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Vibrational energy contributes to the increase in molar entropy, because when the molecules vibrate they are moving and causing disorder. Entropy can be thought of as the disorder in a system.
This is in section 9.7 of the textbook. Vibrational energy levels are due to how close the atoms are since the closer the atoms are, the closer the allowed energies of the atoms are. You can think of vibrational energy levels as rotational energy levels as we learned in Chem 14B when we learned about the n sub shells with n = 1, 2, 3, etc., since molecules are not in one rigid form, yet they vibrate and rotate around each other in the substance.
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