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Compare stability between the two bicyclic compounds.

I: bicyclo[2.2.1]heptan‐1‐ylium; II: bicyclo[2.2.2]octan‐1‐ylium

Both compounds I and II seem to be unstable because of violation of Bredt’s rule: they are sp2-hybridized. Then how to compare the stability between I and II?

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The carbocation's energy would be effectively minimised when it adopts an $\ce {sp^2}$ hybridisation scheme, that is, when it adopts a trigonal planar molecular shape. This would ensure that all the precious s orbital character of the carbon atom would be used for bonding with the other three surrounding atoms, leaving a vacant p orbital. However, this bicyclic structure prevents the carbocation from adopting this scheme, destabilising the carbocation formed. This is the basis of Bredt's rule.

On p. 435, Carey & Sundberg (2007) wrote the following:

... bridgehead carbocations become accessible in more flexible structures. The relative solvolysis rates of the bridgehead bromides 1-bromoadamantane, 1-bromobicyclo[2.2.2]octane, and 1-bromobicyclo[2.2.1]heptane illustrate this trend. The relative rates for solvolysis in 80% ethanol at 25 degrees Celsius are shown.

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When there is greater flexibility in the structure, the carbocation is better able to adopt a structure that is closer to the preferred planar structure, thus it is better able to be minimise its energy. This results in a lower activation energy and an increased rate of reaction, explaining the data above.

Reference

Carey, F. A., & Sundberg, R. J. (2007). Advanced Organic Chemistry Part A. Structure and Mechanisms (5th ed.). Springer.

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