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Question 1

for polar molecules, which modes of vibration are IR active?

Answer 1

all modes of vibrations are IR active because the dipole changes

Question 2

for nonpolar modes of vibration, which are IR active and inactive?

Answer 2

the symmetric stretches are IR inactive
the asymmetric stretches and bending motions are IR active

Question 3

for CO2 why do we only see 2 peaks instead of 4?

Answer 3

only 3 of the 4 peaks are IR active, two of the peaks, bending motions are equivalent in energy and overlap at the same peak