Question

Why is a carbocation `sp^2` hybridized around the central carbon?

Answer 1

This is a simple consequence of `"VSEPR........"`

Explanation:

`"VSEPR"`, `"valence shell electron pair repulsion theory"`, proposes that electron pairs around a central atom arrange themselves in the shapes of the Platonic solids, the which arrangement minimizes electrostatic repulsion between the bonding and lone pairs.

Two electron pairs are disposed linearly; three electron pairs are arranged in a trigonal plane; four electron pairs are arranged in a tetrahedron.........

Around the carbon in `""^+CR_3`, there are 3 bonding electron pairs, and thus the bond angle `/_R-C-R` is `120^@`. The boron halides and alkyls, are isoelectronic with `""^+CR_3`, tho here `BR_3` is neutral.