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CHEMICAL BONDING
NOTES

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Lewis Structure VSEPR Theory Hybridisation MOT Dipole Moment Ionic Bond H-Bond
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⚗️

CHEMICAL BOND — BASICS

DEFINITION

Chemical Bond: Force of attraction present between any chemical species like atoms, ions & molecules.

Bond Formation

Bond formation → Exothermic

Bond Dissociation → Endothermic

Cause of Bonding

Modern Concept: Every atom has tendency to form maximum possible bonds to minimize its PE & gain stability.

Classical Concept (Octet Rule): Every atom has tendency to achieve stable outer octet (8e⁻ in valence shell).

Types of Chemical Bonds

Strong Bonds
  • Ionic Bond
  • Covalent Bond
  • Co-ordinate Bond
  • Metallic Bond

Order: O.T.B.O Bond Energy

Weak Bonds
  • Hydrogen Bond
  • Van der Waals Bond

Theories to Explain Bonding

  • ① Octet Rule (Kossel-Lewis Approach)
  • ② VSEPR [Valence Shell Electron Pair Repulsion Theory]
  • ③ VBT [Valence Bond Theory]
  • ④ MOT [Molecular Orbital Theory]
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OCTET RULE & LEWIS DOT STRUCTURE

Octet Rule (Kossel-Lewis Approach)
  • Based on inertness of noble gases
  • Atom can combine either by transfer of valence e⁻ or by sharing to have an octet (8e⁻ in valence shell)
  • In case of H & He: duplet (2e⁻ in valence shell) will be completed

Lewis Symbols

·Li (2s¹)   ·Be· (2s²)   ·B· (2s²2p¹)   ·Ċ· (2s²2p²)   :N̈: (2s²2p³)   :Ö: (2s²2p⁴)   :F̈: (2s²2p⁵)   :Në: (2s²2p⁶)

Formation of Cl₂, O₂, N₂ — Octet by Sharing

MoleculeBonding e⁻Bond Pair / No. of BondsNon-bonding total e⁻Lone Pairs
Cl₂21126
O₂4284
N₂6342

How to Write Lewis Dot Structure

MDJ Formula
\[ \text{No. of Bonds} = \frac{\text{Req. Valence e}^- - \text{Available Valence e}^-}{2} \]

Req. Valence e⁻ = No. of atoms × 8 (octet rule; 2 for H)

EXAMPLES
  • CO: No. of Bonds = (8×2)−(4+6)/2 = 3
  • O₃: No. of Bonds = (8×3)−(6×3)/2 = 3
  • N₃⁻: No. of Bonds = (8×3)−(5×3+1)/2 = 4
  • CO₂: No. of Bonds = (8×3)−(4+12)/2 = 4
  • N₂O: No. of Bonds = (8×3)−(5+5+6)/2 = 4

Limitations of Octet Rule

Exceptions
  1. Existence of Hypervalent compounds [Valence > 8] e.g. PCl₅, SF₆ etc.
  2. Existence of Hypovalent compounds [Valence e⁻ < 8] e.g. LiCl, BF₃ etc.
  3. Odd e⁻ species do not follow octet rule e.g. NO, NO₂ etc.
  4. Existence of compound of inert gas with oxygen & fluorine e.g. XeF₂, KrF₂
  5. It doesn't explain relative stability of molecules (silent about energy)
  6. This theory doesn't account for the shape of molecules
Q: Which is not an exception to Octet Rule?
✅ Ans: (b) SnCl₄ — Sn has 4 bonds → 8e⁻ → follows octet
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FORMAL CHARGE

DEFINITION

It is an extra charge present on atom in any given Lewis structure due to loss or gain of e⁻.

\[ FC = \left[\text{Total Valence e}^-\text{ in free atom}\right] - \left[\text{Total non-bonding (LP) e}^-\right] - \frac{1}{2}\left[\text{Total bonding e}^-\right] \]
MDJ Trick

Formal Charge = Jitne Hone Chahiye (Valence e⁻ in free state) − Jitne Hai (Valence e⁻ in given Lewis structure)

MDJ — Formal Charge Table
Bond TypeFormal Charge
O= or —O—0
O— (single bond, 3 LP)−1
O≡ or —O= (triple or double with less LP)+1

Solved Examples

O₃ Formal Charge

Terminal O (6−6 = 0 LP bond) → FC = 0 or −1

Central O (+1) → FC = +1

Structure (a) is more stable due to symmetrical charge distribution

CO Formal Charge

C: FC = 4−5 = −1  |  O: FC = 6−5 = +1

CO₂ Formal Charge

Structure (a): All FC = 0 → More stable due to absence of charge

O: FC = 0 (both) | C: FC = 0

Avg Formal Charge & Avg X-O Bond Order in Oxoanions

\[ \text{Avg FC} = \frac{\text{Total charge on oxygen atoms}}{\text{No. of O atoms where −ve charge can be placed}} \] \[ \text{Avg X-O Bond Order} = \frac{\text{Total no. of X-O bonds}}{\text{No. of X-O pairs participating in resonance}} \]
SpeciesStructureAvg FC on OAvg X-O Bond Order
CO₃²⁻C with 3 O−2/34/3
NO₂⁻−O−N=O−1/23/2
ClO₄⁻Cl with 4 O−1/47/4
PO₄³⁻P with 4 O−3/45/4
SO₄²⁻S with 4 O−2/4 = −1/26/4 = 3/2
SO₃²⁻S with 3 O−2/34/3
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COVALENT & CO-ORDINATE BOND

Covalent Bond

Bond formed by equal sharing of e⁻

Covalency: Total no. of covalent bonds (σ & π) formed by an atom in a molecule

Note: Max covalency of 2nd period element cannot be more than 4 due to absence of d orbitals (only s and p available)

Fluorine can show only 1 covalency

Co-ordinate Bond

Formed by unequal sharing of e⁻

Co-ordinate bond is formed b/w e⁻ donor & e⁻ acceptor

It cannot be distinguished from covalent bond after formation

Types: (i) σ-Coordinate, (ii) π-Coordinate (also known as Back-Bonding)

Covalency of Elements (Important for NEET)

ElementGround StateCovalencyExcited StateCovalency
B (Boron)2s²2p¹ → 3 covalency3ES1: 4 (σ co-ordinate)4
N (Nitrogen)2s²2p³ → 3 covalency3ES1 (NH₄⁺): 44
P (Phosphorus)3s²3p³3 & 5ES1: 5 (PCl₅), ES2: 6 (PCl₆⁻)5,6
S (Sulphur)3s²3p⁴2ES1: 4 (SF₄), ES2: 6 (SF₆, SO₃)2,4,6
Cl (Chlorine)3s²3p⁵1ES1: 3 (ClF₃), ES2: 5 (ClO₃⁻), ES3: 7 (ClO₄⁻)1,3,5,7
Co-ordinate Bond Examples
SpeciesCo-ordinate Bond
NH₄⁺σ-coordinate tnt (NH₃ + H⁺)
H₃O⁺σ-coordinate tnt (H₂O + H⁺)
PCl₆⁻σ-coordinate tnt (PCl₅ + Cl⁻)
BF₄⁻σ-coordinate tnt (BF₃ + F⁻)
B(OH)₄⁻σ-coordinate tnt (B(OH)₃ + OH⁻)
NH₃·BF₃σ-coordinate tnt (H₃N → BF₃)
CO (C≡O⁺ or ⁻C≡O)π-co-ordinate (Back-bonding)
NO₃⁻σ-coordinate tnt
NO₂ (neutral)σ-coordinate tnt
During formation of NH₃·BF₃
  • Covalency of B & N increases to 4
  • Hybridisation of N: sp³ remains; Hybridisation of B: sp² → sp³
  • Shape of NH₃: Tetrahedral (θ = 109.5°) & BF₃: Tetrahedral (θ = 109.5°)
  • θ increases in NH₃ (109.5° to 109.5°) & decreases in BF₃ (120° to 109.5°)
📐

VSEPR THEORY

Theory

Based on repulsive interactions of e⁻ pairs in valence shell. Every molecule tends to acquire a shape in which repulsion between various e⁻ pairs is minimized & distance between them is maximized.

Overall geometry/shape depends on σ bond pairs & lone pairs.

Repulsion Order

Lone pair–Lone pair > Lone pair–Bond pair > Bond pair–Bond pair

Trick to Find n & m in ABₙLₘ

\[ \frac{\text{Total Valence e}^-}{8} \rightarrow \text{Quotient} = n, \quad \text{Remainder}/2 = m \]
Important Notes
  • A = Central Atom, B = σ bond pair, L = Lone pair
  • n = No. of Bond pair / No. of surrounding atoms
  • m = No. of Lone Pair
  • Do NOT apply this trick for odd e⁻ species or species having hydrogen as surrounding atom
  • MDJ: Jab compound me koi charge present nahi ho, aur surrounding atom oxygen ho to saare "O" double bond consider karo
EXAMPLES WITH TRICK
SpeciesValence e⁻ / 8n (Quotient)m (Rem/2)TypeShape
BF₃24/830AB₃L₀Trigonal Planar
SO₂18/821AB₂L₁Bent
PCl₅40/850AB₅L₀Trigonal Bipyramidal
NO₂⁺16/820AB₂L₀Linear
NO₃⁻24/830AB₃L₀Trigonal Planar
SO₃24/830AB₃L₀Trigonal Planar
XeO₃26/831AB₃L₁Trigonal Pyramidal
XeO₂F₂34/841AB₄L₁See-saw
SO₂Cl₂32/840AB₄L₀Tetrahedral
SOCl₂26/831AB₃L₁Trigonal Pyramidal

Hydrogen as Surrounding Atom — MDJ Trick

Formula (for H as surrounding)

Total Valence e⁻ of central atom − No. of H ± charge on molecule

SpeciesCalculationLone PairsTypeShape
CH₄4−4=00 LPAB₄L₀Tetrahedral (sp³)
NH₃5−3=2 (1 LP)1AB₃L₁Trigonal Pyramidal (sp³)
NH₄⁺5−4−1=0 (0 LP)0AB₄L₀Tetrahedral (sp³)
NH₂⁻5−2+1=4 (2 LP)2AB₂L₂Bent (sp³)
H₂O6−2=4 (2 LP)2AB₂L₂Bent (sp³)
PCl₃5−3=2 (1 LP)1AB₃L₁Trigonal Pyramidal
XeF₄8−4=4 (2 LP)2AB₄L₂Square Planar
XeF₆8−6=2 (1 LP)1AB₆L₁Distorted Octahedral
I₃⁻7−2+1=6 (3 LP)3AB₂L₃Linear
I₃⁺7−2−1=4 (2 LP)2AB₂L₂Bent
ICl₂⁻7−2+1=6 (3 LP)3AB₂L₃Linear
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MOLECULAR SHAPES — COMPLETE TABLE

Find Hybridisation from n+m

n+mHybridisationn+mHybridisation
2sp5sp³d
3sp²6sp³d²
4sp³7sp³d³

All ABₙLₘ Types — Shape & Bond Angle

TypeShapeBond AnglePlanar?Example
AB₂L₀Linear180°YesCO₂, BeCl₂
AB₃L₀Trigonal Planar120°YesBF₃, SO₃, AlCl₃
AB₄L₀Tetrahedral109.5°NoCH₄, NH₄⁺, H₂O⁺
AB₅L₀Trigonal Bipyramidale=120°, a=90°NoPCl₅, PF₅
AB₆L₀Square Bipyramidal / Octahedral90°NoSF₆, PCl₆⁻
AB₇L₀Pentagonal Bipyramidale=72°, a=90°NoIF₇
AB₂L₁Bent/V-shape<120°YesSO₂, NO₂⁻
AB₂L₂Bent/V-shape<109.5°YesH₂O, OF₂, H₂S
AB₂L₃Linear180°YesXeF₂, I₃⁻
AB₃L₁Trigonal Pyramidal≈107°NoNH₃, PCl₃, XeO₃
AB₃L₂Bent T-shape90°YesClF₃, BrF₃
AB₄L₁See-sawNon-planarNoSF₄, XeO₂F₂
AB₄L₂Square Planar90°YesXeF₄, ICl₄⁻
AB₅L₁Square PyramidalNon-planar, a=eNoIF₅, BrF₅
AB₅L₂Pentagonal Planar72°YesXeF₅⁻
AB₆L₁Distorted Octahedral (Capped Octahedral)Non-planarNoXeF₆
Important Notes on VSEPR
  • In Trigonal Bipyramidal — Lone pair always occupies equatorial position
  • In Square Bipyramidal/Octahedral — First LP at any position, 2nd is always opposite at 180°
  • In AB₂L₃, AB₂L₃, AB₄L₂ — Lone pairs on opposite position → no effect on bond angle
  • Q: In which geometry there is no effect of lone pair on bond angle?
    Ans: AB₂L₃ (Linear) ✓ | AB₂L₃ ✓ | AB₄L₂ ✓ | AB₅L₂ ✓
⚛️

VALENCE BOND THEORY & HYBRIDISATION

Hybridisation

Mixing of orbitals; according to NCERT only valence shell orbitals can mix due to less energy gap.

No. of hybrid orbital = No. of atomic orbitals participating in hybridisation = σ bond + Lone pair (n+m)

Important Points of Hybridisation

Key Rules
  • It is orbitals which hybridise, not electrons
  • Orbitals having paired e⁻, single e⁻ & vacant orbitals all can participate in hybridisation
  • Excitation or promotion of e⁻ is NOT essential condition
  • Hybridisation is reconstruction & reorganisation of orbitals
  • The hybridised orbitals are always equivalent in energy & shape
  • Only those orbitals need to hybridise which form σ bond & keep the lone pair
  • So, no. of hybrid orbital = σ bond + Lone pair (n+m)
  • MDJ: S↓ = θ↓ | S↑ = θ↑ ("S angle ki dukan hai")

d-Orbitals Used in Hybridisation

  • sp³d → uses dz²
  • sp³d² → uses dz², dx²−y²
  • sp³d³ → uses dz², dx²−y², dxy
EXAMPLES
  • SF₆ → AB₆L₀ / sp³d² → uses dz², dx²−y²
  • XeF₂ → AB₂L₃ / sp³d → uses s, px, py, pz, dz²
  • XeF₆ → AB₆L₁ / sp³d³ → uses s, px, py, pz, dz², dx²−y², dxy; (dxz, dyz remain pure)

Hybridisation in Odd e⁻ Species

Rule

Orbitals having odd e⁻ can participate in hybridisation only when surrounding atom is High Electronegative.

  • CF₃ radical: 3σ + 1 orbital having odd e⁻ = sp³ (Trigonal Pyramidal)
  • CH₃ radical: surrounding H has low EN → does NOT participate → sp² (Trigonal Planar)
  • Unpaired e⁻ in CH₃ is in pure p orbital
  • NO₂: N → sp², Shape → Bent, θ > 120° (≈134°), paramagnetic
  • ClO₂: Cl → sp³, paramagnetic
  • ClO₃: Cl → sp³

MDJ: Odd e⁻ species mein if N is greater than surrounding atom's EN, then orbital having odd e⁻ will not participate in hybridisation.

Hybridisation in Solid State

Compound (Solid)Ions formedHybridisation
PCl₅ (s)PCl₄⁺ + PCl₆⁻sp³ (Tetrahedral) + sp³d² (Octahedral)
PBr₅ (s)PBr₄⁺ + Br⁻sp³ (PBr₆⁻ does not exist — steric hindrance)
N₂O₄ (s)NO⁺ + NO₃⁻—
N₂O₅ (s)NO₂⁺ + NO₃⁻—
XeF₆ (s)XeF₅⁺ + F⁻—
Cl₂O₆ (s)ClO₂⁺ + ClO₄⁻—

Existing & Non-Existing Molecules

Non-contraction of d-orbitals (Existing)
  • XeF₆ (sp³d³)
  • XeF₂ (sp³d)
  • SF₆ (sp³d²)
Non-Existing
  • XeH₆, XeH₂, SH₆ (H has low EN — d orbital can't contract)
Improper Covalency — Existing vs Non-Existing

Existing:

  • NCl₃
  • BF₄⁻
  • ClF₃

Non-Existing:

  • NCl₅ (N can't exceed 4)
  • BF₆³⁻
  • FCl₂
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BOND ANGLE & APPLICATIONS

Trick to Find Bond Angle

Flowchart
  • VSEPR: AB₂L₀, AB₂L₃ → Linear (180°)
  • Hybridisation: sp > sp² > sp³
  • If hybridisation is same → check Lone Pairs at central atom
  • If L.P. present at central atom: No. of LP ↑ → Bond Angle ↓
  • If L.P. not at central atom → Give answer acc. to Hybridisation
  • If LP & hybridisation both same: Size of surrounding atom ↑ → Bond angle ↑ | Size of central atom ↑ → Bond angle ↓

Important Bond Angle Orders

  1. CO₂ & SO₂ → CO₂ (AB₂L₀) > SO₂ (AB₂L₁)
  2. CO₂, BF₃, NH₄⁺ → CO₂(sp) > BF₃(sp²) > NH₄⁺(sp³)
  3. XeF₂, I₃⁻, CO₂ → XeF₂(Linear) = I₃⁻(Linear) = CO₂(Linear)
  4. SO₃ & SO₂ → SO₃(AB₃L₀) > SO₂(AB₂L₁)
  5. CH₄, NH₃, H₂O → CH₄(AB₄L₀) > NH₃(AB₃L₁) > H₂O(AB₂L₂)
  6. CCl₄ & SiCl₄ → CCl₄(AB₄L₀/sp³) = SiCl₄(AB₄L₀/sp³)
  7. AlCl₃ & BCl₃ → AlCl₃(AB₃L₀/sp³) = BCl₃(AB₃L₀/sp²)
  8. BF₃, BCl₃, BBr₃ → BF₃(AB₃L₀/sp²) = BCl₃(AB₃L₀/sp²) = BBr₃(AB₃L₀/sp²)
  9. NO₂⁺, NO₃⁻, NO₂⁻ → NO₂⁺(Linear) > NO₃⁻(AB₃L₀) > NO₂⁻(AB₂L₁)
  10. NH₂⁻, NH₃, NH₄⁺ → NH₂⁻(AB₂L₂) < NH₃(AB₃L₁) < NH₄⁺(AB₄L₀)
  11. NF₃, NCl₃, NBr₃ → NF₃(AB₃L₁/sp³) < NCl₃(AB₃L₁/sp³) < NBr₃(AB₃L₁/sp³) [Surrounding atom ↑ = θ↑]
  12. NCl₃, PCl₃, AsCl₃ → NCl₃(AB₃L₁/sp³) > PCl₃(AB₃L₁/sp³) > AsCl₃ [Central atom ↑ = θ↓]

Bent's Rule

Rule

Lone pair ko 's' pasand hai   |   High EN element ko 'p' pasand hai

S↓, θ↓   |   S↑, θ↑   |   sp < sp² < sp³ (P↑ → Length of hybrid orbital ↑ → size ↑)

  • H₂O: θ < 109.5° (Lone pair in s orbital → more s character → more p in bond orbital → smaller angle)
  • OF₂ > H₂O (F has high EN → gets more p → O gets more s for LP → Bond pair gets more p → angle ↓)
  • H-O-O-H vs F-O-O-F: F-O bond has more p% → O-O bond more s% → longer O-O in FOOF
  • CH₂F₂: H-C-H > F-C-H > F-C-F (p increases, s decreases)

Drago Rule

Drago Rule

According to Drago: "In some molecules, sp mixing is negligible"

Conditions (ALL THREE must be satisfied):

  1. Lone pair must be in s orbital
  2. EN of surrounding atom (H) must be low
  3. Size of central atom must be large (3rd period or more)

NH₃ — Drago NOT Applicable

  • LP in sp³ (not in s)
  • SA is H (low EN ✓)
  • CA is small (2nd period ✗)

PH₃ — Drago Applicable

  • LP in almost pure s
  • SA is H (low EN ✓)
  • CA is large (3rd period ✓)
  • Mixing Negligible
  • LP in PH₃ in almost pure s-orbital, θ ≈ 90°

Directional Nature of Lone Pairs:

NH₃ > PH₃ > AsH₃ > SbH₃ (Drago Applicable, θ ≈ 90°)

H₂O > H₂S > H₂Se > H₂Te

Above orders are also same for Lewis Basic Nature & Bond Angle.

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OVERLAPPING & BOND IDENTITY

Overlapping = Mixing of orbitals of different atoms (Central atom & surrounding atoms). It is mechanism of covalent bond formation.

Pairing of e⁻ tht in valence shell having opp. spins.

Types of Overlapping

Co-Axial / Head-on Overlapping
  • Along internuclear axis
  • σ-Bond Formation
  • (Hybrid+Hybrid), (Hybrid+Pure), (Pure+Pure) all can form σ
Collateral / Sideways Overlapping
  • Perpendicular to internuclear axis
  • π-Bond Formation
  • Generally molecules in which CA is hybridised
σ > π (Strength)

Hybrid + Hybrid = Always σ | Hybrid + Pure = Always σ | Pure + Pure = σ or π

Types of Pure+Pure Orbital Overlapping

Typex-axisy-axisz-axis
s-sσσσ
s-pxσ00
s-py0σ0
s-pz00σ
px-px (coaxial)σππ
pz-pzππσ
py-pyπσπ
px-py000Zero overlap
dxy-dxyδ/ππδ
dz²-dz²δππ

π Bond Identity (MDJ)

Rules
  • sp → all are Pπ−Pπ type
  • sp² → First one Pπ−Pπ, others are dπ−Pπ type
  • sp³ or any other → All are dπ−Pπ or dπ−dπ type
  • If Central Atom belongs to 2nd period — no d available so no dπ-Pπ bonds
Speciesπ Bond Type
CO₃²⁻Pπ−Pπ
NO₂⁻Pπ−Pπ
NO₃⁻Pπ−Pπ
ClO₄⁻ (sp³)dπ−Pπ
SO₃²⁻ (sp³)dπ−Pπ
PO₄³⁻ (sp³)dπ−Pπ
SO₂ (sp²)1 Pπ−Pπ, 1 dπ−Pπ
SO₃ (sp²)1 Pπ−Pπ, 2 dπ−Pπ

Bond Identity Examples

  • H−H → s−s σ bond
  • H−Cl → s−p σ bond
  • Cl−Cl → p−p σ bond
  • Ethane (C₂H₆): C−C → sp³−sp³ σ, C−H → sp³−1s σ
  • Ethene (C₂H₄): C−H(σ) → sp²−1s (four), C−C(σ) → sp²−sp², C=C(π) → 2pπ−2pπ
  • Ethyne (C₂H₂): C−H(σ) → sp−1s (two), C≡C(σ) → sp−sp, C≡C(π) → 2pπ−2pπ (two)
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BOND STRENGTH & BOND ENERGY

\[ \text{Bond Strength} \propto \frac{1}{\text{Size (Shell no.)}} \]

Bond Strength Comparison Rules

  1. Size same, σ bond (co-axial): s−s < s−p < p−p
  2. Size same, π bond (collateral): Pπ−Pπ < Pπ−dπ < dπ−dπ
  3. Lone Pair-Lone Pair repulsion can show exceptions ONLY in second period elements (only single bonded atoms)

Important Bond Strength Orders

  • 1s−1s > 2s−2s > 3s−3s
  • 2s−2s < 2s−2p < 2p−2p
  • p−p(coaxial) > p−p(collateral) → i.e. σ > π
  • N−N < P−P (LP-LP repulsion more in N)
  • O−O < S−S (LP-LP repulsion)
  • F−F < Cl−Cl < Br−Br (LP-LP repulsion) → halogen order reversed
  • 3pπ−3pπ is weakest bond (generally not exists) → Reason: N₂ exists but P₂ doesn't at room temp
  • N−N < N=N < N≡N | C−C < C=C < C≡C
  • CO₃²⁻ < CO₂ < CO | H₂O₂ < O₃ < O₂
  • C−C > Si−Si > Ge−Ge > Sn−Sn
🧲

DIPOLE MOMENT

DEFINITION

It measures overall polarity in a molecule. It is a Vector Quantity.

Directed toward more EN (more e⁻ density) element.

Direction of Lone Pair: Dipole moment is always away from the molecule.

\[ \mu = q \times d \quad \text{where } q = \text{magnitude of charge, } d = \text{internuclear distance} \]

Unit: Debye | 1 Debye = 3.3 × 10⁻³⁰ C·m

Key Rules
  • If μ = 0 → Non-polar
  • If μ ≠ 0 → Polar
  • ΔEN ↑ → |μ| ↑  |  |μ| ↑ → μ ↑
  • MDJ: If all surrounding atoms are same: AB₂to₇L₀ and AB₄L₂, AB₂L₃ → Symmetrical Structure → μ = 0 / Non-Polar
  • MDJ: LP & Multiple Bond "Bhai-Bhai" — Jo jagah LP ko pasand wahi multiple bond ko pasand

Dipole Moment Resultant Formula

\[ \mu_R = \sqrt{\mu_1^2 + \mu_2^2 + 2\mu_1\mu_2\cos\theta} \]
θ0°60°90°120°180°
cosθ11/20−1/2−1

cosθ ↑ → μR ↑

Important Dipole Moment Orders

  1. CO₂ (0) < SO₂ (≠0)
  2. SO₂ > SO₃ (SO₃ μ=0)
  3. CCl₄ < CH₂F₂ [SA different]
  4. XeF₂ = XeF₄ (both μ=0)
  5. XeO₃ > XeO₄ (XeO₄ μ=0)
  6. PCl₃ > PCl₅ (PCl₃ has LP)
  7. BF₃ = BCl₃ (both AB₃L₀, μ=0)
  8. SF₆ < ClF₄⁺ (AB₄L₁)
  9. BeCl₂ < H₂O (BeCl₂ linear μ=0)
  10. NCl₂ > BCl₂
  11. NH₃ > NF₃ (in NH₃, LP & BP dipoles add; in NF₃ they oppose)
  12. H₂O > OF₂
  13. HF > HCl > HBr > HI  |  HF > NH₃ > PH₃  |  H₂O > NH₃ > PH₃  |  H₂O > H₂S
  14. CH₃Cl > CH₂F₂ > CH₃Br > CH₃I  |  CH₃Cl > CH₂Cl₂ > CHCl₃ > CCl₄
  15. H₂O > HF (According to NCERT)

% Ionic Character from Dipole Moment

\[ \% \text{ Ionic Character} = \frac{\mu_{real}}{\mu_{imaginary}} \times 100 \]
Example — HCl

μ_HCl = 1.02 D = 1.02 × 3.3 × 10⁻³⁰ C·m

μ_imaginary = q × d = 1.6 × 10⁻¹⁹ × 1.27 × 10⁻¹⁰

% Ionic Character = (1.02 × 3.3 × 10⁻³⁰) / (1.6 × 10⁻¹⁹ × 1.27 × 10⁻¹⁰) × 100

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IONIC BOND & LATTICE ENERGY

Ionic / Electrovalent Bond

Bond formed by complete transfer of e⁻. Electrostatic/Coulombic force of attraction b/w oppositely charged ions.

Generally formed b/w metal (electropositive) & non-metal (electronegative).

Properties of Ionic Compounds

Ionic Compound
  • Exist in form of ionic lattice
  • Do not exist in molecular form
  • Strong electrostatic force of attraction
  • Generally solid
  • Do not show isomerism (non-directional bond)
  • Polar & readily soluble in polar solvent like water
  • High Melting Point & Boiling Point
Covalent Compound
  • Molecular solid
  • Exist in form of molecules
  • Weak Van der Waals force b/w molecules
  • Low Melting/Boiling Point

Electrical Conductivity

CompoundStateIon Present?MobilityConductance
IonicSolid✓✗✗
Liquid (Molten)✓✓✓
Aqueous✓✓✓
CovalentSolid✗✗✗
Liquid (Molten)✗✗✗
Aqueous✓✓✓

Note: Metals are always conductors of electricity due to presence of free e⁻

Hydration of Ionic Compounds

Hydration

Tendency of ionic compound (break into ions). Hydration Energy is Exothermic.

\[ \text{Ionic Potential } (\phi) = \frac{\text{Charge}}{\text{Radius}} \]

Degree of Hydration & Hydration Energy ∝ Ionic Potential

PropertyOrder
Ionic Potential (φ)Li⁺ > Na⁺ > K⁺ > Rb⁺ > Cs⁺
Ionic SizeLi⁺ < Na⁺ < K⁺ < Rb⁺ < Cs⁺
Degree of Hydration / HELi⁺ > Na⁺ > K⁺ > Rb⁺ > Cs⁺
Hydrated Ion SizeLi⁺ > Na⁺ > K⁺ > Rb⁺ > Cs⁺
Ionic Mobility (Conductance for hydrated ion)Li⁺ < Na⁺ < K⁺ < Rb⁺ < Cs⁺

Lattice Energy (U)

Definition

"Energy required to break 1 mole ionic solid into its gaseous constituent ions" OR "Amount of energy released when 1 mole of ionic solid is formed by its constituent gaseous ions."

\[ U \propto \frac{q_1 q_2}{r} \]

If magnitude of charge same: \(U \propto \frac{1}{r}\)

MDJ — Born-Haber Cycle

Released Energy (Exo) > Absorbed Energy (Endo)

Lattice Energy, Electron Affinity > Sublimation, Ionisation Bond Dissociation Energy

Lattice Energy Orders (Important for NEET)

  • NaF > NaCl (smaller anion → less r → more U)
  • NaCl < Na₂O (+1,−2 vs +1,−1 → charge product higher)
  • KCl > RbCl (smaller cation)
  • KCl < K₂O
  • MgO > Na₂O (+2,−2 vs +1,−2)
  • MgO < Al₂O₃ (+2 vs +3)
  • Li₃N > Na₃N → Not exist (Li₃N very stable, high LE; Na₃N does not exist)
  • Alkali Metal: Only Li can form stable Nitride due to very low LE
  • Alkaline Earth metal: All can form stable Nitride due to High LE
⚖️

FAJAN'S RULE

DEFINITION

"Development of covalent character in ionic compound"

Cation (more Zeff) distorts e⁻ cloud of anion → Merging of e⁻ cloud → Covalent Character ↑

Key Relations

Polarisation of anion's e⁻ cloud ∝ Covalent Character in ionic bond

Polarising power (φ for cation) ∝ Polarisation

Polarisability (for anion) ∝ Polarisation

Conditions for Maximum Covalent Character

ConditionPolarising Power/Polarisability ∝Order
Small CationPolarising Power ∝ 1/r⁺Be²⁺ > Mg²⁺ > Ca²⁺ > Sr²⁺
Large AnionPolarisability ∝ r⁻F⁻ < Cl⁻ < Br⁻ < I⁻
High Charge on Cationq⁺ ∝ Polarising PowerM⁺ < M²⁺ < M³⁺ < M⁴⁺
High Charge on Anionq⁻ ∝ PolarisabilityX⁻ < X²⁻ < X³⁻ < X⁴⁻
Important Points
  • Na⁺, K⁺, Rb⁺, Cs⁺ = Low φ (large size, low charge)
  • d-block cations have more polarising power (φ) than s-block cation due to poor shielding of d e⁻
  • e.g. Cu⁺ has more covalent character than Na⁺ (both +1 charge, similar size but Cu has d¹⁰)
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MOLECULAR ORBITAL THEORY (MOT)

MOT Basics

Atomic orbitals combine to form Molecular Orbitals (MO). Electrons are filled in MOs according to Aufbau principle, Hund's rule & Pauli's exclusion principle.

LCAO: Ψ(BMO) = ψ_A + ψ_B  |  Ψ(ABMO) = ψ_A − ψ_B

BMO & ABMO

BMO (Bonding MO)
  • Lower energy than parent AO
  • Higher electron density b/w nuclei
  • Stabilizes the molecule
ABMO (Anti-Bonding MO)
  • Higher energy than parent AO
  • Node b/w nuclei
  • Destabilizes the molecule
  • Denoted by * (sigma*, pi*)

MOT Energy Order (2nd Period Diatomics)

For B₂, C₂, N₂ (Z ≤ 7)
\[ \sigma1s < \sigma^*1s < \sigma2s < \sigma^*2s < \pi2p_x = \pi2p_y < \sigma2p_z < \pi^*2p_x = \pi^*2p_y < \sigma^*2p_z \]
For O₂, F₂, Ne₂ (Z ≥ 8)
\[ \sigma1s < \sigma^*1s < \sigma2s < \sigma^*2s < \sigma2p_z < \pi2p_x = \pi2p_y < \pi^*2p_x = \pi^*2p_y < \sigma^*2p_z \]

Key Formulas

\[ \text{Bond Order (BO)} = \frac{N_b - N_a}{2} \]

Nb = electrons in BMO | Na = electrons in ABMO

MOT Properties
  • BO > 0 → Molecule exists | BO = 0 → Doesn't exist | BO < 0 → Cannot exist
  • BO ↑ → Bond Strength ↑ → Bond Length ↓ → Bond Energy ↑
  • Unpaired e⁻ in MO → Paramagnetic
  • All paired → Diamagnetic

MOT Data — Important Molecules

SpeciesTotal e⁻Bond OrderMagnetic NatureStable?
H₂21DiamagneticYes
He₂40DiamagneticNo
He₂⁺30.5ParamagneticYes
Li₂61DiamagneticYes
Be₂80DiamagneticNo
B₂101ParamagneticYes
C₂122DiamagneticYes
N₂143DiamagneticYes (most stable)
N₂⁺132.5ParamagneticYes
O₂162ParamagneticYes
O₂⁺152.5ParamagneticYes
O₂⁻171.5ParamagneticYes
O₂²⁻181DiamagneticYes
F₂181DiamagneticYes
Ne₂200DiamagneticNo
NO152.5ParamagneticYes
NO⁺143DiamagneticYes (isoelectronic N₂)
CO143DiamagneticYes
CN⁻143DiamagneticYes
Important MOT Facts
  • O₂ is paramagnetic — cannot be explained by Lewis structure (proof of MOT's superiority)
  • N₂ has highest bond order (3) among homonuclear diatomics → most stable
  • Bond order: O₂⁺ > O₂ > O₂⁻ > O₂²⁻
  • Bond length: O₂⁺ < O₂ < O₂⁻ < O₂²⁻
  • Isoelectronic species (14e⁻): N₂, CO, CN⁻, NO⁺ — all have BO = 3
💧

HYDROGEN BOND & VAN DER WAALS FORCES

Hydrogen Bond

Electrostatic attraction b/w H atom (attached to highly EN atom) and lone pair of another electronegative atom.

Condition: F, O, N must be present (very high EN & small size)

Bond energy: ~2−10 kcal/mol (weaker than covalent but stronger than VdW)

Types of Hydrogen Bond

Intermolecular H-Bond

Between different molecules of same or different compounds.

e.g. HF, H₂O, NH₃, alcohols, carboxylic acids

Effect: Increases BP, MP, viscosity, surface tension

Intramolecular H-Bond

Within same molecule (chelation). Forms a ring.

e.g. o-nitrophenol, o-chlorophenol, salicylaldehyde

Effect: Decreases BP, MP compared to para/meta isomers

Important Effects of H-Bond

  • H₂O has anomalously high BP due to intermolecular H-bonding
  • H-bond strength: H−F > H−O > H−N (EN order)
  • o-nitrophenol has lower BP than p-nitrophenol (intramolecular vs intermolecular H-bond)
  • Ice is lighter than water (H-bond makes open cage structure → lower density)
  • Water has max density at 4°C
  • DNA double helix structure is held by H-bonds (A=T with 2 H-bonds, G≡C with 3 H-bonds)
  • BP order: H₂O > HF > NH₃ (H₂O has two H-bonds per molecule)

Van der Waals Forces

London Dispersion Forces

Temporary dipole-induced dipole interactions. Present in all molecules. Strongest in large polarisable molecules.

Strength ∝ Polarisability ∝ Size of molecule

Dipole-Dipole Forces

Between permanent dipoles of polar molecules.

Stronger than London forces for similar-sized polar molecules.

VdW Force Orders (Halogen family)

F₂ < Cl₂ < Br₂ < I₂ (size ↑ → polarisability ↑ → London forces ↑ → BP ↑)

For hydrides: BP order within group normally increases down group, but NH₃, H₂O, HF are exceptions due to H-bonding.

BP order of hydrides: H₂O > H₂Te > H₂Se > H₂S

BP order of Group 15: NH₃ > BiH₃ > SbH₃ > AsH₃ > PH₃

BP order of Group 17: HF > HI > HBr > HCl

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