Carbocation Rearrangements and Change in Ring Size

Carbocation rearrangements may give products where there is change in ring size. An example is shown below:
 

Fig. 1: A carbocation rearrangement with ring change is shown. The rearrangement gives a more stable tertiary carbocation

Another example of carbocation rearrangement and ring change (ring expansion) is shown in Fig. 2.  The reaction is a pinacol rearrangement and in this case leads to ring expansion. 

Fig. 2: A carbocation rearrangement with ring change is shown. The rearrangement gives a more stable tertiary carbocation since it is stabilized by the lone pairs of the oxygen atom. This rearrangement is known as the pinacol – pinacolone rearrangement.