Chemical Bonding and Molecular Structure (JEE/NEET)

1. Ionic Bond (Electrovalent Bond)

• Formed by the complete transfer of electrons from a metal (low Ionization Energy) to a non-metal (high Electron Affinity).
• Lattice Enthalpy: The energy released when one mole of an ionic crystal is formed from its gaseous ions.
• Conditions for Strong Ionic Bond:
  1. Low Ionization Energy of Cation.
  2. High Electron Gain Enthalpy of Anion.
  3. High Lattice Energy.
• Force of attraction \( F \propto \frac{q_1 q_2}{r^2} \)

2. Fajans' Rule (Covalent Character in Ionic Bonds)

• No bond is 100% ionic. Fajans' rule predicts the covalent character in ionic compounds.
• Polarization: The distortion of the electron cloud of the anion by the cation.
• Conditions for high covalent character (High Polarization):
  1. Small size of Cation.
  2. Large size of Anion.
  3. High charge on Cation or Anion.
  4. Cations with pseudo-noble gas configuration (\(ns^2 p^6 d^{10}\)), e.g., \(Cu^+, Ag^+\).
• Trend: Melting Point: \( \text{NaCl} > \text{MgCl}_2 > \text{AlCl}_3 \) (Covalent character increases, MP decreases).

3. Dipole Moment (\(\mu\))

• Measure of polarity in a bond. It is a vector quantity.
• Formula: \( \mu = q \times d \) (Charge × Distance)
• Unit: Debye (D). \( 1D = 3.33 \times 10^{-30} \text{ C}\cdot\text{m} \).
• Resultant Dipole: \( \mu_R = \sqrt{\mu_1^2 + \mu_2^2 + 2\mu_1\mu_2 \cos \theta} \)
• Important Exception: Dipole moment of \( NH_3 > NF_3 \).
  In \( NH_3 \), the orbital dipole matches the bond dipoles. In \( NF_3 \), the orbital dipole opposes the bond dipoles.

4. VSEPR Theory (Valence Shell Electron Pair Repulsion)

• Used to predict the geometry of molecules based on minimizing repulsion between electron pairs.
• Repulsion Order: Lone Pair-Lone Pair (lp-lp) > lp-bp > bp-bp.
• Key Geometries:
  • \(sp\) (2 bp): Linear (\(180^\circ\)). Example: \(BeCl_2\).
  • \(sp^2\) (3 bp): Trigonal Planar (\(120^\circ\)). Example: \(BF_3\).
  • \(sp^2\) (2 bp + 1 lp): Bent/V-shape. Example: \(SO_2\).
  • \(sp^3\) (4 bp): Tetrahedral (\(109.5^\circ\)). Example: \(CH_4\).
  • \(sp^3\) (3 bp + 1 lp): Pyramidal. Example: \(NH_3\).
  • \(sp^3\) (2 bp + 2 lp): Bent/V-shape. Example: \(H_2O\).
  • \(sp^3d\) (5 bp): Trigonal Bipyramidal. Example: \(PCl_5\). (Axial bonds > Equatorial bonds length).
  • \(sp^3d^2\) (6 bp): Octahedral. Example: \(SF_6\).

5. Hybridization (Valence Bond Theory)

• Mixing of atomic orbitals to form new equivalent hybrid orbitals.
• Steric Number (Z) = \( \frac{1}{2} [V + M - C + A] \)
  Where:
  \(V\) = Valence electrons of central atom
  \(M\) = Number of monovalent atoms (H, F, Cl, etc.)
  \(C\) = Charge on cation
  \(A\) = Charge on anion
• If \(Z=2 \rightarrow sp\), \(Z=3 \rightarrow sp^2\), \(Z=4 \rightarrow sp^3\), \(Z=5 \rightarrow sp^3d\), etc.

6. Molecular Orbital Theory (MOT)

• Electrons fill molecular orbitals (MOs) rather than atomic orbitals.
• Bond Order (B.O.): Indication of bond strength and stability.
• \( \text{Bond Order} = \frac{1}{2} (N_b - N_a) \)
  Where \(N_b\) is electrons in Bonding MO and \(N_a\) is electrons in Antibonding MO.
• Significance:
  1. B.O. > 0: Molecule exists.
  2. B.O. = 0: Molecule does not exist.
  3. Isoelectronic species have the same Bond Order.
• Magnetic Nature:
  Unpaired electrons \(\rightarrow\) Paramagnetic (attracted to magnetic field).
  Paired electrons \(\rightarrow\) Diamagnetic (repelled by magnetic field).
• Important Orders (for diatomic molecules like \(O_2, F_2\)):
  \( \sigma(1s) < \sigma^*(1s) < \sigma(2s) < \sigma^*(2s) < \sigma(2p_z) < \pi(2p_x)=\pi(2p_y) < \pi^*(2p_x)=\pi^*(2p_y) < \sigma^*(2p_z) \)
• Example: \(O_2\) (16e) is paramagnetic (2 unpaired electrons in \(\pi^*\) orbitals).

7. Hydrogen Bonding

• Electrostatic attraction between covalently bonded H atom and a highly electronegative atom (F, O, N).
• Intermolecular H-Bond: Between different molecules (e.g., \(H_2O\), \(HF\)). Increases BP/MP and viscosity.
• Intramolecular H-Bond: Within the same molecule (e.g., o-Nitrophenol). Leads to lower BP compared to para-isomer due to lack of molecular association.

8. Formal Charge

• Used to determine the most stable Lewis structure (lowest energy).
• \( \text{F.C.} = V - L - \frac{1}{2}S \)
  Where:
  \(V\) = Valence electrons in free atom
  \(L\) = Non-bonding (lone pair) electrons
  \(S\) = Bonding (shared) electrons