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I'm wondering exactly if this is the correct way to draw this but if this were an elimination reaction, it would have to be flipped.
My question is (assuming I drew out the chair correctly) why would this be an elimination and not substitution. we're given what seems to be a strong base, but are using a polar protic solvent. I thought maybe the solvent would act to stabilize the carbocation, favoring an substition or/
I think this drawing helps to visualize it, |dw:1449433005381:dw| Your drawing was correct, however the way you've drawn the elimination happening is not possible since the hydrogen and bromine have to be anti to each other, but that's not possible! The only way it would be possible is if this went through an E1 mechanism, which isn't possible since the base is too strong. Instead what I believe happens is the bridgehead carbon's hydrogen which is anti to the bromine will be eliminated giving his product: |dw:1449433626914:dw|
|dw:1449433704563:dw| There's the mechanism, so it's actually a very geometric sort of situation to consider. It's pretty confusing to draw this thing like you've drawn it, since doing the ring flip is so difficult when it's attached to another ring! See if you can draw the ring flipped version of your molecule in the Newman projection. Can you flip only one of the rings? Can you flip both rings at the same time?
It's been a while but I don't remember, I think i read something where the two ringed structure cannot undergo a flip
so the strength of the base matters more as to whether it's E2 Vs E1 even more so than the solvent?