Bonding in carbon compounds Knowledge-Based Study

Study notes

1. Tetravalency of Carbon

   Carbon is positioned in Group 14 of the periodic table with an atomic number of 6. Its ground-state electronic configuration is:

   $1s^2 2s^2 2p_x^1 2p_y^1 2p_z^0$

   In its ground state, carbon possesses only two unpaired electrons in its valence shell, which would theoretically allow it to form only two covalent bonds. However, in virtually all organic compounds, carbon is tetravalent, meaning it forms four covalent bonds.

   Orbital Promotion

   To achieve tetravalency, one electron from the filled $2s$ orbital absorbs energy and is promoted to the vacant $2p_z$ orbital. This produces an excited-state configuration:

   $1s^2 2s^1 2p_x^1 2p_y^1 2p_z^1$

   This excited state provides four unpaired electrons available for covalent bond formation. The energy required for this promotion is completely compensated by the release of energy when two additional chemical bonds are formed.

   Orbital Hybridization

   Simple overlap of one $s$ and three $p$ orbitals cannot account for the identical bond lengths, bond energies, and symmetric geometries observed in hydrocarbons. Carbon overcomes this through hybridization—the mathematical mixing of atomic orbitals of slightly different energies to form an equal number of identical hybrid orbitals.

   Types of Hybridization in Hydrocarbons

   • $sp^3$ Hybridization (Alkanes): One $2s$ and three $2p$ orbitals mix to yield four equivalent $sp^3$ hybrid orbitals. These orbitals point toward the vertices of a regular tetrahedron with bond angles of $109.5^\circ$. An example is methane ($\text{CH}_4$) or ethane ($\text{C}_2\text{H}_6$).
   • $sp^2$ Hybridization (Alkenes): One $2s$ and two $2p$ orbitals mix to form three equivalent $sp^2$ hybrid orbitals arranged in a trigonal planar geometry with bond angles of $120^\circ$. One unhybridized $p$ orbital remains perpendicular to the plane. An example is ethene ($\text{C}_2\text{H}_4$).
   • $sp$ Hybridization (Alkynes): One $2s$ and one $2p$ orbital mix to generate two equivalent $sp$ hybrid orbitals directed at $180^\circ$ to each other (linear geometry). Two unhybridized $p$ orbitals remain mutually perpendicular. An example is ethyne ($\text{C}_2\text{H}_2$).

   Covalent Overlap Types

   In hydrocarbons, covalent bonds are formed through two distinct modes of orbital overlap: end-to-end and lateral.

   Sigma ($\sigma$) Bonds

   • Formed by the coaxial (head-on) overlap of hybrid orbitals ($sp^3$, $sp^2$, or $sp$) with each other or with hydrogen $1s$ orbitals.
   • Electron density is concentrated directly along the internuclear axis.
   • $\sigma$ bonds are symmetrical and allow free rotation of attached groups around the bond axis (as in alkanes).

   Pi ($\pi$) Bonds

   • Formed by the sideways (parallel or lateral) overlap of unhybridized $p$ orbitals.
   • Electron density is concentrated above and below the internuclear plane, with a nodal plane along the axis.
   • Because lateral overlap is less effective than end-to-end overlap, a $\pi$ bond is generally weaker and more chemically reactive than a $\sigma$ bond.
   • The presence of a $\pi$ bond restricts free rotation around the carbon-carbon axis, leading to stereoisomerism in alkenes.

   Bond Composition Summary

   Every single bond is a $\sigma$ bond. A double bond consists of one $\sigma$ bond and one $\pi$ bond. A triple bond consists of one $\sigma$ bond and two $\pi$ bonds.

   Bond Length and Bond Strength Trends

   The type of hybrid orbital and the number of shared electron pairs significantly influence bond properties:

   • Bond Order: Increases from single ($\text{C}-\text{C}$) to double ($\text{C}=\text{C}$) to triple ($\text{C}\equiv\text{C}$).
   • Bond Length: Decreases as bond order increases. Single bonds are the longest ($\approx 154\text{ pm}$), double bonds are intermediate ($\approx 134\text{ pm}$), and triple bonds are the shortest ($\approx 120\text{ pm}$). Higher s-character in the hybrid orbital pulls electron density closer to the nucleus, further reducing bond length.
   • Bond Dissociation Energy: Increases with bond order. The triple bond is the strongest and requires the most energy to break completely, although its $\pi$ components remain individually susceptible to addition reactions.

   Catenation

   Carbon uniquely exhibits extensive catenation—the ability of an element to form stable, covalent chains with atoms of the same kind. Due to the high carbon-carbon bond strength and small atomic radius of carbon, hydrocarbons can form unbranched chains, highly branched frameworks, and stable ring systems.