A carbon atom can hybridize in the \(s p^{2}\) configuration. (a) What is the angle between the hybrid orbitals?

Hybrids form depending on the number of atomic orbitals mixed. In an sp² hybridization, one s and two p orbitals are mixed, resulting in a formation of three equivalent sp² hybrid orbitals. These orbitals are in the same plane and arranged symmetrically around the central atom.

In sp² hybridization, the central atom (in this case, carbon) is surrounded by three hybrid orbitals, which are in the same plane and symmetrically arranged. The geometry of sp² hybrid orbitals is planar trigonal. That is, the three orbitals lie in a plane with the central atom at the center of an equilateral triangle.

To find the angle between the hybrid orbitals, we can use the properties of an equilateral triangle. In an equilateral triangle, all interior angles are equal and sum up to 180 degrees (in a plane). Therefore, the angle between each pair of sp² hybrid orbitals is: \(\angle\) = (180 degrees) / (number of angular regions - 1) = 180° / (3 - 1) = 180° / 2 = 90° But this is only considering half of an equilateral triangle. To consider the full equilateral triangle, the angle becomes: \(\angle\) = 2 * 90° = 180° The geometry of sp² hybridization dictates that every angle between the hybrid orbitals should be equal, resulting in: \(\angle\) = 180° / 3 = 60° Thus, the angle between the sp² hybrid orbitals is 60 degrees.