Why Am I Struggling with This Nucleophilic Reaction Problem?

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The discussion revolves around a chemistry problem involving substitution reactions, specifically SN1 and SN2 mechanisms. The participant has struggled with achieving the correct answer, focusing on the top bromine atom for substitution. They recognize that forming a double bond at the bridgehead is not possible and question the stability of carbocations, noting that the top carbocation would be disubstituted. The geometry of the molecule raises concerns about the feasibility of backside attack for SN2, leading to the conclusion that SN1 is more likely. The participant confirms that the bridgehead bromine does not participate in reactions due to stability issues. Ultimately, they clarify that the reaction occurs through an SN1 mechanism at the non-bridgehead site. The conversation highlights the importance of understanding carbocation stability and molecular geometry in determining the appropriate reaction pathway.
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I have attempted this problem several times, but I keep on getting an incorrect answer. I have tried mostly substitution reactions (SN1 and SN2) on the top bromine atom, and I know that a double bond cannot be formed at the bridgehead. Any help in the right direction is greatly appreciated. Thanks!

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What is the order of carbocation stability?
 
Also, given the geometry of the problem, is SN1 or SN2 more likely?
 
Would SN2 be more likely? I tried a substitution at the top bromine atom with the nucleophile -CN, but it was incorrect. I'm not sure where to go from there. For SN1, the carbocation at the top would be disubstituted. I'm assuming that the bromine at the bridgehead doesn't participate in any reactions.
 
Natalie456 said:
I'm assuming that the bromine at the bridgehead doesn't participate in any reactions.
Why not?
 
Natalie456 said:
Would SN2 be more likely?
Geometrically, does it look like a nucleophile will be able to attack the backside of either of the halogenated carbons?
 
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I guess, geometrically, it doesn't look like it will be able to attack either from the backside. So it would be an SN1, then? Also, I thought there could be no reaction at the bridgehead because it cannot be planar, or it is too unstable. Is this correct?
 
I got it! Thank you so much for helping me reason through it!
 
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Natalie456 said:
Also, I thought there could be no reaction at the bridgehead because it cannot be planar, or it is too unstable. Is this correct?
Yes, that sounds right. Ignore where I was going before with that.

Natalie456 said:
I guess, geometrically, it doesn't look like it will be able to attack either from the backside. So it would be an SN1, then?
This would be my guess.
 
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Natalie456 said:
I got it! Thank you so much for helping me reason through it!
Well, now I've thoroughly confused myself. Was it an Sn1 on the non-bridgehead? I need more caffeine.
 
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Oh. Sorry. It was an Sn1 on the non-bridgehead!
 
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