Stable chair configuration

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Stable chair configuration

Chemistry
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@Winterlove right away these questions aren't that bad but they depend on whether or not you can go from ring to the chair conformation
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I know that when T-bu and br are in equatorial postions in the chair, that chair configuration is most stable, but when that occurs, they are both in gauche interation, whereas if they were in axial, it would be anti.
Let's translate this to the cyclohexane chair conformation. UP = Dash, Wedge = down. |dw:1444188487612:dw|
I take your figure, I number the carbons, and dashes = down, and wedges = up |dw:1444188614338:dw|
|dw:1444188818878:dw| I use the above figure as reference and put the groups on the appropriate carbons in the positions, up or down in their respective carbons |dw:1444188687289:dw|
clearly in this depiction, the term butyl group in the equatorial position, as well as the bromine group. right away i can tell that this is probably going to be the most stable. we will now do a ring flip to check. when we do a ring flip every group moves a carbon over, and their positions change. if it's axial it becomes equatorial and vise versa. we want to ensure that the number of 1.3 di axial interactions are minimized and clearly in the second figure that's not the case. |dw:1444188966752:dw|
I understand that the first strucure only has two 1,3 diaxial interactions. The second strucure had four, 1,3 diaxial interactions, like you said. However, in the second stucture, t-bu and br are in an anti configuration which is beneficial. In the first strucuture, t-bu and br are in gauch interaction increasing steric strain. So I'm confused with how to deduce which one is more stable when both have some stable and unstable characteristics.
@Winterlove do you have like the energies of the gauche interactions? maybe you could sum those up and see which structure has more energy. I think I see what you're saying, but I think that, for this case perhaps the 1,3 di-axial interactions cause repulsion between groups, that's the way I understood it and if there are more of them the molecule undergoes a ring flip to minimize repulsion. that's a good observation though for that i'm not as sure regarding the fischer projection
This was a question on my quiz. We weren't provided any energies. I'll try to figure out the energies from my textbook. Thanks a bunch.
did they give you the answer?
I got the answer right. The most stable one was the one with 2 diaxial interactions like you said. But I just guessed it at the time. I checked my textbook, the one with 4 dixial interactions has a total energy of 15.2 and the one with 2 diaxial and 1 gauche is 11.8. So it's not that big of a difference

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