1.9 sp Hybrid Orbitals and the Structure of Acetylene

sp Hybridization and Acetylene Structure

Carbon atoms can mix their orbitals to form new hybrid orbitals suited for bonding. In sp hybridization, one s orbital and one p orbital combine to create two equivalent sp orbitals. Understanding this hybridization is essential for explaining why acetylene has a triple bond, a linear shape, and some distinctive chemical properties.

Formation of sp Hybrid Orbitals

sp hybridization occurs when a carbon atom mixes its 2s orbital with just one of its three 2p orbitals. This produces two sp hybrid orbitals that point in opposite directions, 180° apart, giving a linear geometry.

• Each sp orbital holds one electron available for bonding.
• The two remaining 2p orbitals ($2p_x$ and $2p_y$) stay unhybridized. They sit perpendicular to each other and perpendicular to the sp orbitals.
• sp hybrids have 50% s character and 50% p character. That's more s character than $sp^2$ (33% s) or $sp^3$ (25% s). Why does this matter? Electrons in orbitals with more s character are held closer to the nucleus, making sp-hybridized carbons more electronegative than $sp^2$ or $sp^3$ carbons.

sp Orbitals in Acetylene's Structure

Acetylene ($C_2H_2$) is the simplest alkyne, and every atom in the molecule sits along a single straight line. Here's how the bonding works:

1. Each carbon undergoes sp hybridization, producing two sp orbitals.
2. One sp orbital on each carbon overlaps head-on with an sp orbital on the other carbon, forming a $\sigma$ bond between the two carbons.
3. The remaining sp orbital on each carbon overlaps with a hydrogen 1s orbital, forming a C–H $\sigma$ bond.
4. Each carbon still has two unhybridized p orbitals. These overlap sideways (laterally) with the corresponding p orbitals on the other carbon, forming two $\pi$ bonds.

The carbon-carbon triple bond therefore consists of one $\sigma$ bond and two $\pi$ bonds. The two $\pi$ bonds are oriented in perpendicular planes relative to each other, creating a cylinder of electron density around the $\sigma$ bond axis.

Because the sp orbitals point 180° apart, acetylene's bond angle is exactly 180°, and the molecule is perfectly linear: H–C≡C–H.

Acetylene vs. Other Carbon Molecules

Comparing acetylene, ethene, and ethane shows how hybridization directly affects bond length, bond strength, and geometry:

The trend is straightforward: as you go from single to double to triple bonds, bond length decreases and bond strength increases. This happens because greater s character means the bonding electrons are held more tightly, and the additional $\pi$ bonds increase the total orbital overlap between the two carbons.

Valence Bond Theory and Molecular Geometry

Valence bond theory explains covalent bonds as the result of atomic orbitals overlapping. Hybridization is the key concept that connects the type of bonding a carbon atom does to the shape of the molecule:

• sp → 2 hybrid orbitals → linear (180°)
• $sp^2$ → 3 hybrid orbitals → trigonal planar (120°)
• $sp^3$ → 4 hybrid orbitals → tetrahedral (109.5°)

A useful shortcut: count the number of electron groups (bonds + lone pairs) around a carbon. Two groups means sp, three means $sp^2$, and four means $sp^3$. For acetylene, each carbon has two electron groups (one triple bond and one single bond to H), confirming sp hybridization.