🥼Organic Chemistry Unit 1 Review

Valence bond theory explains covalent bonding as the overlap of atomic orbitals, which are regions in space where electrons are most likely found. When two atomic orbitals overlap, the atoms share electrons, forming a covalent bond. This shared arrangement is lower in energy than two isolated atoms, which is why the bond forms in the first place. Think of two hydrogen atoms coming together to form $H_2$ : the molecule is more stable than two separate H atoms because the electrons are attracted to both nuclei simultaneously.

The extent of orbital overlap determines how strong the bond will be:

Greater overlap produces a stronger bond
Overlap depends on orbital size, shape, and energy (s orbitals, being spherical and close to the nucleus, tend to overlap more effectively than p orbitals)

Atoms can also undergo hybridization, where atomic orbitals mix to form new hybrid orbitals with different shapes and energies. This concept becomes central when explaining the geometry of carbon-based molecules (covered in more detail with $sp^3$ , $sp^2$ , and $sp$ hybridization).

Characteristics of sigma bonds

Sigma ( $\sigma$ ) bonds form through direct, end-to-end overlap of atomic orbitals. They're the first bond that forms between any two atoms, and they're the strongest type of covalent bond because electron density is concentrated directly between the two nuclei.

Key features of sigma bonds:

Cylindrical symmetry around the bond axis, meaning you can rotate around the bond without changing the electron density distribution. This is why single bonds allow free rotation.
Electron density is concentrated along the internuclear axis, providing maximum stabilization.
Can form from several types of orbital overlap:
- s-s overlap: the H-H bond in $H_2$
- s-sp $^3$ overlap: a C-H bond in methane
- sp $^3$ -sp $^3$ overlap: the C-C bond in ethane

Every single bond you encounter in organic chemistry is a sigma bond. Double bonds contain one sigma bond plus one pi bond, and triple bonds contain one sigma bond plus two pi bonds.

Bond strength and length

Bond dissociation energy (BDE) measures the energy required to homolytically break a bond in the gas phase. A higher BDE means a stronger bond. For example, the H-H bond in $H_2$ has a BDE of about 436 kJ/mol, while the weaker Cl-Cl bond in $Cl_2$ is about 242 kJ/mol.

Bond length is the distance between the nuclei of two bonded atoms, measured in picometers (pm) or angstroms (Å). Shorter bonds are generally stronger bonds.

Four main factors affect bond strength and length:

Atom size: Bonds between smaller atoms tend to be shorter and stronger. The H-H bond (74 pm) is much shorter than the Cl-Cl bond (199 pm) because hydrogen atoms are far smaller than chlorine atoms.
Orbital overlap: Greater overlap produces shorter, stronger bonds. s orbitals overlap more effectively than p orbitals because of their shape.
Bond order: Higher bond order means shorter and stronger bonds. In carbon-carbon bonds: C-C in ethane (154 pm, 368 kJ/mol) vs. C=C in ethene (134 pm, 614 kJ/mol) vs. C≡C in ethyne (120 pm, 839 kJ/mol).
Resonance: Delocalization of electrons across resonance structures can give bonds intermediate character, affecting both their strength and length. The C-O bonds in a carboxylate ion, for instance, are identical and intermediate between a single and double bond.

The electrostatic attraction between bonded atoms can be modeled using Coulomb's law:

$E = \frac{Q_1 Q_2}{4\pi\epsilon_0 r}$

$E$ = electrostatic potential energy
$Q_1$ , $Q_2$ = charges on the interacting particles
$\epsilon_0$ = permittivity of free space
$r$ = distance between the charges (related to bond length)

A more negative value of $E$ corresponds to a stronger attractive interaction. As $r$ decreases (shorter bond), the magnitude of the attraction increases, which aligns with the general trend that shorter bonds are stronger.

Advanced Bonding Theories

Valence bond theory has limitations. Molecular orbital (MO) theory offers a more complete picture by combining atomic orbitals into molecular orbitals that belong to the entire molecule, rather than to individual atoms. You'll likely encounter MO theory later when explaining phenomena like bond order in $O_2$ or the stability of certain ions.

VSEPR (Valence Shell Electron Pair Repulsion) theory complements valence bond theory by predicting molecular geometry based on how electron pairs around a central atom arrange themselves to minimize repulsion.

🥼Organic Chemistry Unit 1 Review