Final answer:
Carbocation rearrangements include hydride shifts, methyl shifts, ring expansions, and transannular shifts, which serve to stabilize the carbocation intermediate in reactions such as SN1 and E1.
Step-by-step explanation:
When assessing the type of carbocation rearrangement that has taken place in a reaction, we look for the movement of groups (hydrogens, alkyls, etc.) which stabilize the carbocation formed during the reaction, such as in SN1 reactions or E1 reactions. A hydride shift involves the movement of a hydrogen atom with its pair of electrons from one carbon to an adjacent carbocation. A methyl shift, similarly, involves the transfer of a methyl group. A ring expansion occurs when a carbocation adjacent to a cycloalkane ring migrates to form a larger ring, thereby stabilizing the positive charge. Lastly, a transannular shift involves the movement of a group across a ring to stabilize a carbocation.
To determine which type of rearrangement occurred, we compare the structure of the reactants to the structure of the stable carbocation intermediate. Typically, the most stable carbocation will be the one that forms preferentially. Depending on the reaction, this would inform us whether a hydride, methyl, ring expansion, or transannular shift took place.