Sulfur trioxide, SO3, is a trigonal planar molecule with D3h symmetry. a.) deter

Question

Sulfur trioxide, SO3, is a trigonal planar molecule with D3h symmetry.

a.) determine the number of normal (fundamental) vibration modes for this molecule

b.) Normal coordinate analysis gives the following symmetries for the vibrational modes: A1', A2'',E',E'. Is this total consistent with the result in "a"? explain. (each E symmetry is doubly degenerate meaning two vibration modes with the same energy.)

c.) Which of these symmetries are IR active?

d.) How many fundamental absorptions should be observed in the IR spectrum of SO3?

e.) The nitrate ion, NO3-, is trigonal planar. How many fundamental absorptions should be observed in the IR spectrum of NO3-? Explain.

Explanation / Answer

a non-linear molecule has 3N - 6 vibrational degrees of freedom whereas a linear molecule has 3N -5 degrees of freedom

Hence SO3 has N=4 i.e 4 atoms

Number of modes = 12-6 = 6

b) Yes it is consistent. Since E is double degenarate. We have 4 modes from E, 2 from E' and two from E'', one A1' and one A2''. Hence 6 normal modes

c) Point group is D3h, we would expect three IR active peaks. Asymmetric stretch highest peak, two bending modes. The symmetric stretch is IR inactive

d)

A2’’ mode is IR active, while the E’ mode is both IR and Raman active

therefore exhibit three absorptions in their IR spectra

e) NO3- has D3h Symmetry

The IR spectra are dominated by the antisymmetric stretching mode of NO3 -, which is doubly degenerate in the bare ion but splits into its two components for most microhydrated ions studied here due to asymmetric solvation of the nitrate core.

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