Chemical Bonding – Polarisation, Fajan’s Rule, Metallic Bonding & Intermolecular Forces

Recap: Ionic Bond & Electrovalency

• Ionic (electrovalent) bond = electrostatic attraction between a cation (usually groups IA–IIIA) and an anion (groups IVA–VIIA).

• Electrovalency = total number of electrons lost or gained by an atom during ion formation.

• Key physical traits of ionic compounds

  • Hard, brittle crystalline solids.

  • High melting (MP) & boiling points (BP).

  • Good solubility in polar solvents (e.g. $H_2O$).

  • Conduct electricity only in fused/aqueous state (mobile ions).

Lattice Enthalpy (U) & Hydration Enthalpy (∆Hₕyd)

• Lattice enthalpy $U$: Energy required to completely separate 1 mol of a crystalline ionic solid into isolated gaseous ions. $M^+X^- (s) \longrightarrow M^+(g)+X^-(g);\; \Delta H = U$

  • Larger $U$ ⇒ easier formation & greater stability of ionic solid.

• Hydration enthalpy $\Delta H<em>{hyd}$: Energy released when 1 mol of gaseous ions is solvated by water molecules. $M^{n+}(g)+xH</em>2O\,(l) \longrightarrow [M(H<em>2O)</em>x]^{n+}; \; \Delta H = \Delta H_{hyd}$

  • Greater (more negative) $\Delta H_{hyd}$ ⇒ smaller ionic mobility in an electric field.

  • Order for alkali cations: Li^+>Na^+>K^+>Rb^+ (largest |∆Hₕyd| for smallest ion).

• Relationship to MP: Higher lattice energy ≈ higher MP, assuming negligible covalent character.

Polarisation & Fajan’s Rule

• Polarisation: Distortion of the anion’s electron cloud by a nearby cation.

• Polarising power (PP) of cation ∝ ability to cause distortion.

• Polarizability (P) of anion ∝ ease with which its cloud is distorted.

• Fajan’s Rule predicts covalent character in an ostensibly ionic bond:

  1. Smaller cation ⇒ larger PP ⇒ ↑covalent character (CC).

  2. Larger anion ⇒ higher P ⇒ ↑CC.

  3. Greater charge on cation/anions ⇒ ↑PP or P ⇒ ↑CC.

  4. Cations with pseudo-inert gas configuration ($ns^2np^6nd^{10}$) polarise more than those with simple noble-gas configuration ($ns^2np^6$).

Quantitative Trends & Example Comparisons

Size of Cation (keeping anion constant, Cl⁻)

• BeCl2 > MgCl2 > CaCl2 > SrCl2 > BaCl_2

  • Cation size ↑ ⇒ polarisation ↓ ⇒ covalent character ↓ ⇒ MP ↑.

Size of Anion (keeping cation constant, Li⁺)

• LiF < LiCl < LiBr < LiI

  • Anion size ↑ ⇒ polarisation ↑ ⇒ covalent character ↑ ⇒ MP ↓.

Charge on Cation (keeping anion constant, Cl⁻)

• NaCl < MgCl2 < AlCl3 (ionic → moderately covalent → largely covalent)

Charge on Anion (keeping cation constant, Al³⁺)

• AlF3 < Al2O_3 < AlN (ionic → covalent)

Pseudo-inert Gas Case

• $CuCl$ (18 e⁻, 3d electrons) is more covalent than $NaCl$ (8 e⁻).

• General rule when charge & size are similar: PP($d^{10}$) > PP($s^2p^6$).

Worked Examples (NEET/Boards)

• Least ionic among $NaI, MgI<em>2, AlI</em>3, CsI$ → $AlI_3$ (highest cation charge + largest anion).

• Highest polarising power among $Na^+, Mg^{2+}, Al^{3+}, Ca^{2+}$ → $Al^{3+}$.

• Order of covalent character: BeCl_2 > LiCl > NaCl (AIPMT 2005 answer).

• Bond dissociation vs atomic size: Larger $E_{diss}$ ⇒ smaller atoms; $C–D$ bond (485 kJ mol⁻¹) implies atom D is the smallest.

Applications of Fajan’s Rule

1. Solubility

   • Ionic ⇌ polar solvent; Covalent ⇌ non-polar solvent.

   • $Ag<em>2S$ < $Ag</em>2O$ solubility because $S^{2-}$ is larger → compound more covalent.

   • $Fe(OH)<em>3$ < $Fe(OH)</em>2$ solubility; $Fe^{3+}$ polarises more than $Fe^{2+}$.

2. Colour

   • Bigger anions polarised → partial absorption of visible light.

   • $AgCl$ white, $AgBr, Agl, Ag<em>2CO</em>3$ yellow; similarly $SnCl<em>2$ white, $SnI</em>2$ black.

3. Melting Point & Hardness

   • Covalent character ↑ ⇒ Lattice energy ↓ ⇒ MP ↓, crystals softer.

4. Lattice Energy Trend
   $\%IC + \%CC = 100$ – increasing covalent character necessarily decreases ionic character.

Metallic Bonding

• Metallic bond = attractive force between metal cations & mobile valence electrons.

• Electron-Sea Model (Drude-Lorentz):

  • Metals = 3-D array of cations immersed in a sea of delocalised electrons.

  • No electron locked to a specific atom; electrons act as glue.

• Consequent properties

  • Electrical & thermal conductivity: electrons drift under E-field or temperature gradient.

  • Malleability & ductility: layers slide without fracture as electron sea redistributes.

Intermolecular Forces (IMF)

• Secondary forces between molecules/ions; weaker than primary (ionic/covalent) bonds.

• Include van der Waals, dipole–dipole, $H$-bonding, London dispersion, etc.

• Example: liquid water networked via hydrogen bonds.

Typical NEET/Board Question Types

• Ranking compounds by ionic/covalent character, MP, solubility.

• Identifying highest polarising power/ polarizability.

• Linking colour or bond dissociation energy to atomic size.

• Distinguishing metallic, ionic, covalent, coordinate bonds in solids.

Learning Outcomes (Session)

• Define & apply Fajan’s Rule.

• Predict trend in MP, solubility, colour from polarisation considerations.

• Explain metallic bonding via electron-sea model & relate to metal properties.

• Recognise and categorise intermolecular forces.

Homework / Practice Mapping (quick reference)

• Textbook & Tatva exercises covering: lattice enthalpy, Fajan’s rule, metallic bond, IMF, hybridisation, VSEPR, MO theory.

• Assignments 1–9 & Tatva numbers as listed (consult hand-out for Q numbers).

Consolidated Summary

• Smaller cation, larger anion, higher charges, pseudo-noble gas configuration → greater polarisation → more covalent character.

• More covalent ⇒ lower lattice energy, lower MP, lower solubility in polar solvents, often coloured.

• Metallic bond arises from electrostatic attraction between a positive ion lattice & delocalised electrons, imparting conductivity and ductility.

• Intermolecular forces control physical states & properties of molecular substances and are weaker than bonds within molecules.