Discussion
The CORRECT statement regarding the following three normal modes of vibration of SO3 is
Answer: B
The correct statement is (I) is infrared inactive while (II) and (III) are infrared active.
A mode is IR active only if it changes the dipole moment. SO3 is trigonal planar (D3h).
- (I): all three S-O bonds stretch in phase (the symmetric stretch, A1'). The molecule keeps its full symmetry and its dipole stays zero, so this mode is IR inactive (it is Raman active).
- (II): S moves out of the plane one way and the three O atoms the other (A2''). This creates a dipole along the three-fold axis, so it is IR active.
- (III): one S-O bond shortens while the other two lengthen, an asymmetric stretch (E'). The in-plane dipole changes, so it is IR active.
A zero permanent dipole does not make every mode inactive: what matters is whether the vibration makes the dipole oscillate, so the 'none of the modes' option is wrong, and the options calling (III) inactive or (I) active are wrong too.
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