Revision: Std. XI >> Chemical Bonding MAH-MHT CET (PCM/PCB) Chemical Bonding

A chemical bond may be defined as the force of attraction between any two atoms in a molecule to maintain stability.

or

A chemical bond may be defined as the force of attraction between any two atoms, in a molecule, to maintain stability.

Reduction is defined as the phenomenon in which an atom gains an electron to form a negatively charged ion called an anion.
During the formation of ionic bond one atom undergoes oxidation while another atom undergoes reduction.

Oxidation is the loss of electrons during a reaction by a molecule, atom or ion. In terms of electron transfer, oxidation is defined as the phenomenon in which an atom loses an electron to form a positively charged cation.
During the formation of ionic bond one atom undergoes oxidation while another atom undergoes reduction.

A metallic atom, which loses electron(s), becomes a positively charged ion and is known as a cation.

The chemical compounds formed as a result of the transfer of electrons from one atom of an element to one atom of another element are called ionic (or electrovalent) compounds.

An ion is a charged particle which is formed due to the gain or the loss of one or more electrons by an atom.

A non-metallic atom, which gains electron(s), becomes a negatively charged ion and is known as an anion.

A metallic element, whose one atom readily loses electron(s) to form a positively charged ion, is an electropositive element.

A non-metallic element, whose atom readily accepts electron(s) to form a negatively charged ion, is an electronegative element.

The cation and the anion being oppositely charged attract each other and form a chemical bond. Since this chemical bond formation is due to the electrostatic force of attraction between a cation and an anion, it is called an electrovalent (or an ionic) bond.

The number of electrons that an atom of an element loses or gains to form a electrovalent bond is called its electrovalency.

The molecule formed due to the sharing of electrons (covalent bond) is called a covalent molecule.

The chemical bond formed between two combining atoms by mutual sharing of one or more pairs of electrons is called a covalent bond.

The chemical bond that is formed between two combining atoms by mutual sharing of one or more pairs of electrons is called a covalent (or a molecular) bond, and the compound formed due to this bond is called a covalent compound.

The bond formed between two atoms by sharing a pair of electrons, provided entirely by one of the combining atoms but shared by both, is called a coordinate bond. 

Number of covalent bond between the two atoms is known as bond order. Integral bond order values of 1, 2 and 3 correspond to single, double and triple bonds, respectively. Isoelectronic molecules and ions have identical bond order.

Bond order ∝ Bond enthalpy ∝`\"1"/"Bond length"\`

Bond length is defined as the equilibrium distance between the nuclei of two covalently bonded atoms in a molecule.

It is the angle between bonded orbitals containing bonding electron pairs around the central atom in a molecule or complex ion.

Bond enthalpy is defined as the amount of energy required to break one mole of a bond of one type, present between two atoms in a gaseous state.

The equilibrium distance between two nuclei bonded to each other is known as bond length. It is expressed in Å or pm or nm.

1 pm = 10^-12 m, 1 Å = 10^-10 m, 1 nm = 10^-9 m

The minimum amount of energy required to break a bond into one mole of gaseous molecule is known as bond enthalpy.

Bond enthalpy ∝ `\"1"/"Size of atoms"\`

∝ `\"1"/"Number of lone pair of electrons"\` ∝ Multiplicity of bond

Dipole moment is defined as the product of the magnitude of charge (q) and distance (d) separating the centres of positive and negative charges.

Its direction is from positive end to negative end. 

µ = q × d

Its unit in CGS system is debye (D).

\[\mathrm{Bond~Order}=\frac{N_b-N_a}{2}\]

where N_b = number of electrons in bonding MOs, N_a = number of electrons in antibonding MOs.

• Bond order > 0 → molecule is stable

• Bond order = 0 or negative → molecule is unstable (does not exist)

\[\mu=\sqrt{n(n+2)}\text{BM (Bohr Magneton)}\]

where n = number of unpaired electrons. If any unpaired electron is present → paramagnetic; if none → diamagnetic.

In 1916, Kossel and Lewis independently proposed a theory of chemical combination.

• Atoms of different elements take part in chemical combination to complete their octet (8 electrons) or duplet (2 electrons) in the outermost shell.
• All valence shell (outer-shell) electrons of atoms are represented in Lewis structures using dots surrounding the element symbol.
• Lewis structures show only valence electrons of each atom — inner shell electrons are not shown.

Carbon, nitrogen, oxygen, and fluorine always obey the octet rule in their stable compounds. However:

• Second-row elements like B and Be often have fewer than 8 electrons (incomplete octet).
• Third-row elements can exceed 8 electrons (expanded octet) using d-orbitals.

An ionic bond is formed by the complete transfer of one or more electrons from an electropositive atom to an electronegative atom, resulting in oppositely charged ions that attract each other.

Key conditions for ionic bond formation:

• One atom must have low ionisation enthalpy (easily loses electron) — typically a metal

• The other must have high electron affinity (easily gains electron) — typically a non-metal

• Large difference in electronegativity between the two atoms

Example: Na + Cl → Na⁺ + Cl⁻ → NaCl

• Sodium (2,8,1) loses 1 electron → Na⁺ (2,8)

• Chlorine (2,8,7) gains 1 electron → Cl⁻ (2,8,8)

Ionic solids are crystalline structures containing cations and anions held together by strong electrostatic ionic bonds.

Lattice enthalpy is defined as the energy required to completely separate one mole of a solid ionic compound into its gaseous constituent ions.

For NaCl, lattice enthalpy = −788 kJ mol⁻¹

The higher the lattice enthalpy, the stronger the ionic bond and the more stable the ionic solid

Lattice enthalpy depends on:

• Ionic charge — higher charge → greater lattice enthalpy
• Ionic radius — smaller ions → greater lattice enthalpy (ions are closer together)

The Born-Haber cycle relates lattice enthalpy to measurable thermodynamic quantities (sublimation enthalpy, ionisation enthalpy, electron gain enthalpy, bond dissociation enthalpy).

• Carbon forms covalent bonds by sharing electrons to achieve a noble gas configuration.
• Covalent bonds can be single, double, or triple, as seen in molecules like H₂, O₂, and N₂.
• Covalent compounds have low melting and boiling points and are poor conductors of electricity.
• Carbon has allotropes such as diamond, graphite, and fullerene (C₆₀), each with different physical properties.

Lewis structures use dots (lone pairs) and dashes (bonds) to represent all valence electrons in a molecule. Key examples:

Steps to draw Lewis structure:

1. Count total valence electrons (add electrons for negative charge; subtract for positive)
2. Arrange atoms — least electronegative atom is usually in the centre
3. Connect atoms with single bonds
4. Complete octets on outer atoms first, then on central atom
5. If central atom has deficit, form multiple bonds

Formal charge is a bookkeeping tool — it is the hypothetical charge on an atom in a Lewis structure assuming electrons in bonds are equally shared. It helps identify the most stable (lowest energy) Lewis structure.

\[F.C.=V.E.-N.E.-\frac{B.E.}{2}\]

where:

• V.E. = Total number of valence electrons of the atom in a free state
• N.E. = Total number of non-bonding (lone pair) electrons on that atom
• B.E. = Total number of bonding (shared) electrons around that atom

Key rules:

• The sum of formal charges in a neutral molecule = 0
• The sum of formal charges in an ion = charge of that ion
• The most stable Lewis structure has formal charges as close to zero as possible
• Negative formal charge should be on the more electronegative atom

Example — CO₃²⁻ and Ozone (O₃): Both have multiple valid Lewis structures (resonance), and formal charges help identify the preferred one.

The octet rule is a useful guideline but not universal. Three important exceptions:

• Proposed by Sidgwick and Powell (1940) and further developed by Nyholm and Gillespie.
• The geometry of a molecule depends on the total number of valence shell electron pairs (bond pairs + lone pairs) around the central atom.
• Electron pairs repel each other and arrange themselves as far apart as possible to minimise repulsion.
• Repulsion order:
  lp–lp > lp–bp > bp–bp, and lone pairs occupy more space than bond pairs.
• Presence of lone pairs reduces bond angle; if no lone pairs → molecular geometry = electron pair geometry.

VSEPR Geometry Table:

• Proposed by Heitler and London (1927), further developed by Pauling and Slater.
• A covalent bond is formed when half-filled valence atomic orbitals of similar energies overlap, each containing one unpaired electron.
• Greater the overlap → stronger the bond.

Types of Orbital Overlap:

Hybridisation & Shapes:

Hybridisation is the process of mixing orbitals of nearly similar energy from the same atom to form a new set of equivalent orbitals of exactly equal energy called hybrid orbitals.

\[H=\frac{1}{2}[V+Y-C+A]\]

where V = valence electrons of central metal atom, Y = number of monovalent atoms surrounding central atom, C = total positive charge, A = total negative charge on the molecule.

Characteristics of Hybridisation:

• Number of hybridised orbitals = number of orbitals that participated in hybridisation.
• Hybridised orbitals are always equivalent in energy and shape.
• Hybrid orbitals are more effective in forming stable bonds than pure atomic orbitals.
• Hybrid orbitals are directed in space in some preferred directions → determines geometry of the molecule.

Importance:

• Successfully explains the formation, directional nature, and geometry of covalent bonds
• Explains why bond angle in water (104.5°) is less than tetrahedral angle through lone pair repulsion
• Explains why bond strength increases with greater orbital overlap

Limitations:

• Cannot satisfactorily explain the paramagnetic nature of O₂ (O₂ has 2 unpaired electrons, but VBT shows all electrons paired in a double bond)
• Fails to explain the electronic spectra of molecules
• Cannot account for the equal bond lengths in resonance structures (e.g., benzene)
• Does not explain why some molecules are coloured

These limitations led to the development of Molecular Orbital Theory (MOT).

Molecular orbitals (MOs) are formed by the linear combination of atomic orbitals (LCAO).

Two types of MOs form:

• Bonding MOs — lower energy than the original atomic orbitals; electrons here stabilise the molecule (σ, π)
• Antibonding MOs — higher energy; electrons here destabilise the molecule (σ*, π*)

Energy Order of MOs for Diatomic Molecules:

For O₂, F₂ (electrons > 14):

For B₂, C₂, N₂ (electrons ≤ 14):

Electronic Configurations and Bond Properties of Diatomic Molecules:

Even ionic bonds have some degree of covalent character. The polarising power of the cation distorts the electron cloud of the anion, inducing covalency. This is explained by Fajan's Rules:

Covalent character increases when:

• The cation is small and highly charged (high charge density → high polarising power)
• The anion is large (easily polarised / high polarisability)
• Both ions have high charge

\[\text{Polarising power}\propto\frac{1}{\text{Size of cation}}\propto\text{Size of anion}\propto\text{Charge on ions}\]

Greater the polarising power → More covalent character in the ionic bond.

Resonance occurs when a single Lewis structure cannot adequately represent the actual structure of a molecule — multiple valid Lewis structures (called canonical forms) can be drawn.

• The actual molecule does not switch between these structures; it is a resonance hybrid — a weighted average of all canonical forms.

• The energy of the resonance hybrid is always lower than the energy of any single canonical form (this energy difference is called resonance energy or resonance stabilisation energy).

• All canonical forms must have: same positions of atoms, same number of paired and unpaired electrons, similar energy.

Classic examples:

• CO₃²⁻ (carbonate ion): 3 equivalent resonance structures — each C − O bond is neither single nor double, but intermediate (~1.33 bond order)
• Ozone (O₃): 2 resonance structures with bond length ~128 pm (intermediate between O − O single bond ~148 pm and O = O double bond ~121 pm)