Part 2 Chemistry summary:

Sn1 Reactions; Carbocation Stability (Hyperconjugation)

Cathy is an unstable singer due to the charge placed on her, the carbocation, by the leaving group's departure; atoms that are charged are unstable, and want to become neutral. Because she is with Adrian and Brandon, who represent two substituents bonded directly to the central carbon, she only feels comfortable singing in the garage. Cathy is similar to a secondary carbocation and is moderately stable. When Danielle joins of the group, Cathy becomes a tertiary carbocation and stable enough to sing in a competitive environment. The group with Danielle, a three substituent carbocation, is more stable than the group without Danielle, reflecting the differences between a tertiary and secondary carbocation's stability.

Extended Summary here.