Chemical Bonding and Molecular Structure

Chemical Bond: Force of attraction between atoms holding them together. Octet rule (Lewis): Atoms tend to attain 8 electrons (or 2 for H, He) in outer shell.

Ionic (Electrovalent) Bond: Formed by complete transfer of electrons from metal (low IE) to non-metal (high EN). Examples: NaCl, MgO, CaF₂.

Conditions favoring ionic bond:

• Low IE of metal (s-block, especially heavy alkali metals)
• High EN of non-metal (halogens, oxygen)
• High lattice energy

Lattice Energy ($U$): Energy released when 1 mole of ionic crystal is formed from gaseous ions. Magnitude depends on: $$U \propto \frac{q_1 q_2}{r_+ + r_-}$$

Higher for: (i) higher charges, (ii) smaller ionic radii.

Born-Haber Cycle: Thermodynamic cycle to calculate lattice energy using Hess's law. For NaCl:

$$\Delta_f H^\ominus = \Delta_{\text{sub}} H_{Na} + \frac{1}{2}\Delta_{\text{diss}} H_{Cl_2} + IE_{Na} + EA_{Cl} + U$$

Solving for $U$ gives lattice energy.

Fajan's Rules: Predict ionic vs covalent character. Covalent character increases when:

1. Smaller cation (high charge density, high polarizing power)
2. Larger anion (more polarizable)
3. Higher charge on either ion
4. Cation with $d$-electrons (e.g., $Cu^+$ more polarizing than $Na^+$ of similar size)

Polarizing power $\propto$ charge/radius² of cation. Polarizability of anion $\propto$ size and charge of anion.

Examples:

• LiCl is more covalent than NaCl (smaller Li⁺)
• AgCl is more covalent than NaCl (Ag⁺ has pseudo-noble configuration; $d$-electrons)
• AlCl₃ is more covalent than NaCl (higher charge on Al³⁺)

Properties of Ionic Compounds:

• High melting and boiling points
• Hard and brittle
• Soluble in polar solvents (water), insoluble in nonpolar
• Conduct electricity in molten state or aqueous solution

Covalent Bond: Formed by sharing of electrons between atoms of similar EN. Lewis (1916) — atoms share electron pairs to attain noble gas configuration.

Types of Covalent Bonds:

• Single bond: 1 shared pair (e.g., H-H)
• Double bond: 2 shared pairs (e.g., O=O)
• Triple bond: 3 shared pairs (e.g., N≡N)

Coordinate (Dative) Bond: Both electrons of the shared pair come from one atom. e.g., NH₄⁺, H₃O⁺, NH₃→BF₃.

Lewis Structure (Steps):

1. Count total valence electrons
2. Determine central atom (least electronegative, except H)
3. Connect with single bonds
4. Distribute remaining electrons as lone pairs (outer atoms first, then central)
5. Form multiple bonds if octet incomplete on central atom

Limitations of Octet Rule:

• Incomplete octet: BeCl₂ (4 e⁻ on Be), BF₃ (6 e⁻ on B), LiCl
• Expanded octet: PF₅, SF₆, IF₇ (central atom can use $d$-orbitals)
• Odd-electron molecules: NO, NO₂, ClO₂
• Predicts equal bond properties for some species, but reality differs

Formal Charge: $$\text{FC} = (\text{valence electrons}) - (\text{lone pair electrons}) - \frac{1}{2}(\text{bonding electrons})$$

Sum of formal charges = total charge on species. The most stable Lewis structure has formal charges closest to zero, and negative formal charge on the more electronegative atom.

Resonance: When a molecule cannot be represented by a single Lewis structure; actual structure is a hybrid of contributing forms. Real molecule has lower energy than any single structure (resonance stabilization).

Examples of Resonance:

• O₃ (ozone): two resonance structures, equal bond lengths
• CO₃²⁻: three equivalent structures; all C–O bonds equal
• Benzene: two Kekulé structures (alternating double bonds); actual bonds are intermediate
• NO₂⁻, NO₃⁻, $\text{SO}_3$

Conditions for Resonance:

• Atoms in same position
• Same number of paired and unpaired electrons
• Differ only in placement of $\pi$ electrons or lone pairs

VSEPR Theory (Valence Shell Electron Pair Repulsion):

• Electron pairs around central atom orient to minimize repulsion
• Order of repulsion: Lone pair – lone pair (lp-lp) > lp-bp > bp-bp
• Lone pairs occupy more space than bond pairs → distort bond angles

Steric Number (SN) = Lone pairs + bonded atoms (sigma bonds only) = Total number of electron domains.

Shapes (with lone pairs):

Bond Angle Variation: As EN of central atom decreases or lone pairs increase, bond angle decreases. e.g., NH₃ ($107°$) > PH₃ ($94°$) > AsH₃ ($91°$).

Hybridization: Mixing of atomic orbitals to form new equivalent hybrid orbitals.

Steric Number → Hybridization: SN 2 → sp; 3 → sp²; 4 → sp³; 5 → sp³d; 6 → sp³d².

Bond Length: Distance between nuclei in bonded atoms. Order: single > double > triple. Bond Energy: Energy required to break bond. Order: triple > double > single.

Molecular Orbital Theory (MOT): Atomic orbitals (AOs) combine to form molecular orbitals (MOs). $N$ AOs → $N$ MOs ($N/2$ bonding + $N/2$ antibonding).

Bonding MO ($\sigma, \pi$): Lower energy than parent AOs (constructive interference). Antibonding MO ($\sigma^*, \pi^*$): Higher energy (destructive interference).

Energy Order:

For molecules up to N₂ (Li₂, Be₂, B₂, C₂, N₂): $$\sigma 1s < \sigma^*1s < \sigma 2s < \sigma^*2s < \pi 2p_x = \pi 2p_y < \sigma 2p_z < \pi^*2p_x = \pi^*2p_y < \sigma^*2p_z$$

For O₂ and beyond (O₂, F₂, Ne₂): $$\sigma 1s < \sigma^*1s < \sigma 2s < \sigma^*2s < \sigma 2p_z < \pi 2p_x = \pi 2p_y < \pi^*2p_x = \pi^*2p_y < \sigma^*2p_z$$

Bond Order: $$\text{Bond order (BO)} = \frac{1}{2}(N_b - N_a)$$ where $N_b$ = bonding electrons, $N_a$ = antibonding electrons.

• BO = $0$: molecule does not exist (e.g., He₂)
• BO > $0$: molecule is stable
• Higher BO → shorter bond, higher energy

Magnetic Behaviour:

• All electrons paired → diamagnetic
• Unpaired electrons → paramagnetic
• MOT correctly predicts $O_2$ is paramagnetic (2 unpaired in $\pi^*$ orbitals)

Example: O₂ (16 electrons):

• Config: $\sigma 1s^2\,\sigma^*1s^2\,\sigma 2s^2\,\sigma^*2s^2\,\sigma 2p_z^2\,\pi 2p_x^2 = \pi 2p_y^2\,\pi^*2p_x^1 = \pi^*2p_y^1$
• BO = $(10-6)/2 = 2$
• Paramagnetic (2 unpaired)

Hydrogen Bonding: Special dipole-dipole interaction when H is attached to highly EN atom (F, O, N). Donor: H-F, O-H, N-H. Acceptor: another F, O, N.

• Intermolecular H-bonding: Between molecules. e.g., H₂O, NH₃, HF, alcohols, carboxylic acids.
• Intramolecular H-bonding: Within molecule. e.g., o-nitrophenol, salicylaldehyde.

Effects: high boiling points, anomalous density of water (max at $4°$C), high heat of vaporization, ice less dense than water, life-sustaining properties of water.

Dipole Moment ($\mu$): Measure of polarity of bond/molecule. Unit: Debye (D); $1$ D = $3.336 \times 10^{-30}$ C·m. $$\mu = q \times d$$ Vector quantity; net dipole = vector sum of bond dipoles.

NF₃ < NH₃ in dipole moment despite F being more electronegative — because the lone pair on N points in the opposite direction in NF₃ but the same direction in NH₃ for the bond dipoles.