[reddie]

I'm stumped on how to apply a certain formula for calculating the vibrational heat capacity of ammonia:



I'm trying to find the vibrational heat capacity of NH3, but I'm not sure how to apply the formula correctly. There are 4 fundamental frequencies (v3 and v4 are doubly degenerate). I thought that Q_N would be equal to Q_v1*Q_v2*Q_v3²*Q_v4². I couldn't get the derivative of ln(Q_N) so I'm having a hard time figuring how to plug in the vibrational frequencies into equation 2.33 so that I get a reasonable answer.

I expected that it ought to go to 3R at high temperatures, since all 6 vibrational levels should be accessible.

Thanks for your *delete me*

[Hunt]

I think you're on the right track , but where's the problem in differentiating LnQ? I think you should have no problem there although your book has already given your the answer for a single mode of vibration. You can see this in the image I attached below :

 



eq 4.48 is the one you need, and it is not difficult to derive it. You need to sum from j =1 till j = alpha ( degrees of freedom ) = 3n - 6 = 6 for ammonia molecule.

As T tends towards infinity , Cv_vib = 6R according to the equipartition theorem.

You can also check the source here