Chemical Bonding

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1. Introduction to Bonding Chemical Bond: An attractive force holding atoms together. Octet Rule: Atoms tend to achieve 8 valence electrons. Exceptions: H (2), Li (2), Be (4), B (6), elements from Period 3 onwards (can expand octet). Types: Ionic, Covalent, Metallic. 2. Ionic Bonding Formation: Complete transfer of electrons (metal to non-metal). Electronegativity Difference ($\Delta EN$): Typically $> 1.7-1.9$. Factors Favoring Ionic Bond: Low ionization energy of metal. High electron affinity of non-metal. High lattice energy of ionic compound. Lattice Energy (U): Energy released when 1 mole of ionic solid is formed from gaseous ions. Born-Landé Equation (simplified): $U \propto \frac{Z^+ Z^-}{r_0}$, where $Z^+, Z^-$ are charges, $r_0$ is internuclear distance. Factors: $U \propto |q_1 q_2| / (r_+ + r_-)$. Higher charge, smaller size $\rightarrow$ higher lattice energy. Born-Haber Cycle: A thermochemical cycle to calculate lattice energy using Hess's Law. $\Delta H_{f}^\circ = \Delta H_{sub} + IE + \frac{1}{2}BE + EA + U$ Where $\Delta H_{f}^\circ$ = Enthalpy of formation, $\Delta H_{sub}$ = Enthalpy of sublimation, $IE$ = Ionization energy, $BE$ = Bond dissociation energy, $EA$ = Electron affinity, $U$ = Lattice energy. 3. Covalent Bonding Formation: Sharing of electrons (between non-metals). Electronegativity Difference: Nonpolar Covalent: $\Delta EN Polar Covalent: $0.4 \le \Delta EN \le 1.7$. Dipole Moment ($\mu$): Measure of polarity in a bond or molecule. $\mu = q \times d$ (where $q$ is charge magnitude, $d$ is distance). Units: Debye (D), $1D = 3.335 \times 10^{-30} C \cdot m$. Percentage Ionic Character = $\frac{\mu_{observed}}{\mu_{ionic (calculated)}} \times 100\%$. Fajan's Rules: Predicts the degree of covalency in an ionic bond. Small cation, large anion $\rightarrow$ more covalent character. High charge on cation/anion $\rightarrow$ more covalent character. Cations with pseudo noble gas configuration ($ns^2np^6nd^{10}$) are more polarizing than noble gas configuration ($ns^2np^6$) of similar size and charge. (e.g., $Cu^+$ vs $Na^+$). 3.1 Lewis Structures & Formal Charge Formal Charge (FC): $FC = (\text{Valence e}^-) - (\text{Non-bonding e}^-) - \frac{1}{2}(\text{Bonding e}^-)$. Sum of FCs = total charge on ion/molecule. Resonance: Delocalization of electrons over multiple bonds (e.g., $O_3$, $CO_3^{2-}$). Actual structure is a hybrid. 3.2 VSEPR Theory (Valence Shell Electron Pair Repulsion) Predicts molecular geometry based on minimizing electron pair repulsion. Steric Number (SN): Number of atoms bonded to central atom + number of lone pairs on central atom. Summary of Geometries: SN Hybridization Lone Pairs Molecular Geometry Bond Angles Example 2 $sp$ 0 Linear $180^\circ$ $BeCl_2$, $CO_2$ 3 $sp^2$ 0 Trigonal Planar $120^\circ$ $BF_3$, $SO_3$ 3 $sp^2$ 1 Bent $ $SO_2$, $O_3$ 4 $sp^3$ 0 Tetrahedral $109.5^\circ$ $CH_4$, $CCl_4$ 4 $sp^3$ 1 Trigonal Pyramidal $107^\circ$ $NH_3$, $PCl_3$ 4 $sp^3$ 2 Bent $104.5^\circ$ $H_2O$, $H_2S$ 5 $sp^3d$ 0 Trigonal Bipyramidal $90^\circ, 120^\circ$ $PCl_5$ 5 $sp^3d$ 1 Seesaw $ $SF_4$ 5 $sp^3d$ 2 T-shaped $ $ClF_3$ 5 $sp^3d$ 3 Linear $180^\circ$ $XeF_2$, $I_3^-$ 6 $sp^3d^2$ 0 Octahedral $90^\circ$ $SF_6$ 6 $sp^3d^2$ 1 Square Pyramidal $ $BrF_5$ 6 $sp^3d^2$ 2 Square Planar $90^\circ$ $XeF_4$ 3.3 Valence Bond Theory & Hybridization Hybridization Formula: $H = \frac{1}{2}(V + M - C + A)$ Where $V$ = valence electrons of central atom, $M$ = number of monovalent atoms, $C$ = charge of cation, $A$ = charge of anion. If $H=2 \rightarrow sp$, $H=3 \rightarrow sp^2$, $H=4 \rightarrow sp^3$, $H=5 \rightarrow sp^3d$, $H=6 \rightarrow sp^3d^2$, $H=7 \rightarrow sp^3d^3$. Sigma ($\sigma$) Bonds: Head-on overlap (stronger). Pi ($\pi$) Bonds: Sideways overlap (weaker). Single bond: $1 \sigma$. Double bond: $1 \sigma, 1 \pi$. Triple bond: $1 \sigma, 2 \pi$. 3.4 Molecular Orbital Theory (MOT) Bond Order (BO): $BO = \frac{1}{2}(N_b - N_a)$ Where $N_b$ = number of electrons in bonding MOs, $N_a$ = number of electrons in antibonding MOs. If $BO > 0$, molecule is stable. Higher BO $\rightarrow$ stronger bond, shorter bond length. MO Configuration for Diatomic Molecules: For $N_2$ and below (total electrons $\le 14$): $\sigma 1s, \sigma^* 1s, \sigma 2s, \sigma^* 2s, \pi 2p_x = \pi 2p_y, \sigma 2p_z, \pi^* 2p_x = \pi^* 2p_y, \sigma^* 2p_z$ For $O_2$ and above (total electrons $> 14$): $\sigma 1s, \sigma^* 1s, \sigma 2s, \sigma^* 2s, \sigma 2p_z, \pi 2p_x = \pi 2p_y, \pi^* 2p_x = \pi^* 2p_y, \sigma^* 2p_z$ Magnetic Properties: Paramagnetic: Contains unpaired electrons. Diamagnetic: All electrons are paired. 4. Metallic Bonding "Electron Sea" model: Delocalized valence electrons shared among positive metal ions. Explains conductivity, malleability, ductility, luster. 5. Intermolecular Forces (IMFs) Weaker than intramolecular bonds. Affect physical properties. Order of strength: Ion-Dipole $>$ Hydrogen Bonding $>$ Dipole-Dipole $>$ London Dispersion Forces (LDFs). London Dispersion Forces (LDFs): Present in all molecules. Temporary induced dipoles. Strength $\propto$ Molecular Weight (or number of electrons), surface area. Dipole-Dipole Forces: Between polar molecules. Strength $\propto$ Dipole moment. Hydrogen Bonding: H bonded to F, O, or N. Strongest type of dipole-dipole. Ion-Dipole Forces: Between an ion and a polar molecule (e.g., solvation of ionic compounds). 6. Hydrogen Bonding Types: Intermolecular H-bonding: Between two different molecules (e.g., $H_2O, NH_3$). Increases boiling point, viscosity. Intramolecular H-bonding: Within the same molecule (e.g., o-nitrophenol). Decreases boiling point, increases volatility.