— Analytical Chemistry — Spectroscopy Chemistry Question
Infrared spectroscopy
How many vibrational modes does a CO, a H2O, a benzene, or a C60 molecule undergo? Pick the most appropriate answer for each molecule.
A) 1, B) 2, C) 3, D) 4, E) about 30, F) 54, G) 120, H) 174, I) 720, J) not possible to determine based on the information provided.
Model Answer
The number of vibrational modes is given by 3 N – 6 for non–linear and 3N – 5 for linear molecules, where N is the number of atoms in the molecule. Hence for CO: 1, H2O: 3, C6H6: 30, C60: 174.
Two unknown diatomic molecules show a single peak of vibrational absorption in the infrared region of the electromagnetic spectrum. Molecule XY absorbs at a higher frequency than molecule WZ.
Which of the following statements are correct?
1) XY and WZ are heteronuclear
2) XY has a stronger bond than WZ
3) XY has a larger mass than WZ
4) The vibrational eigen frequency of XY is higher than that of WZ
Choose the correct answers from the following ones:
A) 1, B) 2, C) 3, D) 4, E) 1 and 2, F) 1 and 3, G) 1 and 4, H) 2 and 3, I) 2 and 4, J) 3 and 4, K) 1, 2 and 3, L) 1, 2 and 4, M) 1, 3 and 4, N) 2, 3 and 4, O) 1, 2, 3 and 4, P) all are incorrect.
Model Answer
The fact that the molecules have a vibrational infra red absorption implies that the molecules have a permanent dipole moment, hence these diatomic molecules must be heteronuclear.
For a simple harmonic oscillator–type diatomic molecule, the eigen frequency is given by the equation
ν = 1 / (2π) √(k / μ)
where k is the force constant and μ the reduced mass of the molecule. In the absence of any further information, nothing can be said about the reduce masses or the force constants (though bond strength is not related to k, but more likely to bond dissociation energy). The eigen frequency is equal to the frequency of the absorbed photons because the vibrational energy is given by Eν = (v+½) hν and the energy for the resonance transition is ΔE = Ev=1 – Eν=0 = hν.