Question

Why is there an empty `p` orbital in `"Al"` of `"AlCl"_3?`

Answer 1

Per the literature, `AlCl_3` is defined as a trigonal planer geometry based on three `sp^2` hybrid orbitals from the aluminum. The 3rd p-orbital is simply not involved in the hybridization.

Explanation:

`Al [Ne]3s^(2)3p_x^1p_y^0p_z^0` => `Al[Ne]3(sp^2)^(1)1(p_z^0)` => Trigonal Planar geometry.

The extra p-orbital is simply not included in the hybridization needed to attach 3 substrates to the central element, Al. Only an s and 2 p-orbitals are needed.