Periodic Properties, Chemical Bonding, and Molecular Geometry

Dmitri Mendeleev and Lothar Meyer independently concluded how elements should be grouped.
Mendeleev predicted the discovery of germanium (eka-silicon) based on its atomic weight and chemical similarity to silicon.
Atomic Size: Defined by the bonding atomic radius (one-half the distance between covalently bonded nuclei). Radius increases down a group and decreases across a period.
Ionic Size: Cations are smaller than parent atoms (electron removal reduces repulsion); anions are larger (electron addition increases repulsion). Size increases down a group.
Isoelectronic Series: Ions with identical electron counts; size decreases as nuclear charge increases.
Ionization Energy (IE): Energy needed to remove an electron from gaseous atoms (e.g., Na(g) + ext{Energy} ightarrow Na^+(g) + e^-). Generally increases across a period and decreases down a group.
IE Exceptions: Discontinuities occur between Groups IIA/IIIA (p-orbital removal) and Groups VA/VIA (electron pair repulsion).
Electron Affinity (EA): Energy change for adding an electron; generally becomes more exothermic from left to right.

Metals: Lustrous, malleable, ductile, good conductors; tend to form cations and basic oxides.
Nonmetals: Brittle, poor conductors; tend to form anions and acidic oxides. Compounds with other nonmetals are molecular.
Alkali Metals (Group 1A): Soft, low densities/melting points, low IE, reactive with water (K + O_2 ightarrow KO_2).
Alkaline Earth Metals (Group 2A): Higher densities and melting points than alkali metals; reactivity increases down the group.
Halogens (Group 7A): Large negative EA; act as strong oxidizers to form metal halides.
Noble Gases (Group 8A): High IE, positive EA, monatomic, and relatively unreactive.

Types of Bonds: Ionic (electrostatic), Covalent (electron sharing), and Metallic (bonded to several atoms).
Octet Rule: G.N. Lewis proposed that atoms gain, lose, or share electrons to reach a count of $8$ valence electrons.
Ionic Energetics: Removal of electron from $Na$ costs $496 ext{ kJ/mol}$ ; adding to $Cl$ returns $349 ext{ kJ/mol}$ . The net exothermic nature is driven by Lattice Energy.
Lattice Energy: Energy required to separate a mole of solid ionic compound into gaseous ions; increases with higher charge and smaller ion size.
Electronegativity: The ability of an atom in a molecule to attract electrons; increases left to right and bottom to top.
Polar Covalent Bonds: Unequal sharing creates a dipole moment ( $\boldsymbol{\nu} = Qr$ ) measured in debyes ( $D$ ). Polarity increases with electronegativity differences.

Formal Charge: $ext{Valence electrons} - [ ext{lone pair electrons} + \frac{1}{2} ext{shared electrons}]$ . Preferred structures minimize charges and place negative charges on the most electronegative atoms.
Resonance: Used for molecules like $O_3$ and benzene ( $C_6H_6$ ) where electrons are delocalized across multiple structures.
Exceptions to the Octet Rule: - Odd number of electrons. - Fewer than $8$ electrons (e.g., $BF_3$ ). - Expanded octets (3rd row elements or below, e.g., $PF_5$ , using d-orbitals).
Bond Enthalpy ( $D$ ): Energy to break a bond. oldsymbol{ ho} H_{rxn} = oldsymbol{ ho} ( ext{bond enthalpies of broken bonds}) - oldsymbol{ ho} ( ext{bond enthalpies of formed bonds}).
Bond Properties: Bond length decreases as the number of shared electron pairs (bond order) increases.

VSEPR Theory: Shapes are determined by minimizing repulsions between electron domains (bonding and nonbonding pairs).
Electron-Domain Geometries: - $2$ domains: Linear ( $180^ ext{o}$ ) - $3$ domains: Trigonal planar ( $120^ ext{o}$ ) - $4$ domains: Tetrahedral ( $109.5^ ext{o}$ ) - $5$ domains: Trigonal bipyramidal (Axial and Equatorial positions) - $6$ domains: Octahedral
Molecular Geometry: Positions of atoms only. Nonbonding pairs are physically larger, increasing repulsion and decreasing bond angles.
Molecular Polarity: Determined by the vector sum of individual bond dipoles.

Valence Bond Theory: Covalent bonds form via orbital overlap. - Sigma ( $\boldsymbol{ au}$ ) bonds: Head-to-head overlap; cylindrical symmetry. - Pi ( $\boldsymbol{\beta}$ ) bonds: Side-to-side overlap; density above and below the axis.
Hybridization: Mixing atomic orbitals into degenerate hybrids: $sp$ (linear), $sp^2$ (trigonal planar), $sp^3$ (tetrahedral).
Multiple Bonds: Consist of one $\boldsymbol{ au}$ bond and one or more $\boldsymbol{\beta}$ bonds.
Molecular Orbital (MO) Theory: Uses wave nature of electrons to form bonding (low energy) and antibonding (high energy) orbitals.
Bond Order: $\frac{1}{2} ( ext{bonding electrons} - ext{antibonding electrons})$ . If Bond Order is $0$ , the molecule (e.g., $He_2$ ) does not exist.

Ionic Bonds: Strongest attraction between positive and negative ions.
Dipole–Dipole Attractions: Forces between polar molecules.
Hydrogen Bonds: Strong dipole attraction where $H$ is bonded to $F$ , $O$ , or $N$ .
Dispersion Forces: Weak temporary dipoles in nonpolar molecules.
Boiling/Melting Points: Directly correlate with the strength of attractive forces (Ionic > Hydrogen Bonding > Dipole-Dipole > Dispersion).