# Carbocation rearrangement with expansion of five-membered ring?

I am confused with this particular problem.

I began the problem with a mechanism as following. In the beginning $\ce{H+}$ protonates the alcohol and leaves as $\ce{H_2O}$. Then everything is about carbocation rearrangement.

But then my professor gave out a different answer saying that ring expansion doesn't happen.

Why doesn't ring expansion take place? Isn't a six-membered ring more stable than a five-membered ring? I am not sure where I am making the mistake.

• With your proposed ring expansion you are going from a tertiary cation to a secondary - ain't going to happen – Waylander May 13 '17 at 16:32
• @Waylander. Generally which of the two products are stable? – Suraj S May 13 '17 at 16:37
• There's also no real driving force for ring expansion here - many of the common examples involve 3- or 4-membered rings which expand in order to reduce the strain present. – orthocresol May 13 '17 at 16:38
• @orthocresol but isn't the 6-membered ring a tad more stable than a 5-membered one? – Pritt Balagopal May 14 '17 at 3:20
• @PrittBalagopal Just a tad, yes. Not quite the same as 4-ring to 5-ring, though. – orthocresol May 14 '17 at 12:16

Your proposed mechanism involves a ring expansion from cyclopentane to cyclohexane. This gives very little driving force in terms of relieving strain in the system. Cyclopentane, in a twisted or "envelope" conformation, has some angle strain ($$102-106^o$$ vs $$109.5^o$$ $$^{ref~1}$$) and it does also has some torsional strain down some of its bonds. This is mostly alleviated by the move to cyclohexane, if it is in a full chair conformation, but the stabilization of the system is minimal ($$25-29kJmol^{-1}$$ $$^{ref~2}$$). Here is a link to a question that deals with ring strain and the calculation of it from $$\Delta H$$ of combustion.
Along with this, your mechanism proposes this ring opening involving an alkyl shift that moves the carbocation from tertiary to secondary. This involves a destabilizing of the cation due to the reduced hyperconjugation (and inductive effect). Studies have shown that a secondary carbocation is around $$67-75kJmol^{-1}$$less stable than a tertiary, for simple substituents (and in the gas phase$$^{ref~3}$$).