EOCE 19.38b solutions manual & MC

[Zellmer, Robert]

Someone asked about EOCE 19.38b.  This is and end-of-chapter
exercise and is in the MC homework.  This problem states "If you heat
a gas such as CO2, you will increase its degrees of translational,
rotational and vibrational motions."  True or False.

The solutions manual states "False".

The problem really is the question is worded poorly.  The fact is
the degrees of freedom (or number of them) themselves don't change.
They are what they are.  The added heat will be distributed between
more of these motions.  Remember the figure of the fraction of molecules
with some kinetic energy versus kinetic energy.  As the temp rises the
distribution of molecules shifts to the right and spreads out.  This
spreading out of the distribution results in more microstates for the
translational motions.  This added heat causes more rotations of the
molecules and inc. the vibrational motions.  Adding heat causes them
to move around more, rotate more and the bonds w/in a molecule to
vibrate more. This leads to more microstates.  You can see pictures in
the solutions manual (although the picture leaves out 1 rotational motion
and 1 vibrational motion).

Here's a link to a discussion of vibrational degrees of freedom in general.

https://chem.libretexts.org/Textbook_Maps/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Spectroscopy/Vibrational_Spectroscopy/Vibrational_Modes/Number_of_Vibrational_Modes_in_a_Molecule <https://chem.libretexts.org/Textbook_Maps/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_%28Physical_and_Theoretical_Chemistry%29/Spectroscopy/Vibrational_Spectroscopy/Vibrational_Modes/Number_of_Vibrational_Modes_in_a_Molecule><https://chem.libretexts.org/Textbook_Maps/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_%28Physical_and_Theoretical_Chemistry%29/Spectroscopy/Vibrational_Spectroscopy/Vibrational_Modes/Number_of_Vibrational_Modes_in_a_Molecule>

You are NOT going to be asked to calculate the actual number of vibrational
degrees of freedom (VDF).  You should know as the number of atoms in a
molecule increases the number of VDF and thus the microstates (the way
energy can be distributed in the molecules).  This increases the entropy of
a substance.  Also, as atoms increase in size (molar mass) the entropy inc.
You can see that if you look at the standard entropy values in Appendix C
for F2, Cl2, Br2 and I2 (in their gaseous states).  You'll see the same thing
for the gases HF, HCl, HBr and HI.

Dr. Zellmer
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