Symmetry of Cyclohexane: How Many Vibrations in Its Spectrum?

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In summary, the point group of the chair conformer of cyclohexane is D3h. Based on this, one might expect to detect 18 Raman active vibrations and 18 infrared active vibrations in its spectrum. However, the attempt at a solution using the given equation resulted in a total of 24 vibrations, which is incorrect. Further clarification or assistance is needed to determine the source of error.
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unknownuser9
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Homework Statement


Determine the point group of the chair conformer of cyclohexane. How many Raman active vibrations and how many infrared active vibrations might you expect to detect in its spectrum?


Homework Equations



(see link below)

The Attempt at a Solution



http://img442.imageshack.us/img442/240/symmetrycw.jpg [Broken]

Im rubbish with LaTex so I've hosted a picture of what I've done in word. I've determined the point group to be D3h but when I use the equation to get the values for the different vibrations, I get a total of 24 when it should be 18 because I started with 18 vectors (3 on each carbon). I am not sure where I am going wrong. Thanks.
 
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Any ideas?
 

1. What is the significance of the symmetry of cyclohexane?

The symmetry of cyclohexane is important because it allows for the molecule to have a more stable and energy-efficient structure. This is due to the fact that the molecule is able to rotate freely around its single bonds without changing its overall shape or energy state.

2. How does the symmetry of cyclohexane affect its physical properties?

The symmetry of cyclohexane results in the molecule having a symmetrical shape, which leads to equal distribution of charge and a nonpolar nature. This makes cyclohexane insoluble in water and less reactive with other polar molecules.

3. Can the symmetry of cyclohexane be broken?

Yes, the symmetry of cyclohexane can be broken by introducing substituents or functional groups to the molecule. This can result in a distorted shape, creating different isomers of cyclohexane with different physical and chemical properties.

4. How does the symmetry of cyclohexane affect its boiling point?

The symmetrical shape of cyclohexane allows for a more efficient packing of molecules, resulting in stronger intermolecular forces. This leads to a higher boiling point compared to other similar sized molecules with less symmetry.

5. How does the symmetry of cyclohexane affect its reactivity?

The symmetry of cyclohexane makes it less reactive compared to other unsymmetrical molecules. This is because the symmetrical shape allows for equal distribution of charge, making it more stable and less likely to undergo reactions with other molecules.

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