6) This question is concerned with vibrational spectra (Infrared and Raman).
a) How many normal modes of vibration are expected in these molecules? (Show calculations)
i) Theobromine (the caffeine-like stimulant that is found in chocolate)
ii) Cyanopolyyne (an organic molecular wire that has been detected spectroscopically in interstellar space, and is postulated to be a precursor to biomolecules: $H C \equiv C-C \equiv C-C \equiv N$
b) In the molecular vibration shown here for trans-1,4-dichlorocyclohexane, both chlorine atoms stretch away from the carbon to which they are bonded (arrows). Will this mode be IR active? $\qquad$ Will this mode be Raman active? $\qquad$ In each case, why or why not?
c) Why are $\mathrm{CH}_{4}$ and $\mathrm{CO}_{2}$ considered greenhouse gases, but $\mathrm{O}_{2}$ and $\mathrm{N}_{2}$ are not?
d) Are the vibrations shown here a degenerate pair (Yes/No)? $\qquad$ Why or why not?

Question

Accepted Answer

∻Solution∻ ‖ 1 ⋮ **Calculate the number of normal modes for Theobromine**: The number of normal modes of vibration for a molecule can be calculated using the formula $3N - 6$ for non-linear molecules, where $N$ is the number of atoms in the molecule. ‖ ‖ 2 ⋮ **Calculate the number of normal modes for Cyanopolyyne**: For linear molecules, the formula is $3N - 5$. Cyanopolyyne is a linear molecule, so we will use this formula to find the number of normal modes. ‖ ‖ 3 ⋮ **Determine IR and Raman activity for trans-1,4-dichlorocyclohexane**: A vibrational mode is IR active if it results in a change in the dipole moment of the molecule. It is Raman active if there is a change in polarizability. ‖ ‖ 4 ⋮ **Explain why $\mathrm{CH}_{4}$ and $\mathrm{CO}_{2}$ are greenhouse gases**: Greenhouse gases absorb and emit infrared radiation due to their molecular vibrations, which involve changes in dipole moment. Molecules like $\mathrm{O}_{2}$ and $\mathrm{N}_{2}$ do not have this property because they are homonuclear diatomic molecules with no permanent dipole moment. ‖ ‖ 5 ⋮ **Determine if the vibrations are a degenerate pair**: Degenerate vibrations are those that have the same energy but occur in different spatial directions. We need to examine the symmetry and energy of the vibrations to answer this. ‖ ∻1 Answer∻ ⚹ The number of normal modes for Theobromine and Cyanopolyyne needs to be calculated using the respective formulas for non-linear and linear molecules. ⚹ ∻2 Answer∻ ⚹ The vibrational mode for trans-1,4-dichlorocyclohexane is IR active if there is a change in dipole moment and Raman active if there is a change in polarizability. ⚹ ∻3 Answer∻ ⚹ $\mathrm{CH}_{4}$ and $\mathrm{CO}_{2}$ are greenhouse gases because they can absorb and emit infrared radiation, unlike $\mathrm{O}_{2}$ and $\mathrm{N}_{2}$, which cannot due to their lack of a permanent dipole moment. ⚹ ∻4 Answer∻ ⚹ Whether the vibrations are a degenerate pair depends on their symmetry and energy. ⚹ ∻Key Concept∻ ⚹ Normal modes of vibration ⚹ ∻Explanation∻ ⚹ The number of normal modes of vibration depends on whether the molecule is linear or non-linear and is calculated using the formulas $3N - 6$ or $3N - 5$, respectively. ⚹ ∻Key Concept∻ ⚹ IR and Raman activity ⚹ ∻Explanation∻ ⚹ A vibrational mode is IR active if it changes the dipole moment and Raman active if it changes the polarizability of the molecule. ⚹ ∻Key Concept∻ ⚹ Greenhouse effect ⚹ ∻Explanation∻ ⚹ Greenhouse gases absorb and emit infrared radiation due to changes in their dipole moment during molecular vibrations, which is not possible for homonuclear diatomic molecules like $\mathrm{O}_{2}$ and $\mathrm{N}_{2}$. ⚹ ∻Key Concept∻ ⚹ Degenerate vibrations ⚹ ∻Explanation∻ ⚹ Degenerate vibrations are those with the same energy occurring in different spatial directions, often associated with the molecule's symmetry. ⚹◊What is the relationship between the normal modes of vibration and the molecular structure of a compound in terms of symmetry and degrees of freedom in vibrational spectroscopy?⍭ Generate me a similar question◊

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