I've just been learning a little thermal chemistry including the equipartition theorem. As part of this, my textbook discusses how to figure out the degrees of freedom for different chemicals.
The answer to one of the exercises says methane has 15 degrees of freedom: 3 for translation, 3 for rotations and 9 for vibrations. I am confused by two of these.
Firstly the text says that diatomic molecules like oxygen gas only have 2 rotational degrees of freedom, because they can't rotate about their axis of symmetry. However methane has an axis of symmetry, so why does it have 3 rotational degrees?
Secondly I don't understand where all the vibration degrees of freedom come from. The molecule has 4 bonds, so wouldn't each bond have one degree for kinetic energy and one for potential energy, for a total of 8 degrees, not 9?