Chemical Bonding

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Chemical Bonding — Key Facts for CUET

Ionic Bonding: Formed by complete transfer of electrons from metal to non-metal. Cations: $Na^+, Mg^{2+}, Al^{3+}$; Anions: $Cl^-, O^{2-}$. Lattice energy (energy released when gaseous ions form solid lattice) follows Born-Lande equation: $U = -\frac{N_AMz^+z^-e^2}{4\pi\epsilon_0 r_0}\left(1-\frac{1}{n}\right)$ where $n$ = Born exponent (4 for NaCl-type).

Covalent Bonding: Formed by sharing of electron pairs between atoms. Bond order = (number of bonding electrons - number of antibonding electrons)/2. A higher bond order means a stronger, shorter bond. $H_2$: bond order 1, bond length 74 pm. $O_2$: bond order 2. $N_2$: bond order 3, bond length 110 pm (triple bond).

VSEPR Theory: Shape predicted by steric number (SN = number of bond pairs + number of lone pairs):

• SN=2: Linear (180°) — e.g., $CO_2$, $BeCl_2$
• SN=3: Trigonal planar (120°) if no lone pairs, bent (<120°) if 1 lone pair — e.g., $BF_3$, $SO_2$
• SN=4: Tetrahedral (109.5°) if no lone pairs, trigonal pyramidal (<109.5°) if 1 lone pair, bent if 2 lone pairs — e.g., $CH_4$, $NH_3$, $H_2O$

⚡ Exam tip: For dipole moment, a molecule with polar bonds is NOT necessarily polar. $CO_2$ has two C=O bonds (each polar, μ = 2.35 D for isolated bond) but is LINEAR, so net dipole = 0. Compare: $H_2O$ has μ = 1.85 D (bent, not cancelled).

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Chemical Bonding — Chemistry Study Guide

Lewis Structures: Octet rule (with exceptions): H shares 2 electrons, B stabilises with 6, P and S can expand octet.

• $PCl_5$: P has 10 electrons around it (expanded octet)
• $SF_6$: S has 12 electrons (6 bonds)
• $ClO_4^-$: Cl has 12 electrons
• $BH_3$: B has only 6 electrons (electron deficient, acts as Lewis acid)

Formal Charge: $FC = V - N - B/2$ where $V$ = valence electrons, $N$ = nonbonding electrons, $B$ = bonding electrons. For the best Lewis structure, formal charges should be minimised and negative charges on more electronegative atoms.

Hybridisation:

• $sp^3$: 4 equivalent orbitals from s + three p — tetrahedral geometry, e.g., $CH_4$, $C_2H_6$
• $sp^2$: 3 equivalent orbitals — trigonal planar, e.g., $C_2H_4$ (each C), $BF_3$, $C_2H_4$ has a $\pi$ bond in addition to the $\sigma$ framework
• $sp$: 2 equivalent orbitals — linear, e.g., $C_2H_2$, $BeCl_2$
• $dsp^2$: square planar, e.g., $[Ni(CN)_4]^{2-}$
• $d^2sp^3$: octahedral, e.g., $[Fe(CN)_6]^{3-}$

Molecular Orbital Theory: Bonding molecular orbitals (BMO) are lower in energy than atomic orbitals; antibonding (ABMO) are higher. Electrons fill from lowest to highest energy (Aufbau principle). Examples:

• $H_2$: $(σ1s)^2$, bond order = 1
• $He_2$: $(σ1s)^2(σ^*1s)^2$, bond order = 0 (does not exist)
• $O_2$: $(σ2s)^2(σ^*2s)^2(σ2p_z)^2(π2p_x)^2(π2p_y)^2(π^*2p_x)^1(π^*2p_y)^1$, bond order = 2 (has 2 unpaired electrons — explains paramagnetism)
• $N_2$: $(σ2s)^2(σ^*2s)^2(π2p_x)^2(π2p_y)^2(σ2p_z)^2$, bond order = 3

Intermolecular Forces:

1. London dispersion forces: Instantaneous dipole-induced dipole; strength ∝ molecular mass; the ONLY force between nonpolar molecules. Present in ALL molecules.
2. Dipole-dipole forces: Between polar molecules with permanent dipoles; e.g., HCl, SO₂.
3. Hydrogen bonding: Special dipole-dipole when H is bonded to F, O, or N (F-H, O-H, N-H); e.g., $H_2O$, $NH_3$, $HF$. H-bond in water: ~20 kJ/mol (vs. ~0.1 kJ/mol for London force).

Fajans’ Rule (for ionic vs covalent character):

• Covalent character increases with: small cation, large anion, high charge on cation
• $LiI$ is more covalent than $LiF$ (large anion wins)
• $AlCl_3$ is covalent (small, highly charged $Al^{3+}$)

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Chemical Bonding — Comprehensive Chemistry Notes

Valence Bond Theory (VBT) vs MOT: VBT describes bond formation as overlap of atomic orbitals with spin pairing. Types of orbital overlap:

• Sigma ($\sigma$) bond: Head-on overlap along the internuclear axis; maximum overlap. e.g., s-s overlap in $H_2$, s-p overlap in HCl, p-p ($\sigma$) overlap in $Cl_2$
• Pi ($\pi$) bond: Sideways overlap above and below the internuclear axis; involves two lobes of one p orbital overlapping with two lobes of another. e.g., $C_2H_4$ has one $\pi$ bond (from sideways p-p overlap); $N_2$ has two $\pi$ bonds (from two perpendicular p-p overlaps)

Resonance: When more than one valid Lewis structure can be drawn for a molecule, the actual structure is a resonance hybrid. Examples:

• $O_3$: two equivalent resonance structures with one single and one double O-O bond; actual bond lengths are intermediate (~128 pm vs. 121 pm for O=O and 148 pm for O-O single)
• $CO_3^{2-}$: three equivalent resonance structures; all C-O bonds are equal (141 pm)
• $C_6H_6$ (benzene): two equivalent Kekulé structures; all C-C bonds are 140 pm (intermediate between single 154 pm and double 134 pm)

Bond Parameters:

• Bond length: Measured by X-ray diffraction or rotational spectroscopy. Generally: triple bond < double bond < single bond. C-C: 154 pm, C=C: 134 pm, C≡C: 120 pm.
• Bond enthalpy: Energy to break 1 mole of bonds in gaseous molecules. C-H: 414 kJ/mol, C-C: 347 kJ/mol, C=C: 620 kJ/mol, C≡C: 839 kJ/mol, O-H: 463 kJ/mol.
• Bond angle: Determined by hybridisation and lone pair repulsion. Lone pair–lone pair repulsion > lone pair–bond pair > bond pair–bond pair repulsion. This is why $H_2O$ (104.5°) has a smaller angle than $CH_4$ (109.5°).
• Dipole moment: $\mu = Q \times r$ in Debye (D); 1 D = $3.335 \times 10^{-30}$ C·m. For CO₂: μ = 0 (linear); for H₂O: μ = 1.85 D (bent, 104.5°); for NH₃: μ = 1.47 D (trigonal pyramidal, 107°).

Motivation of Hybridisation: Hybrid orbitals explain the geometry observed by spectroscopy. However, orbitals themselves are mathematical constructs — the physical reality is better described by MO theory. $CH_4$ forms four $sp^3$ orbitals because this gives maximum separation (109.5°) and minimum repulsion.

Coordinate Bond (Dative Bond): Both electrons come from one atom. Examples: $CO$ (C→O coordinate bond from C to O), $NH_4^+$, $H_3O^+$, $NO_2^+$, $BF_3$·$NH_3$. Once formed, a coordinate bond is indistinguishable from a covalent bond.

Metallic Bond: Explained by: (1) Electron sea model — delocalised electrons in a lattice of positive ions; (2) Band theory — overlapping atomic orbitals form energy bands. Conductors have partially filled bands; insulators have a large gap between valence and conduction bands; semiconductors have a small gap.

Born-Haber Cycle for Lattice Energy: For NaCl: $\Delta_f H^\circ = \Delta_{atom}H(Na) + \frac{1}{2}\Delta_{bond}H(Cl_2) + IEA(Na) + EA(Cl) + \Delta_{lattice}H$. With values: $107 + 122 + 496 + (-349) + \Delta_{lattice}H = -411$. $\Delta_{lattice}H = +787$ kJ/mol. This large positive lattice energy makes NaCl stable.

CUET Exam Trends: Questions frequently test: (1) VSEPR shape prediction from formula, (2) Formal charge calculation on Lewis structures, (3) MO theory bond order for $O_2$, $N_2$, $He_2$, (4) H-bonding in water/alcohols and its effects on boiling point, (5) Fajans’ rule for comparing ionic character. JEE 2022 asked: “Which molecule has the highest dipole moment among CH₄, NH₃, H₂O, CO₂?” Answer: NH₃ (μ = 1.47 D) > H₂O (1.85 D wait — actually H₂O has higher μ). Let me recalculate: H₂O has 1.85 D, NH₃ has 1.47 D. So H₂O > NH₃ > CH₄ = 0 > CO₂ = 0.

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