Chemical Bonding - Complete Study Guide

Overview of Chemical Bonding and Classification

• Definition of Chemical Bond:

  • A chemical bond is the attractive force that holds various constituents (atoms, ions, molecules, etc.) together in different chemical species.
  • It involves the redistribution of electrons among combining chemical species.
  • Bond formation is accompanied by a decrease in potential energy, which stabilizes the system; hence, molecules are lower in energy and more stable than isolated free atoms.

• Primary Reasons for Chemical Bond Formation:

  • Decrease in Potential Energy: Attraction between positive nuclei and negative electron clouds lowers system potential energy.
  • Lewis-Kossel Approach (Octet Rule): Atoms undergo bond formation to achieve an octet ($ns^2 np^6$) or nearest noble gas electron configuration in their valence shell.

• Broad Classification of Chemical Forces:

  • Strong Bonds (Intramolecular / Primary bonds):
  • Ionic (Electrovalent) Bond: Formed via complete transfer of electrons between atoms.
  • Covalent Bond: Formed via mutual sharing of valence electrons between atoms.
  • Co-ordinate (Dative) Bond: Special covalent bond where the shared electron pair is contributed entirely by one donor atom (Lewis base) to an acceptor atom (Lewis acid).
  • Metallic Bond: Attraction between positive metal kernels and delocalized valence electron sea.
  • Weak Interactions (Intermolecular / Secondary forces):
  • Hydrogen Bonding: Intermolecular and Intramolecular H-bonding.
  • Van der Waals Forces: Dipole-dipole (Keesom), Dipole-induced dipole (Debye), Dispersion / London forces.
  • Ion-dipole Forces.
  • Ion-induced dipole Forces.
  • Typical / Specialized Bonds:
  • Odd Electron Bond.
  • Back Bonding.
  • Multicentre Bonds: Banana bond ($3c-2e^-$) and ($3c-4e^-$) bond.

Causes of Chemical Combination and Limitations of the Octet Rule

• Driving Forces of Combination:

  1. Tendency to Acquire Minimum Energy: Two approaching atoms attract until attractive forces balance repulsive forces at minimum potential energy.
  2. Tendency to Acquire Noble Gas Configuration: Achieving octet ($ns^2 np^6$) or duplet (for $\text{H}$, $\text{He}$) configuration.

• Limitations and Exceptions to the Octet Rule:

  • Incomplete Octet / Hypovalent Species: Central atom has fewer than 8 valence electrons after bond formation.
  • Examples:
    • $\text{BeF}_2$ ($4$ valence electrons around $\text{Be}$)
    • $\text{BF}_3$ ($6$ valence electrons around $\text{B}$)
    • $\text{AlCl}_3$ ($6$ valence electrons around $\text{Al}$)
    • $\text{BCl}_3$ ($6$ valence electrons around $\text{B}$)
  • Expanded Octet / Hypervalent Species: Central atom has more than 8 valence electrons due to available empty $d$-orbitals in period 3 or higher elements.
  • Examples:
    • $\text{PCl}_5$ ($10$ valence electrons around $\text{P}$)
    • $\text{SF}_6$ ($12$ valence electrons around $\text{S}$)
    • $\text{ClF}_3$ ($10$ valence electrons around $\text{Cl}$)
    • $\text{BrF}_5$ ($12$ valence electrons around $\text{Br}$)
    • $\text{IF}_7$ ($14$ valence electrons around $\text{I}$)
  • Odd Electron Species: Molecules containing an unpaired electron, making octet completion impossible for all atoms.
  • Examples: $\text{NO}$, $\text{NO}_2$, $\text{ClO}_2$
  • Compounds of Noble Gases: Noble gases already possess completed octets ($ns^2 np^6$) or duplets ($1s^2$), yet undergo chemical combinations.
  • Examples: $\text{XeF}_2$, $\text{XeF}_6$, $\text{KrF}_2$
  • Transition Metal Ions: Cations with incomplete $d$-subshells that do not possess noble gas configurations.
  • $\text{Cr}^{3+}$: $[\text{Ar}] 3d^3$ ($2, 8, 11$ electrons)
  • $\text{Mn}^{2+}$: $[\text{Ar}] 3d^5$ ($2, 8, 13$ electrons)
  • $\text{Fe}^{2+}$: $[\text{Ar}] 3d^6$ ($2, 8, 14$ electrons)
  • Pseudo Inert Gas Configuration: Ions having 18 electrons in their outermost shell ($ns^2 np^6 nd^{10}$).
  • $\text{Zn}^{2+}$: $[\text{Ar}] 3d^{10}$ ($2, 8, 18$ electrons)
  • $\text{Cd}^{2+}$: $[\text{Kr}] 4d^{10}$ ($2, 8, 18, 18$ electrons)

Ionic (Electrovalent) Bonding

• Mechanism of Formation:

  • Formed between atoms via complete transfer of one or more electrons from a metallic/electropositive atom to a non-metallic/electronegative atom.
  • Example: Formation of Magnesium Oxide ($\text{MgO}$):     $\text{Mg} (2, 8, 2) + \text{O} (2, 6) \rightarrow \text{Mg}^{2+} (2, 8) + \text{O}^{2-} (2, 8) \rightarrow \text{MgO}$
  • Electrovalency of $\text{Mg} = 2$
  • Electrovalency of $\text{O} = 2$

• Favourable Conditions for Ionic Bond Formation:

  • Low Ionization Energy (I.E.) of the cation-forming metal atom.
  • High Electron Affinity (E.A.) of the anion-forming non-metal atom.
  • High Lattice Energy of the resulting ionic crystal lattice.
  • High Electronegativity Difference ($\triangle \text{E.N.}$) between combining atoms.

• General Characteristics of Ionic Compounds:

  • Non-directional Nature: Electrostatic force of attraction acts uniformly in all space directions around an ion.
  • Physical state: Hard, crystalline, and brittle solids.
  • Electrical conductivity: Excellent electrolytes in molten state or aqueous solution, but non-conducting in solid state.
  • Melting and Boiling Points: High M.P. and B.P. due to strong lattice electrostatic forces.
  • Reaction Kinetics: Fast ionic reactions in polar solvents.

• Advanced Ionic Phenomena:

  • Inert Pair Effect: Reluctance of $s$-electrons of outermost shell to participate in bonding in heavier $p$-block elements.
  • Fajan's Rules: Explains partial covalent character in ionic compounds based on polarising power of cation and polarisability of anion.

Covalent and Coordinate (Dative) Bonding

• Covalent Bond:

  • Formed by mutual sharing of valence electrons between atoms.
  • Shared electron pairs have opposite spins and are localized between the bonded nuclei.
  • Covalency: The number of electron pairs shared by an atom in forming covalent bonds.
  • Types of Covalent Bonds:
  • Single bond (represented by $-$): 1 shared pair ($2$ electrons). Examples: $\text{H}_2$ ($\text{H}-\text{H}$), $\text{Cl}_2$ ($\text{Cl}-\text{Cl}$), $\text{CH}_4$.
  • Double bond (represented by $=$): 2 shared pairs ($4$ electrons). Examples: $\text{O}_2$ ($\text{O}=\text{O}$).
  • Triple bond (represented by \bar{\bar{\tb}} or \tb): 3 shared pairs ($6$ electrons). Examples: $\text{N}_2$ (\text{N}\tb \text{N}).
  • Covalent bonds possess distinct directional properties.
  • Properties: Low M.P. and B.P., poor electrical conductors (except graphite).

• Coordinate (Dative) Bond:

  • A bond formed between two atoms where the shared pair of electrons is provided exclusively by one atom (Donor / Lewis base) to another atom (Acceptor / Lewis acid).
  • Represented by an arrow ($\rightarrow$) directed from donor to acceptor.
  • Examples:
  1. Ammonium Ion ($\text{NH}_4^+$): Donor $\text{NH}_3$ donates a lone pair to acceptor $\text{H}^+$.
  2. Ozone ($\text{O}_3$): Central oxygen donates a lone pair to the terminal oxygen atom ($\text{O}=\text{O}\rightarrow \text{O}$).

• Lewis Dot Structures:

  • Steps for Construction:
  1. Calculate total number of valence electrons contributed by all constituent atoms (add charge for anions, subtract charge for cations).
  2. Arrange atomic symbols showing skeletal atom connectivity.
  3. Distribute electron pairs as single bonds between connected atoms, then complete octets of outer atoms and central atom using remaining electrons as lone pairs or multiple bonds.
  • Oxyacid Structural Rule: In oxyacids, hydrogen atoms are attached directly to oxygen as $-\text{OH}$ groups, except in:
  • Phosphorous acid ($\text{H}_3\text{PO}_3$): Dibasic; one $\text{H}$ is directly bonded to central $\text{P}$.
  • Hypophosphorous acid ($\text{H}_3\text{PO}_2$): Monobasic; two $\text{H}$ atoms are directly bonded to central $\text{P}$.
  • Pyrophosphorous acid ($\text{H}_4\text{P}_2\text{O}_5$): Dibasic; two $\text{H}$ atoms are directly bonded to central $\text{P}$ atoms.

Formal Charge and Resonance

• Formal Charge:

  • Formal charge assigns electric charge to specific atoms within a polyatomic molecule or ion.
  • Formula:     $Q_F = N_A - N_{L.P.} - \frac{1}{2} N_{B.P.}$     Where:
  • $N_A$ = Total number of valence electrons in the free atom.
  • $N_{L.P.}$ = Total number of non-bonding (lone pair) electrons.
  • $N_{B.P.}$ = Total number of bonding (shared) electrons.

• Calculated Examples of Formal Charge:

  • Ozone Molecule ($\text{O}_3$):
  • Central Oxygen Atom $\text{O}(1)$: $Q_F = 6 - 2 - \frac{1}{2}(6) = +1$
  • Double-bonded Oxygen Atom $\text{O}(2)$: $Q_F = 6 - 4 - \frac{1}{2}(4) = 0$
  • Single-bonded Oxygen Atom $\text{O}(3)$: $Q_F = 6 - 6 - \frac{1}{2}(2) = -1$
  • Carbon Monoxide ($\text{CO}$):
  • Carbon atom: $Q_F = 4 - 2 - \frac{1}{2}(6) = -1$
  • Oxygen atom: $Q_F = 6 - 2 - \frac{1}{2}(6) = +1$
  • Ammonium Cation ($\text{NH}_4^+$):
  • Nitrogen atom: $Q_F = 5 - 0 - \frac{1}{2}(8) = +1$
  • Each Hydrogen atom: $Q_F = 1 - 0 - \frac{1}{2}(2) = 0$

• Resonance Theory:

  • When a single Lewis structure cannot adequately account for all experimentally observed properties of a molecule/ion, the actual structure is represented as a resonance hybrid of two or more canonical (resonating) structures.
  • Canonical forms have identical atomic positions, similar energies, and equal numbers of paired/unpaired electrons, but differ in electron pair distribution.
  • Canonical forms do not have real individual existence.
  • Resonance lowers system potential energy; resonance hybrid is more stable than any individual canonical structure.

• Resonance Structure Examples and Bond Orders:

  • Azide Ion ($\text{N}_3^-$):
  • Canonical forms: \text{I}: \bar{\text{N}}=\b{\text{N}}=\bar{\text{N}}, \text{II}: \b{\text{N}}^{2-}-\b{\text{N}}\tb \text{N}, \text{III}: \text{N}\tb \b{\text{N}}-\b{\text{N}}^{2-}.
  • Each $\text{N}-\text{N}$ bond exhibits approximately double bond character.
  • Carbonate Ion ($\text{CO}_3^{2-}$):
  • 3 equivalent canonical forms.
  • $\text{Bond Order} = \frac{\text{Total bonds between C and O}}{\text{Total resonating structures}} = \frac{4}{3} = 1.33$
  • Benzene ($\text{C}_6\text{H}_6$):
  • Kekulé structures interconvert.
  • $\text{Bond Order} = 1.5$
  • Carboxylate Ion ($\text{RCOO}^-$):
  • 2 equivalent canonical forms.
  • $\text{Bond Order} = \frac{2 + 1}{2} = 1.5$

Valence Bond Theory (VBT) and Orbital Overlap

• Foundation of Valence Bond Theory:

  • Introduced by Heitler and London (1927), expanded by Pauling.
  • Based on atomic orbital interactions, electron configurations, and orbital overlap criteria.

• Formation of Hydrogen Molecule ($\text{H}_2$):

  • When two isolated $\text{H}$ atoms approach, three forces emerge:
  1. Electron-electron ($e-e$) repulsion.
  2. Proton-proton ($p-p$) repulsion.
  3. Electron-proton ($e-p$) attraction between nucleus of one atom and electron of the other.
  • Magnitude of attractive forces exceeds repulsive forces, causing potential energy to drop as internuclear distance decreases until force equilibrium is attained.

• Quantitative Potential Energy Parameters for $\text{H}_2$:

  • Equilibrium Bond Length ($r_{ ext{H}- ext{H}}$): $0.74\text{ Å}$ ($74\text{ pm}$).
  • Bond Dissociation Energy ($ ext{BDE}_{ ext{H}- ext{H}}$): $434.2\text{ kJ mol}^{-1}$.
  • Dissociation reaction: $\text{H}_2(g) + 434.2\text{ kJ mol}^{-1} \rightarrow \text{H}(g) + \text{H}(g)$.

• Orbital Overlap Concept:

  • Covalent bonds form via partial interpenetration (overlap) of atomic orbitals containing unpaired electrons with opposite spins.
  • Extent of orbital overlap determines bond strength: greater overlap yields higher bond dissociation energy and stronger bond.

• Types of Overlapping and Nature of Covalent Bonds:

  • Sigma ({ ext{s}}) Bond:
  • Formed by end-to-end (head-on / axial) overlap along the internuclear axis.
  • $s-s$ Overlapping: Overlap of two half-filled $s$-orbitals along the internuclear axis.

* **$s-p$ Overlapping**: Overlap between half-filled $s$-orbital of one atom and half-filled $p$-orbital of another atom.

* **$p-p$ Axial Overlapping**: Overlap between two half-filled $p$-orbitals along the internuclear axis.

• Pi ({ ext{p}}) Bond:
  • Formed by lateral / sidewise / parallel overlap of atomic orbitals perpendicular to the internuclear axis.
  • Electron density concentrated in two saucer-shaped charge clouds above and below the internuclear plane.
  • Types: p{ ext{p}}-p{ ext{p}} and p{ ext{p}}-d{ ext{p}} overlaps.

• Delta ({ ext{d}}) Bond:

  • Formed by four-lobe overlap between $d$-orbitals of parallel planes. All $d$-orbitals except $d_{z^2}$ can form { ext{d}} bonds.

  • Comparative Bond Strengths:

• { ext{s}} bond is significantly stronger than { ext{p}} bond because axial overlap occurs to a much greater extent than lateral overlap.

• A { ext{p}} bond only forms in molecules alongside an existing { ext{s}} bond.

  • Advantages and Limitations of Classical VBT:

• Advantages: Explains bond lengths, bond strengths, quantitative overlap vs. BDE relations, and octet-rule exceptions like $\text{BF}_3$, $\text{AlCl}_3$, $\text{PCl}_5$, $\text{SF}_6$

• Disadvantages: Predicts bond angles of $90^\text{o}$ for $\text{CH}_4$, $\text{NH}_3$, and $\text{H}_2\text{O}$ (based on pure $p$-orbital orientation), failing to match real bond angles ($109.5^\text{o}$ in $\text{CH}_4$, $107^\text{o}$ in $\text{NH}_3$, $104.5^\text{o}$ in $\text{H}_2\text{O}$). This required Pauling's concept of Hybridisation.

Hybridisation Theory

• Definition: Process of intermixing atomic orbitals of slightly different energies of an atom to redistribute energy, forming a new set of equivalent orbitals with identical shape and energy.

• Salient Features:

  1. Number of hybrid orbitals produced equals the exact number of pure atomic orbitals mixed.
  2. Hybrid orbitals are equivalent in shape and energy.
  3. Hybrid orbitals form stronger, more stable covalent bonds than pure atomic orbitals.
  4. Hybrid orbitals direct themselves in space to maximize internuclear distance and minimize electron pair repulsions.

• Essential Conditions:

  • Only orbitals of the valence shell undergo hybridisation.
  • Intermixing orbitals must possess nearly equal energy.
  • Electron excitation is not a prerequisite prior to hybridisation.
  • Fully filled, half-filled, or empty valence orbitals can participate in hybridisation.

• Steric Number Formula for Hybridisation State:   \text{Steric Number (S.N.)} = \text{Number of }\b{\text{s}}\text{-bonds around central atom} + \text{Number of lone pairs on central atom}

• Hybridisation Types and Steric Numbers:

  • $\text{S.N.} = 2 \rightarrow sp$
  • $\text{S.N.} = 3 \rightarrow sp^2$
  • $\text{S.N.} = 4 \rightarrow sp^3$
  • $\text{S.N.} = 5 \rightarrow sp^3d$
  • $\text{S.N.} = 6 \rightarrow sp^3d^2$
  • $\text{S.N.} = 7 \rightarrow sp^3d^3$

• Hybridisation in Ionic Solids / Complex Species:

  • $\text{PCl}_5(s) \rightarrow [\text{PCl}_4]^+ (sp^3) + [\text{PCl}_6]^- (sp^3d^2)$
  • $\text{PBr}_5(s) \rightarrow [\text{PBr}_4]^+ (sp^3) + \text{Br}^-$
  • $\text{XeF}_6(s) \rightarrow [\text{XeF}_5]^+ (sp^3d^2) + \text{F}^-$
  • $\text{N}_2\text{O}_5(s) \rightarrow [\text{NO}_2]^+ (sp) + [\text{NO}_3]^- (sp^2)$
  • $\text{N}_2\text{O}_3(s) \rightarrow [\text{NO}]^+ + [\text{NO}_2]^- (sp^2)$
  • $\text{N}_2\text{O}_4(s) \rightarrow [\text{NO}]^+ + [\text{NO}_3]^- (sp^2)$
  • $\text{I}_2\text{Cl}_6(l) \rightarrow [\text{ICl}_2]^+ (sp^3) + [\text{ICl}_4]^- (sp^3d^2)$
  • $\text{I}_2(l) \rightarrow [\text{I}_3]^+ (sp^3) + [\text{I}_3]^- (sp^3d)$
  • $\text{Cl}_2\text{O}_6(s) \rightarrow [\text{ClO}_2]^+ (sp^2) + [\text{ClO}_4]^- (sp^3)$
  • Note: $\text{PF}_5(s)$ retains trigonal bipyramidal molecular geometry in the solid state.

Valence Shell Electron Pair Repulsion (VSEPR) Theory and Molecular Geometry

• Core Postulates:

  • Developed by Gillespie and Nyholm (1957) to predict molecular geometry.
  • Valence shell electron pairs (bonding and non-bonding) position themselves around central atoms to minimize electrostatic repulsion.
  • Magnitude Order of Electron Pair Repulsions:     $\text{Lone Pair - Lone Pair }(lp-lp) > \text{Lone Pair - Bond Pair }(lp-bp) > \text{Bond Pair - Bond Pair }(bp-bp)$
  • Presence of lone pairs distorts ideal bond angles (e.g., $\text{NH}_3$ drops from $109^\text{o}28'$ to $107^\text{o}$; $\text{H}_2\text{O}$ drops to $104.5^\text{o}$).

• Comprehensive VSEPR Geometry Master Reference:

  • $\text{S.N.} = 2$:
  • $2\text{ bp}, 0\text{ lp} \rightarrow \text{AB}_2 \rightarrow sp \rightarrow \text{Linear } (180^\text{o}) \rightarrow \text{BeCl}_2$
  • $\text{S.N.} = 3$:
  • $3\text{ bp}, 0\text{ lp} \rightarrow \text{AB}_3 \rightarrow sp^2 \rightarrow \text{Trigonal planar } (120^\text{o}) \rightarrow \text{BCl}_3, \text{NO}_3^-, \text{GaF}_3, \text{CO}_3^{2-}$
  • $2\text{ bp}, 1\text{ lp} \rightarrow \text{AB}_2 \rightarrow sp^2 \rightarrow \text{V-shaped / Bent / Angular } (<120^\text{o}) \rightarrow \text{SnCl}_2, \text{O}_3, \text{SO}_2$
  • $\text{S.N.} = 4$:
  • $4\text{ bp}, 0\text{ lp} \rightarrow \text{AB}_4 \rightarrow sp^3 \rightarrow \text{Tetrahedral } (109^\text{o}28') \rightarrow \text{CH}_4, \text{SiF}_4, \text{NH}_4^+$
  • $3\text{ bp}, 1\text{ lp} \rightarrow \text{AB}_3 \rightarrow sp^3 \rightarrow \text{Trigonal pyramidal } (<109^\text{o}28') \rightarrow \text{NH}_3, \text{CH}_3^-$
  • $2\text{ bp}, 2\text{ lp} \rightarrow \text{AB}_2 \rightarrow sp^3 \rightarrow \text{V-shaped / Bent / Angular } (<109^\text{o}28') \rightarrow \text{H}_2\text{O}, \text{SF}_2$
  • $1\text{ bp}, 3\text{ lp} \rightarrow \text{AB} \rightarrow sp^3 \rightarrow \text{Linear} \rightarrow \text{ClO}^-$
  • $\text{S.N.} = 5$:
  • $5\text{ bp}, 0\text{ lp} \rightarrow \text{AB}_5 \rightarrow sp^3d \rightarrow \text{Trigonal bipyramidal } (120^\text{o}, 90^\text{o}) \rightarrow \text{PF}_5, \text{SF}_5^+, \text{SbBr}_5, \text{XeO}_3\text{F}_2$
  • $4\text{ bp}, 1\text{ lp} \rightarrow \text{AB}_4 \rightarrow sp^3d \rightarrow \text{Seesaw } (<120^\text{o}, <90^\text{o}) \rightarrow \text{SF}_4$
  • $3\text{ bp}, 2\text{ lp} \rightarrow \text{AB}_3 \rightarrow sp^3d \rightarrow \text{T-shaped } (<90^\text{o}) \rightarrow \text{ClF}_3, \text{BrF}_3$
  • $2\text{ bp}, 3\text{ lp} \rightarrow \text{AB}_2 \rightarrow sp^3d \rightarrow \text{Linear } (180^\text{o}) \rightarrow \text{ICl}_2^-, \text{XeF}_2, \text{I}_3^-$
  • $\text{S.N.} = 6$:
  • $6\text{ bp}, 0\text{ lp} \rightarrow \text{AB}_6 \rightarrow sp^3d^2 \rightarrow \text{Octahedral / Square bipyramidal } (90^\text{o}) \rightarrow \text{SF}_6, \text{IF}_6^+$
  • $5\text{ bp}, 1\text{ lp} \rightarrow \text{AB}_5 \rightarrow sp^3d^2 \rightarrow \text{Square pyramidal } (<90^\text{o}) \rightarrow \text{IF}_5, \text{XeOF}_4, \text{BrF}_5$
  • $4\text{ bp}, 2\text{ lp} \rightarrow \text{AB}_4 \rightarrow sp^3d^2 \rightarrow \text{Square planar } (90^\text{o}) \rightarrow \text{IF}_4^-, \text{XeF}_4, \text{ICl}_4^-$
  • $\text{S.N.} = 7$:
  • $7\text{ bp}, 0\text{ lp} \rightarrow \text{AB}_7 \rightarrow sp^3d^3 \rightarrow \text{Pentagonal bipyramidal } (72^\text{o}, 90^\text{o}) \rightarrow \text{IF}_7$
  • $6\text{ bp}, 1\text{ lp} \rightarrow \text{AB}_6 \rightarrow sp^3d^3 \rightarrow \text{Distorted octahedral } (<90^\text{o}, <72^\text{o}) \rightarrow \text{XeF}_6, \text{IF}_6^-$
  • $5\text{ bp}, 2\text{ lp} \rightarrow \text{AB}_5 \rightarrow sp^3d^3 \rightarrow \text{Pentagonal planar } (72^\text{o}) \rightarrow \text{XeF}_5^-$

Bond Parameters

• Bond Order:

  • Number of covalent bonds present between two atoms.
  • Isoelectronic species have identical bond orders:
  • $\text{F}_2$ and $\text{O}_2^{2-} \rightarrow \text{Bond Order} = 1$
  • $\text{N}_2$, $\text{CO}$, and $\text{NO}^+ \rightarrow \text{Bond Order} = 3$
  • Higher bond order increases bond enthalpy and decreases bond length.

• Bond Length:

  • Equilibrium internuclear distance between two bonded atoms.
  • Affected by atomic size, bond order, resonance, electronegativity difference, and hybridisation state.

• Bond Angle:

  • Angle between orbitals containing bonding electron pairs around the central atom.
  • Examples: $\text{H}_2\text{O}$ bond angle is $104.5^\text{o}$.
  • Electronegativity trend examples: $\text{OF}_2 (103^\text{o})$ vs $\text{SF}_2 (98^\text{o})$.

• Bond Enthalpy:

  • Energy needed to break $1\text{ mole}$ of bonds of a given type in gaseous state ($\text{kJ mol}^{-1}$).
  • For polyatomic molecules, average bond enthalpy is calculated by dividing total dissociation energy by number of bonds broken.
  • Water example:
  • \text{H}_2\text{O}(g) \rightarrow \text{H}(g) + \text{OH}(g) \text{ } (\triangle_a H_1^\b{\text{s}} = 502\text{ kJ mol}^{-1})
  • \text{OH}(g) \rightarrow \text{H}(g) + \text{O}(g) \text{ } (\triangle_a H_2^\b{\text{s}} = 427\text{ kJ mol}^{-1})
  • $\text{Average Bond Enthalpy} = \frac{502 + 427}{2} = 464.5\text{ kJ mol}^{-1}$

Specialized Rules and Non-Existent Molecules

• Bent's Rule:

  • Lone pairs prefer hybrid orbitals with greater percentage $s$-character.
  • More electronegative substituents prefer hybrid orbitals with smaller percentage $s$-character (higher $p$-character).
  • Application to $\text{PCl}_3\text{F}_2$: Fluorine atoms occupy axial positions (axial orbitals possess lower $s$-character), while Chlorine atoms occupy equatorial positions.

• Drago's Rule:

  • If central atom belongs to 3rd period or lower, possesses at least one lone pair, and electronegativity of attached surrounding atoms is \b{\text{S}} 2.5, hybridisation does not occur significantly.
  • Bonding occurs using almost pure atomic $p$-orbitals, yielding bond angles near $90^\text{o}$.
  • Group 15 Hydride Angles:
  • $\text{NH}_3 = 107^\text{o}48'$
  • $\text{PH}_3 = 93^\text{o}36'$
  • $\text{AsH}_3 = 91^\text{o}48'$
  • $\text{SbH}_3 = 91^\text{o}18'$
  • Group 16 Hydride Angles:
  • $\text{H}_2\text{O} = 104^\text{o}28'$
  • $\text{H}_2\text{S} = 92^\text{o}$
  • $\text{H}_2\text{Se} = 91^\text{o}$
  • $\text{H}_2\text{Te} = 90.5^\text{o}$
  • Trend: $\text{H}_2\text{O} > \text{H}_2\text{S} > \text{H}_2\text{Se} > \text{H}_2\text{Te}$; $\text{NH}_3 > \text{PH}_3 > \text{AsH}_3 > \text{SbH}_3$

• Molecules That Do Not Exist:

  • $\text{SF}_4$, $\text{SF}_6$, and $\text{PF}_5$ exist, but $\text{OF}_4$, $\text{OF}_6$, and $\text{NF}_5$ do not exist (lack of vacant $d$-orbitals in Period 2).
  • $\text{PI}_5(g)$ and $\text{SCl}_6$ do not exist due to steric hindrance, but $\text{TeCl}_6$ and $\text{PI}_5(s)$ exist.
  • $\text{SF}_6$, $\text{PF}_5$, $\text{XeF}_6$, $\text{XeF}_4$, and $\text{XeF}_2$ exist, but $\text{SH}_6$, $\text{PH}_5$, $\text{XeH}_6$, $\text{XeH}_4$, and $\text{XeH}_2$ do not exist (hydrogen cannot contract $d$-orbitals).

Dipole Moment and Intermolecular Interactions

• Dipole Moment ({ ext{m}}):

  • Measure of covalent bond polarity: \b{\text{m}} = \b{\text{d}} \times d
  • Vector quantity directed from positive to negative pole.
  • Units: $\text{C m}$ (S.I.), $\text{esu cm}$ (CGS), or Debye ($\text{D}$).
  • Conversion: $1\text{ D} = 10^{-18}\text{ esu cm} = 3.33 \times 10^{-30}\text{ C m}$.
  • Values: $\text{H}_2\text{O} (1.84\text{ D})$, $\text{SO}_2 (1.63\text{ D})$, $\text{NH}_3 (1.47\text{ D})$, $\text{PH}_3 (0.58\text{ D})$, $\text{NF}_3 (0.24\text{ D})$.
  • Percentage Ionic Character formula:     \text{\% Ionic Character} = \frac{\b{\text{m}}_{\text{observed}}}{\b{\text{m}}_{\text{calculated (100\% ionic)}}} \times 100\%

• Hydrogen Bonding:

  • Electrostatic attraction between a hydrogen atom bonded to strongly electronegative atoms ($\text{F}, \text{O}, \text{N}$) and another electronegative atom.
  • Types: Intermolecular (e.g., $\text{H}_2\text{O}$, alcohols) vs. Intramolecular (e.g., chloral hydrate, $o$-nitrophenol).

• Comprehensive Conceptual Q&A on Hydrogen Bonding:

  1. Structure of Boric acid in solid state: Formed by planar $\text{BO}_3^{3-}$ units connected via intermolecular hydrogen bonds forming a 2D sheet.
  2. Boiling point of $o$-nitrophenol vs $m$- and $p$-nitrophenol: $o$-Nitrophenol forms intramolecular H-bonds, reducing intermolecular association and lowering its boiling point. $m$- and $p$-isomers form strong intermolecular H-bonds.
  3. Maleic acid vs Fumaric acid acidity: Maleic acid anion is stabilized by intramolecular H-bonding after releasing its first proton, making maleic acid a stronger acid than fumaric acid.
  4. Liquid state of $ ext{HF}$ among halogen acids: Strong intermolecular H-bonding causes molecular association in $\text{HF}$.
  5. Liquefaction of $ ext{NH}_3$ vs $ ext{HCl}$: Intermolecular H-bonding in $\text{NH}_3$ enhances attractive forces compared to $\text{HCl}$.
  6. Ice floating on water: Ice forms a 3D cage-like open structure via H-bonding with lower density than liquid water.
  7. Maximum density of water at $4^ ext{o} ext{C}$: Heating ice from $0-4^\text{o}\text{C}$ breaks open cage H-bonds, collapsing the structure and increasing density. Above $4^\text{o}\text{C}$, thermal expansion dominates.
  8. Acidic strength of $ ext{HI}$ vs $ ext{HF}$: $ ext{H}- ext{I}$ bond is much weaker due to larger iodine size, dissociating easily compared to $ ext{H}- ext{F}$.
  9. Wood sticks holding ice cream: Organic cellulose in wood forms strong H-bonds with ice crystals.
  10. Existence of $ ext{KHF}_2$ vs $ ext{KHBr}_2$ / $ ext{KHI}_2$: $[ ext{F}- ext{H} b ext{F}]^-$ is stabilized by extremely strong $[ ext{F}- ext{H} b ext{F}]^-$ H-bonds, absent in heavier halogens.
  11. Solubility of $o$-nitrophenol vs $p$-nitrophenol: Intramolecular H-bonding in $o$-nitrophenol prevents interaction with water, while $p$-nitrophenol forms intermolecular H-bonds with water.
  12. $o$-Hydroxybenzaldehyde liquid vs $p$-hydroxybenzaldehyde solid: Intramolecular H-bonding makes $o$-hydroxybenzaldehyde a low-boiling liquid; $p$-isomer forms intermolecular networks yielding a high-melting solid.
  13. Viscosity of Glycerol vs Ethanol: Glycerol contains three $-\text{OH}$ groups causing extensive 3D intermolecular H-bonding networks.
  14. Boiling point of $ ext{CH}_4$ ($112 ext{ K}$) vs $ ext{H}_2 ext{O}$ ($373 ext{ K}$): Extensive intermolecular H-bonding in water vs weak dispersion forces in $\text{CH}_4$
  15. Molecular weight doubling of Acetic Acid: Acetic acid dimerizes in non-polar solvents via two intermolecular H-bonds.
  16. Lack of effective H-bonding in Chlorine: Large atomic radius of $\text{Cl}$ diffuses charge density, preventing strong H-bond formation despite equal electronegativity with Nitrogen.
  17. Vaporization entropy change of Acetic Acid vs Water: Acetic acid vaporizes partly as dimers, resulting in lower disorder change than water.
  18. Heat of vaporization of Water vs $ ext{HF}$: Water forms 4 H-bonds per molecule on average, compared to 2 per molecule in $\text{HF}$.

• Van der Waals Forces Classification:

  1. Dipole-dipole (Keesom forces): Attraction between polar molecules (e.g., $\text{HCl}$, $\text{H}_2\text{S}$).
  2. Dipole-induced dipole (Debye forces): Polar molecule induces temporary dipole in adjacent non-polar molecule (e.g., $\text{Cl}_2$ in $\text{H}_2\text{O}$).
  3. Instantaneous dipole-induced dipole (London / Dispersion forces): Fluctuating electron density causes transient dipoles in non-polar species (e.g., noble gases, $\text{F}_2$, $\text{N}_2$).

Inorganic Oxyacids and Silicates

• Oxyacids Structure Rules:

  • Contain $\text{X}-\text{O}-\text{H}$ linkage. Acidic hydrogens are attached to oxygen.
  • Non-acidic H exceptions: Phosphorous acid ($\text{H}_3\text{PO}_3$, dibasic), Hypophosphorous acid ($\text{H}_3\text{PO}_2$, monobasic), Pyrophosphorous acid ($\text{H}_4\text{P}_2\text{O}_5$, dibasic).
  • Boric acid ($\text{H}_3\text{BO}_3$) acts as a weak monobasic Lewis acid in water: $\text{B(OH)}_3 + 2\text{H}_2\text{O} \rightarrow [\text{B(OH)}_4]^- + \text{H}_3\text{O}^+$.

• Structural Families of Oxyacids:

  • Pyro Acids: Formed by removing $1\text{ mole}$ $\text{H}_2\text{O}$ from $2\text{ moles}$ of oxyacid. Contain $\text{X}-\text{O}-\text{X}$ linkage.
  • $\text{H}_2\text{S}_2\text{O}_7$ (Pyrosulfuric acid / Oleum): $\text{S}-\text{O}-\text{S}$ bond.
  • $\text{H}_4\text{P}_2\text{O}_7$ (Pyrophosphoric acid): $\text{P}-\text{O}-\text{P}$ bond.
  • Exception: Pyrosulfurous acid ($\text{H}_2\text{S}_2\text{O}_5$) contains an $\text{S}-\text{S}$ bond ($\text{HO}-\text{SO}_2-\text{SO}-\text{OH}$).
  • Hypo Acids: Formed by removing an oxygen atom from the -ous form.
  • $\text{H}_3\text{PO}_2$ (Hypophosphorous acid).
  • $\text{HOX}$ (Hypohalous acid: $\text{HOCl}$, $\text{HOBr}$, $\text{HOI}$).
  • $\text{H}_2\text{N}_2\text{O}_2$ (Hyponitrous acid).
  • Removing oxygen from pyro -ic acid produces hypo -ic acid: $\text{H}_4\text{P}_2\text{O}_6$ (Hypophosphoric acid).
  • Peroxy Acids: Contain peroxy ($-\text{O}-\text{O}-$) linkage; oxidation state of central atom remains unchanged.
  • $\text{H}_2\text{SO}_5$ (Caro's acid / Peroxymonosulfuric acid).
  • $\text{H}_2\text{S}_2\text{O}_8$ (Marshall's acid / Peroxydisulfuric acid).
  • $\text{H}_3\text{PO}_5$ (Peroxyphosphoric acid).
  • $\text{HNO}_4$ (Peroxynitric acid).
  • Ortho and Meta Acids: Removing $1\text{ mole}$ $\text{H}_2\text{O}$ from $1\text{ mole}$ ortho acid yields meta acid ($\text{HPO}_3$, $\text{HBO}_2$).
  • Polyphosphoric Acids: General formula $\text{H}_{n+2}\text{P}_n\text{O}_{3n+1}$ containing $(n-1)$ $\text{P}-\text{O}-\text{P}$ bonds.
  • Thio Acids: Oxygen replaced by sulphur ($\text{H}_2\text{S}_2\text{O}_3$, $\text{HSCN}$, Thionic acids $\text{H}_2\text{S}_{n+2}\text{O}_6$).

• Master Table of Oxyacid Oxidation States:

  • $\text{P}$: $+1$ ($\text{H}_3\text{PO}_2$); $+3$ ($\text{H}_3\text{PO}_3$, $\text{H}_4\text{P}_2\text{O}_5$); $+4$ ($\text{H}_4\text{P}_2\text{O}_6$); $+5$ ($\text{H}_3\text{PO}_4$, $\text{H}_4\text{P}_2\text{O}_7$, $\text{H}_3\text{PO}_5$).
  • $\text{S}$: $+3$ ($\text{H}_2\text{S}_2\text{O}_4$); $+4$ ($\text{H}_2\text{SO}_3$); $+5$ ($\text{H}_2\text{S}_2\text{O}_6$); $+6$ ($\text{H}_2\text{SO}_4$, $\text{H}_2\text{S}_2\text{O}_7$, $\text{H}_2\text{SO}_5$, $\text{H}_2\text{S}_2\text{O}_8$).
  • Halogens ($\text{X}$): $+1$ ($\text{HXO}$); $+3$ ($\text{HXO}_2$); $+5$ ($\text{HXO}_3$); $+7$ ($\text{HXO}_4$).

• Silicates:

  • Derivatives of silicic acid ($\text{H}_4\text{SiO}_4$) with basic tetrahedral unit $\text{SiO}_4^{4-}$.
  • Structural Types:
  • Orthosilicates: $0$ shared oxygens per tetrahedron; unit $\text{SiO}_4^{4-}$.
  • Pyrosilicates: $1$ shared oxygen per tetrahedron; unit $\text{Si}_2\text{O}_7^{6-}$.
  • Cyclic Silicates: $2$ shared oxygens per tetrahedron; formula $(\text{SiO}_3)_n^{2n-}$.
  • Chain Silicates (Pyroxenes): $2$ shared oxygens per tetrahedron; formula $(\text{SiO}_3)_n^{2n-}$.
  • Double Chain (Amphiboles): Average $2.5$ shared oxygens; formula $(\text{Si}_4\text{O}_{11})_n^{6n-}$.
  • 2D Sheet Silicates: $3$ shared oxygens; formula $(\text{Si}_2\text{O}_5)_n^{2n-}$.
  • 3D Framework Silicates: All $4$ oxygens shared; formula $(\text{SiO}_2)_n$
  • Mineral Examples: Feldspar ($\text{K}[\text{AlSi}_3\text{O}_8]$), Ultramarine ($\text{Na}_2[(\text{AlSiO}_4)_6]\text{S}_2$), Zeolite (\text{Na}_2[\text{Al}_2\text{Si}_3\text{O}_{10}]\b{\text{s}} 2\text{H}_2\text{O}).

Allotropes of Carbon, Oxygen, Sulphur, and Phosphorus

• Carbon Allotropes:

  • Diamond: Covalent 3D network, $sp^3$ hybridised, $\text{C}-\text{C}$ bond length $154\text{ pm}$. Extremely hard abrasive. Conversion factor: $1\text{ carat} = 200\text{ mg}$.
  • Graphite: Thermodynamically most stable allotrope ($\triangle H_f = 0$). Layered structure separated by $340\text{ pm}$ via van der Waals forces. $sp^2$ hybridised planar hexagonal rings with $\text{C}-\text{C}$ bond length $141.5\text{ pm}$. Free delocalized { ext{p}}-electrons conduct electricity along sheets.
  • Fullerene ($C_{60}$ / Buckminsterfullerene): Cage-like soccer ball structure made of 20 six-membered and 12 five-membered rings. $sp^2$ hybridised carbons with single bonds ($143.5\text{ pm}$) and double bonds ($138.3\text{ pm}$).
  • Thermodynamic Stability Order: Graphite > Diamond ($\triangle H_f = 1.90\text{ kJ mol}^{-1}$) > Fullerene $C_{60}$ ($\triangle H_f = 38.1\text{ kJ mol}^{-1}$).

• Sulphur Allotropes:

  • Rhombic ({ ext{a}}-Sulphur): Stable at room temperature, yellow solid, m.p. $385.8\text{ K}$, specific gravity $2.06$. Soluble in $\text{CS}_2$.
  • Monoclinic ({ ext{b}}-Sulphur): Needle-shaped crystals, m.p. $393\text{ K}$, specific gravity $1.98$. Stable above transition temperature $369\text{ K}$.
  • Structure: Crown-shaped puckered $S_8$ rings ($\text{S}-\text{S}$ length $205.7\text{ pm}$, bond angle $107^\text{o}$, torsional angle $102.2^\text{o}$).

• Other Forms: Chair-conformation $S_6$, paramagnetic $S_2$ at high temperatures (\b{\text{S}} 1000\text{ K}), Engel's sulphur ({ ext{e}}-Sulphur), Plastic sulphur ({ ext{c}}-Sulphur).

  • Phosphorus Allotropes:

• White Phosphorus: Waxy, toxic, chemiluminescent solid consisting of discrete tetrahedral $P_4$ molecules with severe angle strain ($60^\text{o}$ bond angles). Soluble in $\text{CS}_2$. Reacts with boiling $\text{NaOH}$ yielding phosphine: $P_4 + 3\text{NaOH} + 3\text{H}_2\text{O} \rightarrow \text{PH}_3 + 3\text{NaH}_2\text{PO}_2$

• Red Phosphorus: Polymeric chains of $P_4$ tetrahedra produced by heating white phosphorus at $573\text{ K}$ in inert atmosphere. Non-poisonous, insoluble, non-luminous.

• Black Phosphorus: { ext{a}}-black (sublimes in air) and { ext{b}}-black forms. Most thermodynamically stable form.

• Thermodynamic Stability Order: Black Phosphorus > Red Phosphorus > White Phosphorus.

• Reactivity Order: White Phosphorus > Red Phosphorus > Black Phosphorus.

  • Sulfur Trioxide Allotropes:

• { ext{a}}- ext{SO}_3: Cross-linked solid polymer.

• { ext{b}}- ext{SO}_3: Linear polymeric chain.

• { ext{g}}- ext{SO}_3: Cyclic trimer ($S_3O_9$).

  • Tin Phase Transition:   \text{Grey Tin }(\b{\text{a}}\text{-Sn, diamond structure}) \b{\text{r}} \text{ White Tin }(\b{\text{b}}\text{-Sn, metallic structure}) \text{ at } 13.2^\text{o}\text{C}