Chemical Bonding and Molecular Structure

2.1 Core concepts

• Chemical bond is the attractive force holding constituent atoms/ions together in a molecule; Kossel and Lewis (1916) gave the first satisfactory electronic explanation based on noble-gas inertness (NCERT §4.1, p. 101).
• Lewis dot symbols show the valence electrons of an atom; group valence equals either the number of dots or 8 minus the number of dots (NCERT §4.1, p. 101).
• Kossel view of ionic bond: the highly electronegative halogens and electropositive alkali metals are separated by noble gases; transfer of electrons gives ions with ns²np⁶ configuration that are stabilised by electrostatic attraction — e.g. NaCl, CaF₂ (NCERT §4.1, p. 101).
• Octet rule (Kossel–Lewis, 1916): atoms combine by transfer or sharing of valence electrons to attain an octet in their valence shell (NCERT §4.1.1, p. 102).
• Covalent bond (Langmuir 1919): formed by sharing of an electron pair; sharing 1, 2, 3 pairs gives single, double (e.g. CO₂, C₂H₄), triple (e.g. N₂, C₂H₂) bonds (NCERT §4.1.2, p. 102).
• Writing Lewis structures: sum valence electrons (add for anions, subtract for cations); least electronegative atom is central (e.g. N in NF₃, C in CO₃²⁻); after single bonds, leftover electrons go as multiple bonds or lone pairs so every atom gets an octet (NCERT §4.1.3, p. 103).
• Formal charge = (valence e⁻ in free atom) − (non-bonding e⁻) − ½(bonding e⁻); used to pick the lowest-energy Lewis structure (smallest formal charges). For O₃, central O has F.C. = +1 and the terminal O atoms have 0 and −1 (NCERT §4.1.4, p. 104–105).
• Limitations of octet rule: (i) incomplete octet — LiCl, BeH₂, BCl₃, AlCl₃, BF₃; (ii) odd-electron molecules — NO, NO₂; (iii) expanded octet — PF₅, SF₆, H₂SO₄ (3d orbitals available from period 3 onwards). Octet rule is also silent on shape, molecular energy, and noble-gas compounds like XeF₂, KrF₂ (NCERT §4.1.5, p. 105–106).
• Ionic bond formation is favoured by low ionisation enthalpy of the metal, high (negative) electron gain enthalpy of the non-metal, and large lattice enthalpy. For NaCl, IE(Na) + ΔₑgH(Cl) = +147.1 kJ mol⁻¹ but lattice enthalpy = −788 kJ mol⁻¹, so the crystal is stable (NCERT §4.2, p. 106).
• Lattice enthalpy is the energy required to separate one mole of a solid ionic compound into gaseous ions; NaCl lattice enthalpy = 788 kJ mol⁻¹. It is the true measure of ionic-compound stability, not mere octet completion (NCERT §4.2.1, p. 107).
• Bond length is the equilibrium internuclear distance; covalent radius is half the distance between two like atoms covalently bonded. Typical values: H–H 74 pm, Cl–Cl 199 pm, N≡N 109 pm, O=O 121 pm (Tables 4.2, 4.3) (NCERT §4.3.1, p. 107–108).
• Bond angle is the angle between bonding orbitals around the central atom (e.g. 104.5° in H₂O) (NCERT §4.3.2, p. 108).
• Bond enthalpy is the energy to break one mole of a bond in the gas phase: H–H = 435.8, O=O = 498, N≡N = 946 kJ mol⁻¹. For polyatomics like H₂O, mean bond enthalpy = (502 + 427)/2 = 464.5 kJ mol⁻¹ (NCERT §4.3.3, p. 108–109).
• Bond order in Lewis theory = number of bonds between two atoms: H₂ = 1, O₂ = 2, N₂ = 3, CO = 3. Isoelectronic species have the same bond order (F₂ and O₂²⁻ → 1; N₂, CO, NO⁺ → 3). Higher bond order ⇒ higher bond enthalpy and shorter bond length (NCERT §4.3.4, p. 109).
• Resonance: when one Lewis structure cannot describe a species, several canonical forms with identical nuclear positions but different electron arrangements are drawn — their hybrid represents the real molecule. Examples: O₃ (both O–O bonds equal at 128 pm, between single 148 pm and double 121 pm), CO₃²⁻ (three equivalent C–O bonds), CO₂, benzene. The hybrid has lower energy than any canonical form; canonical forms have no real existence (NCERT §4.3.5, p. 109–110).
• Polarity / dipole moment: μ = Q × r, measured in Debye (1 D = 3.33564 × 10⁻³⁰ C m). HF is polar (μ = 1.78 D); H₂, BF₃, CO₂, CCl₄ have μ = 0 because bond dipoles cancel. H₂O is bent so μ = 1.85 D. NH₃ (1.47 D) > NF₃ (0.23 D) because in NH₃ the lone-pair dipole adds to the N–H bond dipoles whereas in NF₃ it opposes them (NCERT §4.3.6, p. 110–112).
• Fajans rules for partial covalent character of ionic bonds: small cation, large anion, high cation charge, and (n−1)d^n ns⁰ configuration all increase covalent character (NCERT §4.3.6, p. 112).
• VSEPR theory (Sidgwick–Powell 1940; Nyholm–Gillespie 1957): valence-shell electron pairs (bonded + lone) arrange to minimise repulsion. Repulsion order: lp–lp > lp–bp > bp–bp. A multiple bond is treated as one super-pair. Basic geometries: AB₂ linear, AB₃ trigonal planar, AB₄ tetrahedral, AB₅ trigonal bipyramidal, AB₆ octahedral (NCERT §4.4, Table 4.6, p. 112–114).
• With lone pairs (Tables 4.7, 4.8): AB₂E bent (e.g. SO₂, 119.5°), AB₃E trigonal pyramidal (NH₃, 107°), AB₂E₂ bent (H₂O, 104.5°), AB₄E see-saw (SF₄, lp at equatorial position), AB₃E₂ T-shape (ClF₃), AB₄E₂ square planar (XeF₄), AB₅E square pyramidal (BrF₅) (NCERT §4.4, Tables 4.7–4.8, p. 115–117).
• Valence Bond (VB) theory (Heitler–London 1927, Pauling): covalent bond forms when half-filled atomic orbitals with opposite-spin electrons overlap; greater overlap ⇒ stronger bond. For H₂, the potential-energy curve has a minimum at 74 pm corresponding to 435.8 kJ mol⁻¹ of bond enthalpy (NCERT §4.5, p. 117–118).
• σ vs π bond: σ bond by head-on (axial) overlap of s–s, s–p, p–p along internuclear axis; π bond by sidewise overlap of parallel p-orbitals, giving two electron clouds above and below the molecular plane. σ is stronger because of greater overlap. Multiple bonds = 1 σ + 1 (or 2) π (NCERT §4.5.4–4.5.5, p. 120).
• Hybridisation (Pauling): mixing of orbitals of slightly different energies to give equivalent hybrid orbitals. Types: sp (linear, 180°; BeCl₂), sp² (trigonal planar, 120°; BCl₃, C in C₂H₄), sp³ (tetrahedral, 109.5°; CH₄; also explains NH₃ at 107° and H₂O at 104.5° because of lone-pair repulsion), sp³d (trigonal bipyramidal; PCl₅), sp³d² (octahedral; SF₆), dsp² (square planar; [Ni(CN)₄]²⁻), sp³d² also gives square pyramidal BrF₅ (NCERT §4.6, p. 120–125).
• PCl₅ geometry: three equatorial P–Cl bonds at 120°, two axial at 90° to the equatorial plane; axial bonds are longer/weaker due to greater repulsion from equatorial pairs, making PCl₅ reactive (NCERT §4.6.3, p. 125).
• Molecular Orbital (MO) theory (Hund–Mulliken 1932): atomic orbitals of comparable energy and same symmetry combine by LCAO to give equal numbers of bonding (lower energy, electron density between nuclei) and antibonding (higher energy, node between nuclei) MOs. Filling follows aufbau, Pauli, Hund (NCERT §4.7.1, p. 126).
• MO energy order: for O₂, F₂ — σ1s < σ*1s < σ2s < σ*2s < σ2p_z < (π2p_x = π2p_y) < (π*2p_x = π*2p_y) < σ*2p_z. For Li₂, Be₂, B₂, C₂, N₂ — σ2p_z lies above (π2p_x = π2p_y) (NCERT §4.7.4, p. 128–129).
• Bond order = ½(N_b − N_a): positive ⇒ stable, zero/negative ⇒ unstable. H₂ b.o. = 1 (stable, diamagnetic); He₂ b.o. = 0 (does not exist); Li₂ b.o. = 1 (diamagnetic); C₂ b.o. = 2 (both bonds are π; diamagnetic); N₂ b.o. = 3; O₂ b.o. = 2 and is paramagnetic because of two unpaired electrons in π*2p_x, π*2p_y — a landmark success of MOT (NCERT §4.8, p. 129–131).
• Magnetic nature: all electrons paired ⇒ diamagnetic; one or more unpaired ⇒ paramagnetic (e.g. O₂, B₂) (NCERT §4.7.5, p. 129).
• Hydrogen bond: the attractive force between a hydrogen covalently bonded to a highly electronegative atom (F, O, N) of one molecule and an electronegative atom of another molecule; weaker than a covalent bond but stronger than van der Waals forces. Represented by a dotted line (NCERT §4.9, p. 131).
• Types of H-bond: (i) intermolecular — HF, H₂O, alcohols, ice; (ii) intramolecular — within the same molecule, e.g. o-nitrophenol where H sits between two oxygen atoms. H-bonding strongly affects structure and properties (e.g. anomalously high boiling point of water, lower density of ice than water) (NCERT §4.9.2, p. 132).

2.2 Definitions to memorise

2.3 Diagrams / processes to remember

• Fig. 4.1 — Bond length R = r_A + r_B (p. 107).
• Fig. 4.2 — Covalent radius (99 pm) vs van der Waals radius (180 pm) in Cl₂ (p. 107).
• Fig. 4.3 — Resonance hybrid of O₃ from two canonical forms (p. 109).
• Fig. 4.4 — Three canonical structures of CO₃²⁻ (p. 110); Fig. 4.5 — three canonical forms of CO₂ (p. 110).
• Table 4.5 — Dipole moments and geometries: HF 1.78 D linear, H₂O 1.85 D bent, NH₃ 1.47 D trigonal pyramidal, BF₃ 0 D trigonal planar, CO₂ 0 D linear, CCl₄ 0 D tetrahedral (p. 112).
• Tables 4.6–4.8 — VSEPR geometries (p. 114–117).
• Fig. 4.7 / 4.8 — Forces and potential-energy curve in H₂ formation (p. 118).
• Fig. 4.10–4.16 — Hybridisation diagrams for BeCl₂ (sp), BCl₃ (sp²), CH₄ (sp³), NH₃ and H₂O (sp³ with lone pairs), C₂H₄, C₂H₂ (p. 121–124).
• Fig. 4.17 — Trigonal bipyramidal PCl₅ (sp³d) with axial vs equatorial bonds (p. 125).
• Fig. 4.18 — Octahedral SF₆ (sp³d²) (p. 125).
• Fig. 4.20 — Bonding/antibonding MOs from 1s, 2p_z, 2p_x AOs (p. 128).
• Fig. 4.21 — MO occupancy table for B₂ through Ne₂ with bond order and magnetic property (p. 131).
• Fig. 4.22 — Intramolecular H-bond in o-nitrophenol (p. 132).

2.4 Common confusions / NTA trap points

• MOT energy order changes at O₂: for B₂, C₂, N₂ the (π2p) lies below σ2p_z; for O₂, F₂, Ne₂ the σ2p_z lies below (π2p). NTA often inverts this in distractors.
• NH₃ vs NF₃ dipole moments: N is more electronegative than H but less than F. Yet μ(NH₃) > μ(NF₃) because the lone-pair dipole adds in NH₃ but subtracts in NF₃. Easy trap.
• H₂O bent ≠ BeCl₂ linear even though both are AB₂ — H₂O has 2 lone pairs on O (AB₂E₂ → sp³ → bent), BeCl₂ has none (AB₂ → sp → linear).
• C₂ double bond is two π bonds (no σ from 2p_z because σ2p_z is empty in the (π2p)⁴ configuration), unlike most double bonds which are 1σ + 1π.
• Formal charge ≠ oxidation state ≠ real charge. It only helps in picking the best Lewis structure.
• Hybridisation does not require half-filled orbitals — even filled orbitals can hybridise (e.g. the lone-pair-bearing sp³ orbitals of O in H₂O).
• Bond order in resonance hybrid is fractional — in CO₃²⁻ each C–O bond order = 4/3 (1 σ + delocalised π over 3 oxygens).
• Ice less dense than water because tetrahedral H-bonding in ice creates empty cages; this is an H-bonding consequence often asked through MCQs on density/boiling-point anomalies.