Does the following carbocation undergo rearrangement? If so, illustrate the resulting carbocation and provide the corresponding mechanism.

In acidic medium, 1-propanol can undergo isomerization to 2-propanol. Write a plausible mechanism for this reaction and explain why this isomerization is energetically feasible.

Identify which of the given carbocation species is most likely to undergo rearrangement.

In the following partial reactions below, it shows the possibility of 1,2-alkyl and 1,2-hydride shifts. Which is expected to occur? Explain your answer.

Determine if the carbocation below is expected to rearrange. If so, draw the rearranged form and the arrow-pushing mechanism.