Physical Chemistry

Hybridization Mixes Orbitals into New Directions

Mixing s and p orbitals makes directed hybrid lobes. sp spreads to 180 degrees, sp² to 120, sp³ to 109.5, and the fraction of s character sets the bond angle.

Why does carbon always bond in four directions? Pure s and p orbitals alone cannot explain the neat tetrahedral angle of methane. Hybridization is the idea of mixing the s and p orbitals within one atom to make new orbitals that share the same energy and point in definite directions. The ratio of s to p that you mix sets how many directions the orbitals point and the angle between them: sp is linear, sp² is trigonal planar, and sp³ is tetrahedral.

An s orbital is a round ball with no direction, and a p orbital is two lobes reaching front and back. Slide in a little s-character at a time. The s adds to the front lobe and cancels against the back one, so the two lobes become a hybrid with a big lobe on one side and a small one on the other. Only an orbital this directional can reach out far and overlap well to make a bond.

The number of orbitals you mix sets the number of directions. Mix one s with one p and the two sp directions point exactly opposite at 180 degrees; with two p you get three sp² directions in a plane at 120 degrees; with three p you get four sp³ directions in a tetrahedron at 109.5 degrees. Press a button to see how the orbitals on one atom push apart as far as they can and settle at these angles.

Build methane yourself. Carbon holds out four sp³ orbitals along tetrahedral directions. Attach a hydrogen one at a time and each hydrogen's s orbital overlaps head-on with an sp³ lobe to make a σ bond. Once all four are attached you get a fully symmetric CH₄, and every H-C-H angle comes out to exactly 109.5 degrees.

Take apart the double bond of ethene. The two carbons are sp² hybridized, so one σ bond joins them head-on. But each carbon keeps one p orbital, unused in the hybrid, standing perpendicular to the plane. These two overlap side-on to make a π bond above and below the molecular plane. To keep the π overlap the two carbons must stay in the same plane, so the double bond is flat and cannot be freely twisted.

The bond angle changes smoothly with how much s-character is in the hybrid. At 25% s you reach the 109.5 degrees of sp³, at 33% the 120 degrees of sp², and at 50% the 180 degrees of sp. The more s-character, the wider the orbitals spread. Slide the s-character and watch the angle move with it, and you feel why angles widen where s-character piles up, the sense behind Bent's rule.

In PracticeHybridization mixes the s and p orbitals of one atom into new orbitals that have direction. The more s you mix in, the larger the front lobe and the wider the bond angle. sp³ gives the 109.5-degree tetrahedron of methane, CH₄; sp² gives the 120-degree plane that builds the σ framework of ethene, while the leftover p orbital overlaps side-on to form the π bond that pins the molecule flat and blocks rotation; sp is the 180-degree straight line. The link between s-character and bond angle is exactly the intuition behind Bent's rule.

← Physical Chemistry

Was this helpful? Support seegongsik