Carbon atoms can mix their orbitals to form new hybrid orbitals. In sp hybridization, one s and one p orbital combine to create two sp orbitals. These sp orbitals are key to understanding acetylene's structure and bonding.

Acetylene, with its carbon-carbon triple bond, showcases sp hybridization in action. Each carbon atom uses its sp orbitals to form sigma bonds, while unhybridized p orbitals create pi bonds. This results in acetylene's unique linear shape and strong triple bond.

sp Hybridization and Acetylene Structure

Formation of sp hybrid orbitals

• sp hybridization involves mixing one s orbital and one p orbital in a carbon atom
  • Creates two sp hybrid orbitals oriented 180° apart from each other (linear geometry)
  • Each sp orbital contains one electron for bonding
• Formation process combines one 2s orbital and one 2p orbital (usually 2p$_z$)
  • Remaining two 2p orbitals (2p$_x$ and 2p$_y$) are unhybridized and perpendicular to the sp orbitals
• sp hybrid orbitals have equal contributions from s and p orbitals (50% s character, 50% p character)
  • Higher s character makes sp orbitals more electronegative than sp$^2$ and sp$^3$ orbitals (greater attraction for electrons)

Sp orbitals in acetylene structure

• Acetylene (C$_2$H$_2$) is a linear molecule with a carbon-carbon triple bond
• Each carbon atom in acetylene undergoes sp hybridization forming two sp hybrid orbitals
  • One sp orbital forms a $\sigma$ bond with the other carbon atom
  • The other sp orbital forms a $\sigma$ bond with a hydrogen atom (C-H bond)
• Unhybridized 2p orbitals on each carbon atom overlap sideways above and below the internuclear axis
  • Forms two $\pi$ bonds between the carbon atoms
• Carbon-carbon triple bond in acetylene consists of one $\sigma$ bond and two $\pi$ bonds
  • Shorter and stronger than double or single bonds due to increased orbital overlap
• Linear geometry of acetylene results from the 180° orientation of sp hybrid orbitals on each carbon atom
  • This orientation determines the bond angle in acetylene (180°)

Acetylene vs other carbon molecules

• Acetylene (sp hybridization):
  1. Carbon-carbon triple bond length: 120 pm
  2. Carbon-carbon bond energy: 837 kJ/mol
  3. Linear geometry
• Ethene (sp$^2$ hybridization):
  1. Carbon-carbon double bond length: 134 pm
  2. Carbon-carbon bond energy: 614 kJ/mol
  3. Trigonal planar geometry
• Ethane (sp$^3$ hybridization):
  1. Carbon-carbon single bond length: 154 pm
  2. Carbon-carbon bond energy: 347 kJ/mol
  3. Tetrahedral geometry
• Bond length decreases and bond strength increases in the order: single < double < triple
  • Due to increasing s character and greater orbital overlap in the bonding orbitals (sp$^3$ < sp$^2$ < sp)

Valence Bond Theory and Molecular Geometry

• Valence bond theory explains the formation of covalent bonds through orbital overlap
• Hybridization of atomic orbitals determines the molecular geometry of compounds
  • sp hybridization results in linear molecular geometry (e.g., acetylene)
  • sp$^2$ hybridization leads to trigonal planar geometry (e.g., ethene)
  • sp$^3$ hybridization produces tetrahedral geometry (e.g., ethane)