Organic Chemistry

Carbon has atomic number $Z = 6$ and electron configuration $1s^2\,2s^2\,2p^2$. The four valence electrons ($2s^2 2p^2$) can form up to four covalent bonds, a property that makes it the fundamental element of organic chemistry, capable of building chains, branches, and rings of unlimited complexity.

The atomic orbitals of carbon in the valence shell are:

• One 2s orbital (spherical, lower energy)
• Three 2p orbitals (2p_x, 2p_y, 2p_z, dumbbell-shaped, oriented along the Cartesian axes, slightly higher energy)

In the ground state, carbon has configuration $2s^2 2p_x^1 2p_y^1$, with two half-filled orbitals (2p) and one filled (2s). However, to form four equivalent bonds as in methane (CH₄), the orbitals hybridize: the four orbitals (one 2s + three 2p) mix to generate equivalent hybrid orbitals, all half-filled and symmetrically oriented in space.

A sigma bond ($sigma$) forms by head-on overlap along the bond axis; a pi bond ($pi$) forms by lateral overlap above and below the molecular plane, and is weaker and more reactive than a $sigma$ bond.

Real-world applications: carbon's versatility is the basis of life and organic materials: plastics, pharmaceuticals, fuels, textile fibers, polymers. The ability to form stable C—C bonds is what distinguishes organic chemistry from inorganic chemistry.

Hybridization is the linear combination of atomic orbitals to form equivalent hybrid orbitals, with shape and energy intermediate between the starting orbitals. For carbon, three fundamental types exist:

sp³ Hybridization: combination of one 2s orbital + three 2p orbitals → four equivalent sp³ hybrid orbitals.

• Geometry: tetrahedral, bond angles $109.5^circ$
• C—C bond length: $approx 154\,\mathrm{pm}$ (single bond)
• Examples: $mathrm{CH_4}$ (methane), $mathrm{C_2H_6}$ (ethane), $mathrm{C_3H_8}$ (propane)
• All bonds are of type $sigma$

sp² Hybridization: one 2s orbital + two 2p orbitals → three equivalent sp² hybrid orbitals; the third 2p orbital remains unhybridized and forms the $pi$ bond.

• Geometry: trigonal planar, bond angles $120^circ$
• C=C bond length: $approx 134\,\mathrm{pm}$ (double bond: $1sigma+1pi$)
• Examples: $mathrm{C_2H_4}$ (ethylene), $mathrm{C_3H_6}$ (propylene)

sp Hybridization: one 2s orbital + one 2p orbital → two equivalent sp hybrid orbitals; two 2p orbitals remain unhybridized and form two $pi$ bonds.

• Geometry: linear, bond angles $180^circ$
• C≡C bond length: $approx 120\,\mathrm{pm}$ (triple bond: $1sigma+2pi$)
• Examples: $mathrm{C_2H_2}$ (acetylene), $mathrm{HC≡N}$ (hydrogen cyanide)

General rule: the higher the s-character of the hybrid orbital (33% in sp², 50% in sp), the stronger and shorter the bond, and the greater the electronegativity of the hybridized carbon.

Real-world applications: hybridization determines reactivity: sp carbons (acetylenes) are more acidic (pKₐ ≈ 25) than sp³ (pKₐ ≈ 50), enabling selective deprotonation reactions.

Organic molecules can be represented with different types of formulas, each with a different level of detail:

• Lewis formula: shows all atoms, bonds (lines), and lone pairs of electrons (dots). Example: $mathrm{CH_4}$ shows C with 4 single C—H bonds, no lone pairs. Essential for understanding electronic structure and formal charge distribution.
• Condensed formula: writes atoms in sequence, grouping hydrogens bonded to each carbon. Example: $mathrm{CH_3CH_2CH_3}$ for propane, or $mathrm{CH_3(CH_2)_4CH_3}$ for hexane. It is the most common notation in chemical reactions for compactness.
• Skeletal (line-angle) formula: each vertex and line ending represents a carbon atom; hydrogens bonded to carbon are implied (counted by difference, knowing C forms 4 bonds). Single bonds are simple lines, double bonds are parallel lines, triple bonds are three parallel lines. Heteroatom symbols (O, N, Cl, etc.) are explicit.
  Example: n-butane is a zig-zag line of 4 segments; cyclohexane is a hexagon; benzene is a hexagon with a circle or three alternating double bonds.

Formal charge is calculated as: FC = (valence electrons) – (unshared electrons) – ½(shared electrons). A stable Lewis structure minimizes formal charges, placing negative charges on the most electronegative atoms.

For molecules with multiple possible Lewis structures, resonance structures are used (e.g., benzene, carbonate ion). The real structure is a hybrid of all limiting structures.

Real-world applications: the skeletal formula is the universal standard in organic chemistry (scientific publications, CAS databases, pharmacology manuals). Every aspiring chemist must be able to read and write it fluently.

VSEPR theory (Valence Shell Electron Pair Repulsion) predicts molecular geometry based on repulsion between electron pairs (bonding and lone pairs) in the valence shell. In organic chemistry, it applies mainly to carbon, nitrogen, and oxygen atoms.

Carbon geometries by hybridization:

• sp³ Carbon (4 $sigma$ bonds): regular tetrahedron, angles $109.5^circ$. Examples: alkanes, cycloalkanes. The tetrahedral arrangement minimizes repulsion between the 4 bonding electron pairs.
• sp² Carbon (3 $sigma$ bonds + 1 $pi$): trigonal planar, angles $120^circ$. Rotation around the double bond is prevented (the $pi$ bond would break), leading to geometric cis-trans isomerism.
• sp Carbon (2 $sigma$ bonds + 2 $pi$): linear, angles $180^circ$. Examples: alkynes, nitriles.

Angles in nitrogen and oxygen:

• sp³ Nitrogen (3 bonds + 1 lone pair): trigonal pyramidal geometry, angles $approx 107^circ$ (e.g., ammonia, amines). The lone pair occupies more space than a bond, compressing the angles.
• sp³ Oxygen (2 bonds + 2 lone pairs): bent geometry, angles $approx 104.5^circ$ (e.g., water, alcohols, ethers). The two lone pairs further compress the angle.

Angles in cycloalkanes: in 3- and 4-membered rings (cyclopropane, cyclobutane), angles are forcibly smaller than $109.5^circ$, creating ring strain (Baeyer strain) that makes these compounds more reactive (e.g., cyclopropane: angles $60^circ$, enormous strain).

Real-world applications: molecular geometry determines the three-dimensional shape of drugs, affecting their recognition by biological receptors (key-lock principle). Ring strain in cyclopropane makes it useful as an anesthetic gas (rapid ring opening).