orbital hybridization explained
Why does carbon always bond in four directions? Pure s orbitals and p orbitals alone cannot explain the neat tetrahedral angle of methane. Hybridization is the idea of mixing the s and p orbitals inside one atom to make new orbitals of equal energy that point in particular directions. The mix sets how many directions the orbitals point and at what angle. sp² is a flat triangle, and sp³ is a tetrahedron. The mix makes the directions. The directions settle.
An s orbital is a ball with no direction, and a p orbital is two lobes stretched front and back. Mix in a little s character. It adds to the front lobe and cancels in the back lobe, and a hybrid orbital appears with one side grown and the other shrunk. Only an orbital that has become clearly directional can reach out and bond well. One side has to grow for the bond to stand. The directions settle.
The number of orbitals you mix sets the number of directions. Mix one s with one p and two sp directions stand opposite at 180 degrees. Two p orbitals give three directions in a plane at 120 degrees. Three p orbitals give four directions in a tetrahedron at 109.5 degrees. sp² and sp³ are the middle and the end of that series. Press the button and the orbitals of one atom push each other as far apart as they can, and the angle they settle at shows itself. The count sets the angle.
Build methane directly. Carbon holds out four sp³ hybrid orbitals in tetrahedral directions. Attach hydrogens one by one and the s orbital of each hydrogen overlaps a lobe head-on, making a sigma bond. When all four are attached, a fully symmetric CH₄ appears, and every H-C-H angle lands exactly on 109.5 degrees. sp³ hybridization is that frame. Four directions are one molecule.
Take apart the double bond of ethylene. The two carbons are hybridized, so one sigma bond joins them head-on. But each carbon still has one p orbital, unused in the hybrid, standing perpendicular to the plane. The two overlap side by side and make a pi bond above and below the molecular plane. sp² is the frame of that plane. To keep the pi overlap, the two carbons have to stay in the same plane, so a double bond is flat and cannot be twisted at will. The plane stops the twist.
The bond angle changes smoothly with the s character in the hybrid. At 25% s character it is the 109.5 degrees of sp³, at 33% it is the 120 degrees of sp², and at 50% it is the 180 degrees of a straight line. The more s character, the wider the orbitals spread. Push the s character and the bond angle moves with it, and you get a feel for why the angle widens on the side where s character gathers. The character pushes the angle.