🥰Learn Sufficient Notes🥰

1. Introduction to Chemical Bonding

🌟 1. Introduction to Chemical Bonding

🔷 Why do atoms form chemical bonds?

• Atoms form bonds to achieve stability.
• Most atoms are unstable on their own and want to attain the electronic configuration of noble gases (like He, Ne, Ar).
• Noble gases are inert because they have completely filled outer shells.
• Atoms bond to complete their octet (8 electrons in the outer shell) or duplet (for hydrogen and helium).

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🔗 2. Types of Chemical Bonds

There are five main types of chemical bonds:

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🧲 A. Ionic Bond (Electrovalent Bond)

🔹 Definition:

An ionic bond is formed when one atom donates an electron and another atom accepts it, resulting in the formation of oppositely charged ions that attract each other.

🔹 Key Points:

• Formed between a metal (loses electrons) and a non-metal (gains electrons).
• One atom becomes positive ion (cation), the other becomes negative ion (anion).
• Strong electrostatic force holds them together.

🔹 Example:

NaCl (Sodium Chloride)
Na → Na⁺ + e⁻ (sodium loses 1 electron)
Cl + e⁻ → Cl⁻ (chlorine gains 1 electron)
Na⁺ and Cl⁻ attract to form NaCl.

🔹 Properties:

• High melting and boiling points
• Conduct electricity in molten or solution form
• Soluble in water

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🧬 B. Covalent Bond

🔹 Definition:

A covalent bond is formed when two atoms share one or more pairs of electrons.

🔹 Key Points:

• Formed between non-metals.
• No ions are formed.
• The shared electrons help each atom complete its octet.

🔹 Types:

• Single bond (1 pair shared) – e.g., H₂
• Double bond (2 pairs) – e.g., O₂
• Triple bond (3 pairs) – e.g., N₂

🔹 Example:

H₂O (Water)
Each hydrogen shares one electron with oxygen.

🔹 Properties:

• Low melting and boiling points
• Do not conduct electricity
• Exist as gases or liquids (mostly)

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🎯 C. Coordinate Bond (Dative Bond)

🔹 Definition:

A coordinate bond is a type of covalent bond where both electrons in the shared pair come from the same atom.

🔹 Key Points:

• Formed between an atom with a lone pair and an electron-deficient atom or ion.
• Represented as an arrow (→) from donor to acceptor.

🔹 Example:

NH₄⁺ (Ammonium ion)
NH₃ donates a lone pair to H⁺ → NH₄⁺
(NH₃ → H⁺)

🔹 Properties:

• Similar to covalent bonds
• Often found in ions and complex compounds

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⚡ D. Metallic Bond

🔹 Definition:

A metallic bond is the force of attraction between positively charged metal ions and the ‘sea of delocalized electrons’.

🔹 Key Points:

• Found in metals only.
• Electrons are not bound to any one atom, and they move freely.

🔹 Example:

Copper (Cu), Aluminium (Al)

🔹 Properties:

• Good conductors of heat and electricity
• Malleable (can be hammered) and ductile (can be drawn into wires)
• Shiny and strong

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💧 E. Hydrogen Bond

🔹 Definition:

A hydrogen bond is a weak bond formed between a hydrogen atom (attached to a highly electronegative atom) and another electronegative atom nearby.

🔹 Key Points:

• Not a primary bond (like ionic or covalent), but important in biology and chemistry.
• Highly electronegative atoms: F, O, N
• Increases boiling point, solubility, etc.

🔹 Types:

• Intermolecular: Between molecules (e.g., water molecules)
• Intramolecular: Within the same molecule (e.g., o-nitrophenol)

🔹 Example:

H₂O – Water molecules are held together by hydrogen bonds.

🔹 Properties:

• Affects physical properties (boiling point, solubility)
• Responsible for water’s unique properties
• Important in DNA structure (base pairing)

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✅ Summary Table

Bond Type	Electron Transfer/Sharing	Between	Example
Ionic	Transfer (one gives, one takes)	Metal + Non-metal	NaCl
Covalent	Sharing of electrons	Non-metal + Non-metal	H₂O, CO₂
Coordinate	Sharing (both electrons from same atom)	Electron-rich + electron-deficient	NH₄⁺
Metallic	Delocalized electrons (“electron sea”)	Metal atoms	Cu, Fe, Al
Hydrogen Bond	Weak bond via hydrogen and electronegative atoms	Polar molecules	H₂O, NH₃, HF

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2. 🌟 Ionic Bond – Complete Conceptual Explanation

🔹 1. What is an Ionic Bond?

An ionic bond is formed when one atom donates electrons and another atom accepts those electrons.
This usually happens between:

• A metal (which loses electrons easily)
• A non-metal (which gains electrons easily)

⚡ Example:

Na (Sodium) has 1 electron in its outer shell.
Cl (Chlorine) has 7 electrons in its outer shell.

➡ Na donates 1 electron → becomes Na⁺
➡ Cl gains 1 electron → becomes Cl⁻

➡ These oppositely charged ions (Na⁺ and Cl⁻) attract each other and form NaCl – an ionic compound.

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🔹 2. How is an Ionic Bond Formed?

The formation involves 3 steps:

1. Metal loses electrons → becomes a positive ion (cation)
2. Non-metal gains electrons → becomes a negative ion (anion)
3. Electrostatic attraction between cation and anion → ionic bond formed

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🔹 3. Factors Affecting Formation of Ionic Bond

Factor	Meaning	Favorable Condition
Ionization Enthalpy	Energy needed to remove an electron from a gaseous atom (e.g., Na → Na⁺ + e⁻)	Should be low for easy cation formation
Electron Gain Enthalpy	Energy released when a gaseous atom gains an electron (e.g., Cl + e⁻ → Cl⁻)	Should be highly negative
Lattice Energy	Energy released when oppositely charged ions combine to form an ionic solid	Should be high for strong ionic bond

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🔹 4. Lattice Energy

• It is the energy released when one mole of an ionic compound is formed from free ions in the gas phase.
• The higher the lattice energy, the stronger the ionic bond.

📌 Factors increasing lattice energy:

• Higher charge on ions (e.g., Mg²⁺ vs Na⁺)
• Smaller size of ions → stronger attraction

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🔹 5. Born–Haber Cycle (JEE Focus)

It is a thermodynamic cycle that explains the formation of ionic compounds using enthalpy values.

📘 For NaCl: Na _(s) + ½Cl₂ _(g) → NaCl _(s)

Steps involved:

1. Sublimation of Na:
   Na (s) → Na (g) → ∆H₁
2. Ionization of Na:
   Na (g) → Na⁺ (g) + e⁻ → ∆H₂ (ionization energy)
3. Dissociation of Cl₂:
   ½Cl₂ (g) → Cl (g) → ∆H₃
4. Electron gain by Cl:
   Cl (g) + e⁻ → Cl⁻ (g) → ∆H₄ (electron gain enthalpy)
5. Formation of lattice:
   Na⁺ (g) + Cl⁻ (g) → NaCl (s) → ∆H₅ = lattice energy

Total Enthalpy Change (∆H_f​): ∆H_f​ = ∆H₁ ​+ ∆H₂ ​+ ∆H₃ ​+ ∆H₄ ​+ ∆H_5​​

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🔹 6. Fajans’ Rule (Very Important for JEE)

This rule tells when a compound appears ionic but has covalent character due to distortion of electron cloud.

⚠️ Covalent character increases when:

• Cation is small & highly charged (high polarizing power)
• Anion is large & highly charged (easily polarizable)
• Cation has incomplete d-orbitals

📌 Example:

• NaCl is mostly ionic
• AlCl₃ shows covalent character (Al³⁺ is small & highly charged)

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🔹 7. Properties of Ionic Compounds

• Solid, crystalline at room temperature
• High melting & boiling points
• Soluble in water (polar solvents)
• Conduct electricity in molten or aqueous state
• Brittle in nature

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✅ Quick Summary

Concept	Key Point
Ionic bond	Electron transfer between atoms
Ionization Enthalpy	Should be low
Electron Gain Enthalpy	Should be highly negative
Lattice Energy	Should be high
Born-Haber Cycle	Stepwise energy calculation for formation
Fajans’ Rule	Explains covalent nature in ionic compounds

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3. Covalent Bond

🔹 1. What is a Covalent Bond?

A covalent bond is formed when two atoms share electrons to complete their octet (or duplet for hydrogen).

• Usually formed between nonmetals.
• Electrons are shared mutually (unlike ionic bonds where they’re transferred).
• Shared electrons are counted in the outer shell of both atoms.

🧠 Example:

In H₂O:

• Each H atom shares 1 electron with O
• O completes its octet (8 electrons), H completes its duplet (2 electrons)

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🔹 2. Lewis Structures (Electron Dot Structures)

Lewis structures represent valence electrons as dots around chemical symbols.

✍️ Steps to Draw Lewis Structures:

1. Count total valence electrons of all atoms
2. Connect atoms using single bonds (each bond = 2 electrons)
3. Complete octet of outer atoms (except H)
4. Place leftover electrons on central atom
5. Form double/triple bonds if central atom doesn’t have an octet

📘 Example: CO₂

• C = 4 valence e⁻, O = 6 each → total = 4 + 6×2 = 16
• Structure: O=C=O (each O forms a double bond with C)

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🔹 3. Octet Rule

Atoms tend to gain, lose or share electrons to have 8 electrons in their valence shell.

✅ Applies well to:

• Second-period elements: C, N, O, F, etc.

❗ Exceptions (explained later below):

• Incomplete and expanded octets

🥰Learn Sufficient Notes🥰

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🔹 4. Formal Charge

Used to identify the best or most stable Lewis structure.

📘 Formula:

Formal Charge (FC) = Valence e⁻ − (Non-bonding e⁻+ 1/2 × Bonding e⁻)

• Best structure: Least number of formal charges
• Negative charge should be on more electronegative atom

🔎 Example: O₃ (Ozone)

O–O=O and resonance structures
Formal charges help decide most stable form.

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🔹 5. Resonance

When more than one valid Lewis structure is possible for a molecule, the actual molecule is a resonance hybrid of all forms.

• Electrons are delocalized (not fixed in one bond)
• Bond properties are intermediate between single and double

🧠 Example: CO₃²⁻ (Carbonate ion)

• Has 3 resonance structures
• All C–O bonds are equal in length

📌 Key Point:

Resonance structures differ in position of electrons, not atoms.

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🔹 6. Octet Rule Exceptions

🟡 A. Incomplete Octet (Less than 8 electrons)

• Some atoms are stable with fewer than 8 electrons.
• Common in small atoms with less than 4 valence orbitals.

Examples:

Molecule	Central Atom	e⁻ in Outer Shell
BeCl₂	Be	4 (2 bonds × 2 e⁻)
BCl₃	B	6

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🔵 B. Expanded Octet (More than 8 electrons)

• Atoms from period 3 or beyond can accommodate more than 8 electrons due to empty d-orbitals.

Examples:

Molecule	Central Atom	e⁻ in Outer Shell
PCl₅	P	10
SF₆	S	12
IF₇	I	14

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🔴 C. Odd-Electron Molecules

• Total number of valence electrons is odd, so complete octets not possible.

Examples:

• NO (Nitric oxide) → 11 valence electrons
• NO₂ → 17 valence electrons

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✅ Quick Summary Table

Concept	Key Idea
Covalent Bond	Electrons are shared between atoms to complete octet
Lewis Structure	Dot structure showing bonding & lone pairs
Octet Rule	Atoms want 8 electrons in outer shell (duplet for H)
Formal Charge	Helps choose most stable structure
Resonance	Actual molecule is a hybrid of possible Lewis structures
Octet Exceptions	Incomplete (Be, B), Expanded (P, S, I), Odd electrons (NO, NO₂)

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4. Bond Parameters

🔹 1. Bond Length

Definition:
Bond length is the average distance between the nuclei of two bonded atoms in a molecule.

🧠 It tells us how strong or tight the bond is — shorter bond = stronger attraction.

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✅ Key Points:

• Unit: Picometer (pm) or Ångström (Å), where 1 Å = 10⁻¹⁰ m = 100 pm
• Typical Bond Lengths:
  • H–H → 74 pm
  • C–C (single) → 154 pm
  • C=C (double) → 134 pm
  • C≡C (triple) → 120 pm

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🔎 Factors Affecting Bond Length:

Factor	Effect
Bond Order ↑	Bond length ↓ (Triple < Double < Single)
Size of atoms ↑	Bond length ↑ (e.g., F–F < Cl–Cl < Br–Br)
Electronegativity ↑	Bond length ↓ (stronger attraction)

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🔹 2. Bond Angle

Definition:
Bond angle is the angle between two adjacent bonds around a central atom in a molecule.

🧠 It helps determine the shape (geometry) of the molecule.

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✅ Measured in: Degrees (°)

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📘 Examples:

• H₂O → 104.5° (bent shape)
• CO₂ → 180° (linear)
• NH₃ → 107.3° (trigonal pyramidal)
• CH₄ → 109.5° (tetrahedral)

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🔎 Factors Affecting Bond Angle:

Factor	Effect on Bond Angle
Lone pair–bond pair repulsion	Lone pairs repel more → angle ↓
Bond pair–bond pair repulsion	Lesser repulsion → angle ↑
Electronegativity of surrounding atoms	More electronegative → pulls e⁻ → angle ↑

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🔹 3. Bond Enthalpy (Bond Energy)

Definition:
Bond enthalpy is the amount of energy required to break one mole of a specific bond in the gaseous state.

🧠 It represents the bond strength.
Higher bond enthalpy = stronger bond

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✅ Unit: kJ/mol

Example:

• H–H → 436 kJ/mol
• O=O → 498 kJ/mol
• N≡N → 945 kJ/mol (very strong!)

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📌 Average Bond Enthalpy:

For molecules with multiple identical bonds (like H₂O), we take the average of bond energies.

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🔎 Factors Affecting Bond Enthalpy:

Factor	Effect
Bond Order ↑	Bond enthalpy ↑ (Triple > Double > Single)
Bond Length ↑	Bond enthalpy ↓ (longer bonds are weaker)
Electronegativity difference	Can strengthen bond

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🔹 4. Bond Order

Definition:
Bond order is the number of chemical bonds between two atoms.

🧠 It’s a quantitative measure of bond strength and stability.

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✅ General Meaning:

Bond Type	Bond Order
Single bond	1
Double bond	2
Triple bond	3

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📘 Molecular Orbital Theory (MOT) Formula: (complete explanation below here😘)

Bond Order = 1/2 (No. of bonding electrons − No. of antibonding electrons)

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🧠 Example:

In O₂:

• Bonding e⁻ = 10, Antibonding e⁻ = 6

Bond Order = ½ ​(10−6) = 2

→ O₂ has a double bond.

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🔎 Effect of Bond Order:

Bond Order ↑	Bond Length ↓	Bond Enthalpy ↑	Stability ↑

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🔹 5. Dipole Moment

Definition:
Dipole moment is the measure of polarity of a molecule. It is produced when there is separation of positive and negative charges in a molecule.

🧠 It depends on:

• Electronegativity difference
• Bond length
• Geometry of the molecule

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✅ Formula:

μ = q × d

Where:

• μ = dipole moment
• q = magnitude of charge
• d = distance between charges

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✅ Unit: Debye (D)

(1 D = 3.33564 × 10⁻³⁰ C·m)

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📘 Examples:

Molecule	Dipole Moment	Nature
HCl	1.08 D	Polar
H₂O	1.84 D	Polar (bent shape)
CO₂	0	Non-polar (linear)
CH₄	0	Non-polar
NH₃	1.46 D	Polar

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🔎 Key Concept:

Even if bonds are polar, the molecule can be non-polar if the dipoles cancel each other (due to symmetrical shape).

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✅ Summary Table: Bond Parameters

Parameter	Definition	Unit	Key Influence
Bond Length	Distance between nuclei of bonded atoms	pm or Å	Bond order, atomic size
Bond Angle	Angle between two adjacent bonds	Degrees (°)	Lone pairs, electronegativity, hybridization
Bond Enthalpy	Energy to break one mole of bonds in gas phase	kJ/mol	Bond order, length, stability
Bond Order	Number of shared electron pairs between atoms	Unitless	Bond strength, length, stability
Dipole Moment	Measure of charge separation in a molecule	Debye (D)	Electronegativity difference, geometry

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5. VSEPR Theory and Shapes of Molecules

1. Introduction to VSEPR Theory

VSEPR stands for Valence Shell Electron Pair Repulsion theory. It is a simple and powerful model used to predict the shape of molecules based on the repulsions between electron pairs around a central atom.

• Basic idea: Electron pairs (bonding and lone pairs) around the central atom repel each other.
• These electron pairs arrange themselves as far apart as possible to minimize repulsion.
• The spatial arrangement determines the molecular shape and bond angles.

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2. Types of Electron Pairs

• Bonding pairs (BP): Electron pairs shared between atoms forming bonds.
• Lone pairs (LP): Non-bonding electron pairs localized on the central atom.

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3. Electron Pair Geometry vs Molecular Geometry

• Electron Pair Geometry (EPG): Shape formed by all electron pairs (bonding + lone pairs) around the central atom.
• Molecular Geometry (MG): Shape formed by only the atoms (ignores lone pairs).

Example:

• Water (H₂O):
  • Electron pair geometry: Tetrahedral (4 electron pairs)
  • Molecular geometry: Bent (because 2 lone pairs)

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4. Steps to Predict Molecular Shape Using VSEPR

1. Determine the Lewis structure of the molecule.
2. Count the total valence electrons on the central atom.
3. Count bonding pairs and lone pairs around the central atom.
4. Use the VSEPR formula AXₙEₘ, where:
   • A = central atom
   • X = number of bonded atoms
   • E = number of lone pairs on central atom
5. Find the electron pair geometry from AXₙEₘ notation.
6. Determine the molecular geometry by considering only atom positions (ignore lone pairs for shape).

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5. Common Electron Pair Geometries and Molecular Shapes

AXₙEₘ Notation	Electron Pair Geometry	Molecular Geometry	Bond Angle (approx.)	Example
AX₂	Linear	Linear	180°	CO₂
AX₃	Trigonal Planar	Trigonal Planar	120°	BF₃
AX₂E	Trigonal Planar	Bent	~117°	SO₂
AX₄	Tetrahedral	Tetrahedral	109.5°	CH₄
AX₃E	Tetrahedral	Trigonal Pyramidal	~107°	NH₃
AX₂E₂	Tetrahedral	Bent	~104.5°	H₂O
AX₅	Trigonal Bipyramidal	Trigonal Bipyramidal	90°, 120°	PCl₅
AX₄E	Trigonal Bipyramidal	See-Saw	<120°, <90°	SF₄
AX₃E₂	Trigonal Bipyramidal	T-shaped	~90°	ClF₃
AX₂E₃	Trigonal Bipyramidal	Linear	180°	XeF₂
AX₆	Octahedral	Octahedral	90°	SF₆
AX₅E	Octahedral	Square Pyramidal	~90°	BrF₅
AX₄E₂	Octahedral	Square Planar	90°	XeF₄

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6. Influence of Lone Pairs on Bond Angles

• Lone pairs repel more strongly than bonding pairs because lone pairs are localized closer to the central atom.
• This repulsion compresses bond angles between bonding pairs.
• Trend in repulsion strength: LP–LP > LP–BP > BP–BP

Example:

• NH₃ (1 lone pair): bond angle ~107° < 109.5°
• H₂O (2 lone pairs): bond angle ~104.5° < 107°

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7. Advanced Concepts — Multiple Bonds and VSEPR

• Multiple bonds (double, triple) are treated as a single electron group in VSEPR.
• However, multiple bonds have higher electron density, so they can slightly influence bond angles.
• Example:
  • SO₂ has a double bond and a single bond, influencing its bent shape and bond angles.

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8. Resonance and VSEPR

• Resonance structures do not affect electron pair count but can influence bond order and bond length.
• VSEPR predicts shape based on total electron pairs, not on resonance forms.

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9. Application to Ions and Polyatomic Molecules

• Count total valence electrons including charge.
• For negative ions, add electrons; for positive ions, subtract electrons.
• Predict geometry same way using AXₙEₘ notation.

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10. Summary Table of Common Shapes

Shape	Bond Angle (°)	Example
Linear	180	CO₂, BeCl₂
Trigonal Planar	120	BF₃
Bent (V-Shaped)	104.5 – 120	H₂O, SO₂
Tetrahedral	109.5	CH₄
Trigonal Pyramidal	~107	NH₃
Trigonal Bipyramidal	90, 120	PCl₅
Octahedral	90	SF₆

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Important Tips for JEE & NEET

• Practice drawing Lewis structures before predicting shapes.
• Memorize common shapes and corresponding bond angles.
• Understand how lone pairs affect molecular geometry.
• Practice with polyatomic ions and molecules with expanded octets (PCl₅, SF₆).
• Use VSEPR theory to predict shapes for both neutral molecules and ions.

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6. Valence Bond Theory (VBT)

🔹 1. Valence Bond Theory (VBT)

➤ Basic Concept:

Valence Bond Theory explains how atoms combine to form a molecule by overlapping atomic orbitals.

➤ Key Points:

• A covalent bond is formed when two atomic orbitals overlap and the electrons are paired with opposite spins.
• The greater the overlap, the stronger the bond.
• Bond formation is exothermic (energy is released).

➤ Types of Orbital Overlaps:

Type	Orbitals Involved	Bond Formed
s-s overlap	2 s-orbitals	Sigma (σ) bond
s-p overlap	s and p orbital	Sigma (σ) bond
p-p overlap	2 p-orbitals	Sigma (σ) or Pi (π) bond

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🔹 2. Hybridization

➤ Definition:

Hybridization is the mixing of atomic orbitals of similar energy to form new hybrid orbitals that are identical in shape and energy, used in bonding.

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➤ Types of Hybridization (with Examples):

✅ sp Hybridization (Linear)

• Orbitals mixed: 1 s + 1 p → 2 sp orbitals
• Geometry: Linear
• Bond angle: 180°
• Example: BeCl₂, C₂H₂ (ethyne)

✅ sp² Hybridization (Trigonal Planar)

• Orbitals mixed: 1 s + 2 p → 3 sp² orbitals
• Geometry: Trigonal Planar
• Bond angle: 120°
• Example: BF₃, C₂H₄ (ethene)

✅ sp³ Hybridization (Tetrahedral)

• Orbitals mixed: 1 s + 3 p → 4 sp³ orbitals
• Geometry: Tetrahedral
• Bond angle: 109.5°
• Example: CH₄ (methane), NH₃, H₂O

✅ sp³d Hybridization (Trigonal Bipyramidal)

• Orbitals mixed: 1 s + 3 p + 1 d → 5 sp³d orbitals
• Geometry: Trigonal Bipyramidal
• Bond angles: 90° and 120°
• Example: PCl₅, SF₄

✅ sp³d² Hybridization (Octahedral)

• Orbitals mixed: 1 s + 3 p + 2 d → 6 sp³d² orbitals
• Geometry: Octahedral
• Bond angle: 90°
• Example: SF₆, [Fe(CN)₆]³⁻

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🔹 3. Sigma (σ) and Pi (π) Bonds

➤ Sigma (σ) Bond:

• Formed by head-on overlap (along the internuclear axis)
• Stronger than π bonds
• Can be formed from s-s, s-p, or p-p orbitals
• All single bonds are sigma bonds

➤ Pi (π) Bond:

• Formed by sidewise overlap of unhybridized p-orbitals
• Weaker than σ bonds
• Found in double and triple bonds
  • Double bond = 1 σ + 1 π
  • Triple bond = 1 σ + 2 π

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🔹 4. Comparison Table: Sigma vs Pi Bonds

Property	Sigma (σ) Bond	Pi (π) Bond
Overlap type	End-to-end	Sideways
Orbital overlap	s-s, s-p, or p-p	p-p only
Strength	Strong	Weaker
Electron density	Along internuclear axis	Above and below internuclear axis
Rotation possible?	Yes	No (restricted due to π cloud)
First or second/third bond?	Always the first	Always second or third

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🔹 5. Applications in JEE/NEET Questions

• Predicting molecular geometry using hybridization
• Comparing bond angles and shapes (e.g., NH₃ < CH₄ < H₂O)
• Determining bond order and bond strength
• Identifying types of bonds (σ or π) in a molecule
• Using VBT to explain paramagnetism or diamagnetism (though Molecular Orbital Theory is more accurate for this)

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🔹 6. Tips to Remember

• Number of hybrid orbitals = Number of bonded atoms + lone pairs on central atom.
• Bond strength ∝ extent of orbital overlap.
• Hybrid orbitals are always used to form sigma bonds.
• Unhybridized p-orbitals are used for forming pi bonds.

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7. Molecular Orbital Theory (MOT)

🔷 1. Molecular Orbital Theory (MOT)

➤ What is MOT?

MOT explains the formation of molecules using quantum mechanics, where atomic orbitals combine to form molecular orbitals (MOs) that are delocalized over the entire molecule.

➤ Key Assumptions:

• Electrons are not localized between two atoms (unlike in VBT), but are present in molecular orbitals.
• These orbitals are formed by linear combination of atomic orbitals (LCAO).
• MOs can be bonding, antibonding, or non-bonding.

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🔷 2. LCAO (Linear Combination of Atomic Orbitals)

➤ Principle:

Two atomic orbitals (AOs) of similar energy and symmetry combine to form:

• One bonding molecular orbital (MO) (constructive interference)
• One antibonding molecular orbital (MO*) (destructive interference)

➤ Types of MOs:

Type	Symbol	Nature	Energy	Electron Density
Bonding	σ, π	Stabilizing	Lower	Between nuclei
Antibonding	σ*, π*	Destabilizing	Higher	Away from nuclei

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🔷 3. Molecular Orbital Energy Level Diagrams

There are two types of MO diagrams depending on the atomic number (Z):

✅ (A) For Z ≤ 7 (e.g., B₂, C₂, N₂):

Energy order:
σ1s < σ1s < σ2s < σ2s < π2p < σ2p < π2p < σ2p

✅ (B) For Z ≥ 8 (e.g., O₂, F₂, Ne₂):

Energy order:
σ1s < σ1s < σ2s < σ2s < σ2p < π2p < π2p < σ2p

✅ Note: The switch in π2p and σ2p order is due to s-p mixing (orbital mixing), which occurs only for lighter elements.

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🔷 4. MO Diagrams (up to O₂)

✅ O₂ (Z = 8):

Configuration (Total electrons = 16):
1s² 1s² 2s² 2s² 2p(σ)² 2p(π)⁴ 2p(π*)²

8 bonding electrons and 4 antibonding electrons in 2p orbitals

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🔷 5. Bond Order (BO)

➤ Formula:

Bond Order=12(Nb−Na)\text{Bond Order} = \frac{1}{2} \left( N_b – N_a \right)Bond Order=21​(Nb​−Na​)

Where:

• NbN_bNb​ = Number of electrons in bonding MOs
• NaN_aNa​ = Number of electrons in antibonding MOs

➤ Implications:

• Higher bond order → stronger and shorter bond
• BO = 0 → molecule doesn’t exist (unstable)

Molecule	Total e⁻	MO Configuration (valence)	Bond Order	Magnetic
H₂	2	σ1s²	1	Diamagnetic
He₂	4	σ1s² σ*1s²	0	Diamagnetic (doesn’t exist)
B₂	10	π2p²	1	Paramagnetic
C₂	12	π2p⁴	2	Diamagnetic
N₂	14	π2p⁴ σ2p²	3	Diamagnetic
O₂	16	π2p⁴ π*2p²	2	Paramagnetic
F₂	18	π2p⁴ π*2p⁴	1	Diamagnetic
Ne₂	20	π2p⁴ π2p⁴ σ2p²	0	Diamagnetic (unstable)

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🔷 6. Paramagnetism and Diamagnetism

➤ Based on unpaired electrons in MO diagram:

Property	Explanation	Example
Paramagnetic	One or more unpaired electrons	O₂, B₂
Diamagnetic	All electrons are paired	H₂, N₂, F₂

✅ O₂ is paramagnetic, a fact that Valence Bond Theory fails to explain, but MOT explains clearly.

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🔷 7. Visual Summary of MO Filling for Homonuclear Diatomic Molecules

Molecule	Atomic Number (Z)	MO Order Used	Magnetic Nature	Bond Order
B₂	5	π2p < σ2p	Paramagnetic	1
C₂	6	π2p < σ2p	Diamagnetic	2
N₂	7	π2p < σ2p	Diamagnetic	3
O₂	8	σ2p < π2p	Paramagnetic	2
F₂	9	σ2p < π2p	Diamagnetic	1

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🔷 8. MOT vs VBT (for JEE/NEET)

Feature	VBT	MOT
Localized or Delocalized?	Localized bonds	Delocalized orbitals
Explains O₂ Paramagnetism?	❌ No	✅ Yes
Bond Strength Prediction	Approximate	Accurate
Magnetic Behavior	❌ Limited	✅ Precise
Useful for	Basic bonding	Advanced bonding and stability

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🔷 9. Tips for JEE/NEET MCQs

• Use MO diagram to quickly find bond order.
• Count unpaired electrons for magnetism.
• Remember switch in MO energy order after O₂.
• Practice MO diagrams for B₂ to O₂ (most frequently asked).

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8. Coordinate Bond (Dative Bond)

✅ Definition:

A coordinate bond (also called a dative covalent bond) is a type of covalent bond in which both electrons in the shared pair come from the same atom.

✅ In normal covalent bonds, each atom contributes one electron to the bond.
✅ In a coordinate bond, one atom donates both electrons to the other.

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✅ Key Characteristics:

Feature	Description
Electron donor	Atom with a lone pair (acts as Lewis base)
Electron acceptor	Atom with vacant orbital (acts as Lewis acid)
Bond type	Covalent, but both electrons from one atom
Represented by	An arrow (→) from donor to acceptor
Strength	Similar to covalent bonds
Directional?	Yes, like covalent bonds

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🔷 How Coordinate Bond Forms

1. One atom has a lone pair (e⁻ donor).
2. Another atom has a vacant orbital (e⁻ acceptor).
3. The donor donates both electrons into the vacant orbital of the acceptor.

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🔷 Important Examples

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✅ 1. Ammonium ion (NH₄⁺)

Reaction:
NH₃ + H⁺ → NH₄⁺

• NH₃ (ammonia) has a lone pair on nitrogen.
• H⁺ has no electrons (just a proton).
• Nitrogen donates both electrons to H⁺, forming a coordinate bond.

Diagram:
N → H⁺ (forms NH₄⁺)

Result:

• All four N–H bonds in NH₄⁺ are equivalent.
• The coordinate bond becomes indistinguishable from covalent bonds after formation.

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✅ 2. Hydronium ion (H₃O⁺)

Reaction:
H₂O + H⁺ → H₃O⁺

• H₂O has two lone pairs on oxygen.
• H⁺ has no electrons and accepts a lone pair.
• A coordinate bond forms from O → H⁺.

Structure:
O → H⁺ (forms H₃O⁺)

Result:

• H₃O⁺ has 3 O–H bonds that are equivalent in nature.

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✅ 3. Aluminium chloride dimer (Al₂Cl₆)

• AlCl₃ is electron-deficient (only 6 valence electrons on Al).
• It dimerizes to form Al₂Cl₆ by forming coordinate bonds.

How?

• Two AlCl₃ molecules share 2 Cl atoms via their lone pairs: Cl → Al ← Cl (bridge chlorines donate lone pairs)

Result:

• 2 coordinate bonds per dimer.
• Each Al now completes its octet.
• Al₂Cl₆ exists as a dimer in solid and liquid phase.

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🔷 Comparison: Covalent vs Coordinate Bonds

Property	Covalent Bond	Coordinate Bond
Electron source	Each atom contributes 1 e⁻	One atom donates both e⁻
Symbol	A single line (–)	An arrow (→)
Directional	Yes	Yes
After formation	Indistinguishable from covalent	Same

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🔷 FAQs / Conceptual Clarifications

🔹 Is coordinate bond weaker than covalent bond?

Not necessarily. Once formed, it behaves similarly to a covalent bond.

🔹 Does it follow the octet rule ?

Yes. The acceptor atom completes its octet using the lone pair from the donor.

🔹 Is coordinate bond polar ?

Yes, usually polar, because the electron pair is donated from one atom.

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🔷 Tips for JEE/NEET

✅ Coordinate bond is always formed between a Lewis base (lone pair donor) and Lewis acid (vacant orbital).

✅ Remember examples:

• NH₃ + H⁺ → NH₄⁺
• H₂O + H⁺ → H₃O⁺
• AlCl₃ dimer → Al₂Cl₆
• CO (C → O) has partial coordinate bond character
• Metal complexes (e.g., [Cu(NH₃)₄]²⁺) involve coordinate bonds

✅ Questions often ask:

• Identify coordinate bond
• Explain bonding in polyatomic ions
• Predict shapes using coordinate bonding

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9. Hydrogen Bonding

✅ 1. Definition of Hydrogen Bonding

A hydrogen bond is a type of weak electrostatic attraction between:

• A hydrogen atom covalently bonded to a highly electronegative atom (like N, O, or F), and
• Another electronegative atom having a lone pair of electrons.

It’s stronger than van der Waals forces, but weaker than covalent bonds.

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✅ 2. Conditions for Hydrogen Bonding

➤ Hydrogen bonding occurs when:

1. H is bonded to N, O, or F (very electronegative).
2. The electronegative atom must have a lone pair.
3. High electronegativity and small atomic size make hydrogen bonding stronger.

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✅ 3. Types of Hydrogen Bonding

🔹 A. Intermolecular Hydrogen Bonding

• Between two molecules.
• Occurs in associated molecules like H₂O, HF, alcohols.

Examples:

• Water (H₂O)
• Hydrogen fluoride (HF)
• Alcohols (R–OH)
• Carboxylic acids (R–COOH)

Effect:
Leads to association of molecules, forming dimers, polymers, etc.

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🔹 B. Intramolecular Hydrogen Bonding

• Within the same molecule.
• Happens when –OH or –NH₂ is close to a suitable atom in the same molecule.

Examples:

• o-nitrophenol (intra), p-nitrophenol (inter)
• Salicylaldehyde
• Anthranilic acid

Effect:
Leads to chelation or ring-like structures, and may decrease solubility in water.

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✅ 4. Representation of Hydrogen Bonding

• Intermolecular:
  H–O···H–O (between different molecules)
• Intramolecular:
  O–H···O=N (within same molecule)

The dotted lines (···) show hydrogen bonds.

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✅ 5. Order of Strength of Hydrogen Bonds

F–H···X > O–H···X > N–H···X

Because:
F > O > N in electronegativity
→ Stronger H-bond

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✅ 6. Effects of Hydrogen Bonding on Physical Properties

Property	Effect of Hydrogen Bonding
Boiling point	↑ Increases significantly (H₂O > H₂S)
Melting point	↑ Increases due to bonding
Solubility	↑ In polar solvents like water
Density	Water has max density at 4°C due to H-bonds
Volatility	↓ Decreases (less evaporation)
Viscosity	↑ Increases (e.g., glycerol)
Anomalies	H₂O is liquid but H₂S is gas due to H-bonds

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✅ 7. Important Examples with Explanation

🔹 Water (H₂O)

• Strong intermolecular hydrogen bonding
• High b.p. (100°C) despite low molecular mass
• Ice is less dense than water due to open H-bonded structure

🔹 Hydrogen Fluoride (HF)

• H-bonding forms infinite zig-zag chains
• Explains its high boiling point

🔹 Alcohols (R–OH)

• H-bonding causes higher boiling points and solubility in water

🔹 Carboxylic Acids (R–COOH)

• Form dimers through H-bonding in nonpolar solvents (benzene)

🔹 o-Nitrophenol vs p-Nitrophenol

• o-Nitrophenol: Intramolecular H-bond → lower solubility, lower b.p.
• p-Nitrophenol: Intermolecular H-bond → higher solubility and b.p.

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✅ 8. Order of Boiling Points Due to H-Bonding (Important for NEET/JEE)

H₂​O > HF > NH₃ ​> H₂​S > PH_3​​

→ Molecules with H-bonding have much higher boiling points than expected from size/trend alone.

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✅ 9. MCQ Cracker Points (Memory Boost)

Concept	Example / Tip
H-bond between molecules	Intermolecular (water, alcohol)
H-bond within a molecule	Intramolecular (o-nitrophenol)
Water is liquid, H₂S is gas	Due to H-bonding
Boiling point anomaly	H₂O > H₂S (despite smaller size)
Intramolecular reduces solubility	o-nitrophenol less soluble
Dimers in acid	Carboxylic acid in benzene

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🔚 Final Tip:

Always look for –OH, –NH₂ groups and nearby electronegative atoms (O, N, F) to predict H-bonding.

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10.Metallic Bonding

✅ 1. What is Metallic Bonding?

Metallic bonding is the type of chemical bonding that occurs between metal atoms due to the delocalization of electrons.

It is responsible for the typical properties of metals like conductivity, luster, malleability, and ductility.

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✅ 2. Electron Sea Model (Free Electron Theory)

The Electron Sea Model is the most widely accepted model for explaining metallic bonding.

📌 Key Points:

• Metals consist of positively charged metal ions (kernels) arranged in a regular pattern (metallic lattice).
• The valence electrons are delocalized—they move freely throughout the lattice, forming a “sea of electrons.”
• These free electrons hold the metal cations together through electrostatic attraction.

Metallic bond = Electrostatic attraction between the metal cations and the delocalized electron sea.

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✅ 3. Visual Representation

Metal structure:
[+ ]    [+ ]    [+ ]
   \   |   /    /  
   ~~~~ e⁻ ~~~~
   /    |   \  \

- [+] = metal cation
- e⁻ = free-moving electrons

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✅ 4. Factors Affecting Strength of Metallic Bond

Factor	Effect
Number of valence electrons	More delocalized electrons → stronger metallic bond
Charge on cation	Higher charge → stronger attraction
Size of cation	Smaller size → stronger metallic bond (less shielding)
Electron density	Higher density → stronger bonding

Example: Na < Mg < Al (bond strength increases across group)

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🔷 5. Physical Properties Explained by Metallic Bonding

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🔹 A. Electrical Conductivity

• Cause: Free electrons move when voltage is applied.
• Metals like Cu, Ag, Al are excellent conductors.
• Conductivity decreases with temperature (due to lattice vibrations).

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🔹 B. Thermal Conductivity

• Energy transfer by vibrating metal ions and free electrons.
• Efficient in metals because electrons can carry energy rapidly.

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🔹 C. Malleability and Ductility

• Malleability: Ability to be beaten into sheets (e.g., gold foil).
• Ductility: Ability to be drawn into wires (e.g., copper wire).

Why?
Layers of metal ions can slide over each other without breaking the metallic bond because the electron sea flows and adjusts around new positions.

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🔹 D. Luster (Shininess)

• Metals reflect light due to the interaction of light with free electrons.

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🔹 E. High Melting and Boiling Points

• Strong electrostatic attraction between positive metal ions and free electrons requires high energy to break.
• Exceptions: Mercury (Hg) is liquid at room temp due to weak bonding (low coordination and relativistic effects).

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🔹 F. Alloy Formation

• Metallic bonding allows mixing of different metal atoms (like Cu + Zn = Brass).
• Electrons delocalize uniformly across the mixture.

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🔷 6. Comparison with Other Bonds

Property	Ionic Bond	Covalent Bond	Metallic Bond
Particle interaction	Cation–anion	Shared electrons	Cations–electron sea
Directional?	No	Yes	No
Conductivity	Only molten/aq	Mostly insulators	High
Malleability	Brittle	Brittle	High

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🔷 7. Exam Focus (JEE/NEET)

🔥 Frequently Asked Concepts:

Concept	Explanation
Why metals conduct electricity?	Due to mobile delocalized electrons
Why metals are malleable?	Ions can slide without breaking metallic bond
Order of metallic bond strength	Al > Mg > Na (due to more valence e⁻ and smaller size)
Why Hg is liquid at room temp?	Very weak metallic bonding
Difference between metals and alloys	Alloys are mixtures; metallic bonding still applies

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🔷 Quick Revision Table: Metallic Bonding Summary

Property	Explained by
Electrical conductivity	Free electrons
Thermal conductivity	Electron + lattice vibration
Malleability	Electron sea flexibility
High melting point	Strong electrostatic attraction
Luster	Electron excitation & reflection
Ductility	Easy ion layer shift

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🔚 Final Memory Key:

“Metal = Positive ions + Sea of mobile electrons
= strong, shiny, ductile, and conductive!”

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11. Comparison of Bond Types: Ionic vs Covalent vs Coordinate vs Metallic

✅ 1. Definition Table

Bond Type	Definition
Ionic Bond	Electrostatic force of attraction between oppositely charged ions (cation and anion).
Covalent Bond	Mutual sharing of electrons between atoms (usually non-metals) to complete the octet.
Coordinate (Dative) Bond	Type of covalent bond where both electrons are contributed by one atom only.
Metallic Bond	Electrostatic attraction between metal cations and a sea of delocalized electrons.

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✅ 2. Detailed Comparison Table

Property	Ionic Bond	Covalent Bond	Coordinate Bond	Metallic Bond
Formation	Transfer of electrons from metal to non-metal	Mutual sharing of electrons	Shared pair donated by one atom	Electrostatic attraction between metal ions and free electrons
Participants	Metal + Non-metal	Non-metal + Non-metal	Lone pair donor (Lewis base) + acceptor (Lewis acid)	Metal atoms
Bond Nature	Electrostatic	Localized, directional	Localized, directional	Non-directional
Electron Sharing	Complete transfer	Equal/unequal sharing	One-sided sharing	Delocalized electrons
Polarity	High (due to charge separation)	Polar or non-polar	Polar	Non-polar
Bond Strength	Strong (solid lattice)	Moderate to strong	Similar to covalent	Varies (strong in transition metals)
Conductivity	In molten/aqueous state only	Usually poor	Poor	Excellent (free electrons)
Melting/Boiling Point	High	Low to moderate	Moderate	High (except mercury)
Solubility	Soluble in polar solvents (like water)	Soluble in non-polar solvents	Similar to covalent	Insoluble in most solvents
Physical State	Solid (crystalline)	Solid, liquid, gas	Solid/liquid (depends)	Solid (except Hg)
Examples	NaCl, CaF₂	H₂O, CH₄, Cl₂	NH₄⁺, H₃O⁺, AlCl₃	Cu, Fe, Al, Ag

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✅ 3. Visual Summary (Memory Trick)

Bond	Key Idea
Ionic	Electron Transfer & Strong Lattice
Covalent	Sharing between atoms
Coordinate	Donation of electron pair
Metallic	Sea of Mobile Electrons in metal lattice

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✅ 4. Examples-Based Comparison

Compound	Bond Type	Explanation
NaCl	Ionic	Na⁺ donates, Cl⁻ accepts electrons
H₂O	Covalent	O shares electrons with H
NH₄⁺	Coordinate	N donates lone pair to H⁺
Al₂Cl₆	Coordinate + Ionic	Al–Cl coordinate bonds + ionic component
Cu, Ag	Metallic	Delocalized electrons in lattice

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✅ 5. Exam-Oriented Tips (JEE/NEET)

Concept	Trick
Bond type & electronegativity	High ΔEN → Ionic; low ΔEN → Covalent
NH₄⁺, H₃O⁺, AlCl₃	Coordinate bonds involved
Metallic luster/conductivity	Due to delocalized electron sea
Ionic compounds break in water?	Yes (ion-dipole interaction)
Covalent = bad conductors?	Yes, except graphite (delocalized π-electrons)

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✅ 6. Important Questions to Practice

1. Compare conductivity of ionic and metallic compounds.
2. Identify the type of bond in AlCl₃ and NH₄⁺.
3. Why is NaCl solid at room temperature?
4. Why is graphite conductive but diamond is not?
5. Which bond type is strongest and why?

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🔚 Final Takeaway Summary Table

Bond Type	Electrons	Example	Special Property
Ionic	Transferred	NaCl	High melting point, soluble in water
Covalent	Shared	CH₄	Low m.p./b.p., poor conductors
Coordinate	Donated	NH₄⁺	Directional, lone pair required
Metallic	Delocalized	Cu	High conductivity, malleable

🔷 Difference Between Sigma (σ) and Pi (π) Bonds

Feature	Sigma (σ) Bond	Pi (π) Bond
1. Definition	Bond formed by head-on (end-to-end) overlap of orbitals	Bond formed by sidewise (lateral) overlap of p-orbitals
2. Orbital Overlap	s–s, s–p, or p–p (along internuclear axis)	Only p–p (parallel) orbitals involved
3. Symmetry	Cylindrically symmetrical around bond axis	Not symmetrical — contains two lobes above and below the bond axis
4. Strength	Stronger due to better overlap	Weaker due to lesser extent of overlap
5. Formation Order	First bond formed between atoms is always σ	π bond is formed after σ bond, only in double/triple bonds
6. Free Rotation	Allows free rotation of atoms around bond axis	Restricts rotation due to electron cloud above/below plane
7. Electron Density	Concentrated between nuclei	Concentrated above and below the plane of nuclei
8. Involvement in Bond Types	Found in single, double, and triple bonds (always one)	Found in double (1) and triple (2) bonds
9. Examples	H–H, C–H, Cl–Cl	C=C (1 σ + 1 π), C≡C (1 σ + 2 π)
10. Detection (Advanced)	Can be detected via rotation & IR spectroscopy	Affects UV-visible & IR spectra; causes restricted rotation in alkenes
11. Representation	σ	π

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🔶 Diagrams:

🔹 Sigma Bond (σ): Head-on Overlap

   ↑↓       ↑↓
   1s + 1s → σ
   Overlap along internuclear axis

🔹 Pi Bond (π): Sidewise Overlap

p-orbital          p-orbital
      ↑↓                 ↑↓
      |                  |
     lobe               lobe
       ↔← π bond (above & below the bond axis)

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✅ Quick Visual Memory Aid:

Type	Orientation	Strength	Rotation
σ (Sigma)	Along bond axis	Strong	Free
π (Pi)	Above/Below axis	Weak	Restricted

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✅ In Double and Triple Bonds:

Bond Type	No. of σ Bonds	No. of π Bonds	Example
Single (–)	1	0	H–Cl, CH₄
Double (=)	1	1	C=C in ethene
Triple (≡)	1	2	C≡C in ethyne

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🔶 Advanced Notes for JEE/NEET:

• π bonds are more reactive due to higher electron density away from the nucleus.
• The restricted rotation of π bonds explains the cis-trans (geometrical) isomerism in alkenes.
• Hybrid orbitals (like sp³, sp², sp) always form σ bonds; unhybridized p orbitals form π bonds.

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🔚 Final Summary:

“Sigma bonds form the backbone of molecules; pi bonds add structure and reactivity.”

• ✅ Every bond starts with σ, pi bonds come later in multiple bonds.
• ✅ Strength: σ > π
• ✅ Reactivity: π > σ
• ✅ Mobility: σ = Free rotation; π = Restricted

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