BR Isomerism

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DPTinthemaking15

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In BR I'm having a tough time with this concept. It says "Within a staggered conformation of Butane with CH3 groups, Anti is considered the most stable structure over its counterpart Gauche." I understand that steric hindrance is why it is considered the "most stable." But I am currently reading about Cyclohexane. So three- and four-membered rings are reactive, while five- and six-membered rings are considered stable. Well in Cyclohexane it iterates that chair conformation offers two substituent positions: equatorial and axial, and equatorial is considered more stable than axial. But here is my question, since axial looks similar to the staggered Anti compound, how is it not considered more stable? Is it because it can form more hydrogen bonds?

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Actually it doesn't, in the anti-conformation the larger groups are 180 degree apart whereas in the axial position they are eclipsed.

Look at this picture for instance:
LFzn1oluSVuRPr5N41xP_49.png


Picture yourself looking at the molecule from the 109.5 mark. Not all are the two axial H's eclipsed but also, the blue H destabilizes the Red (axial H)! Something that is known as 1,2 di-axial interactions.
 
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You're right in that there are anti staggered relationships with the axial positions on adjacent carbons, but you also get flagpole interactions with the axial groups on every other carbon (carbons 1, 3, 5 or carbons 2, 4, 6), as you see in the pic that 5words posted.

If you have large groups on the axial positions, you'll have undesirable steric interactions; they occupy a smaller amount of space than if you have them at the equatorial positions. Look at the picture, clearly the equatorial blue hydrogens are more spread out than the red axial ones.
 
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