Condensed Summary here.
Part 2 Chemistry Extended Summary:
Sn1 Reactions; Carbocation Stability (Hyperconjugation)
An Sn1 reaction involves the departure of a leaving group as the first step; the departure of a
leaving group forms a carbocation, or a carbon with a positive charge.
Carbocations are innately unstable due to the fact that they have a positively charged carbon;
as molecules generally wish to be neutral, any sort of charge on a molecule results in instability. It is
important to note, however, that certain types of carbocations are more stable than others. This occurs
due to the positive charge’s ability to be spread out over a larger surface area. Tertiary carbocations
have more surface area than secondary carbocations; therefore tertiary carbocations are more stable
than secondary carbocations. The least stable are primary carbocations, which have the least surface
area. Tertiary carbocations consist of a carbon bonded to three groups other than hydrogen; a secondary
consists of a carbon bonded to two groups other than hydrogen; and primary carbocations are a single
carbon bonded one group other than hydrogen.
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.
An important thing to note about carbocation stability is that it’s not an active sharing of the
charge (resonance). This type of sharing is called hyperconjugation because it occurs simply due to
more groups to help distribute the charge around a greater area. Another way to think of carbocation
stability is to have a certain amount of water and two pans of different sizes. A large pan can hold the
water better than a smaller pan because the water has more space to spread out. Sigma bonds on the
adjacent carbons are in the same plane as the empty pi orbitals of the carbon with the positive charge,
resulting in this charge distribution.