let's think specifically about Cp/R

What is the value of Cp/R for a monatomic gas? is it the same for all monatomic gases?

Now what is it for a linear rotor? Is it the same for N2, O2, CO2?

What about I2 -- that value is a little bit different -- why?

What is the value of Cp/R for water? Methane? Could you tell whether SO2 was linear or bent by looking at Cp/R?

How and why does Cp/R differ for a really floppy molecule like 1-propanol and a really rigid molecule like benzene?

And if you can work your way through all of that you should have a really good idea about the relationship between Cp/R and "fully excited" vibrational modes.