Ring expansion means rearrangement
More stable’ usually means ‘more substituted’, but cations can also be made more stable if they become less strained. So, for example, four-membered rings adjacent to cations readily re arrange to five-membered rings in order to relieve ring strain.
This time the cation is formed by protonation of an alkene, not departure of a leaving group, but writing a mechanism should now be a straightforward matter to you.
Although the rearrangement step transforms a stable tertiary cation into a less stable secondary cation, relief of strain in expansion from a four- to a five-membered ring makes the alkyl migration favourable. A synthesis of the natural product α-caryophyllene alcohol makes use of a similar ring expansion. Notice the photochemical [2+2] cycloaddition (Chapter 34) in the synthesis of the starting material.
Rearrangement of this tertiary alcohol in acid gives the target natural product. The four membered ring has certainly disappeared but it may not be obvious at first what has taken its place.
As usual, numbering the atoms makes clear what has happened: carbon 7 has migrated from carbon 6 to carbon 5. Loss of water gives a tertiary carbocation that undergoes rearrangement to a secondary carbocation with expansion of a four- to a five-membered ring.
