Chapter 12 – Metallic Bonding, Polyatomic Ions, and Radii

Metallic Crystals & Electron Delocalization

• Metallic crystals resemble ionic lattices except that the outer-shell (valence) electrons are shared throughout the entire solid.
• Picture of overlap:
  • Each metal nucleus is surrounded by overlapping orbitals of neighboring atoms.
  • Overlaps create a 3-D “electron sea” or superhighway.
• Delocalization
  • Electrons are not tied to one nucleus; they can migrate quickly from one region to another.
  • If an external electron is “pushed” into one side of a wire, it repels resident electrons, propagating motion until an electron exits the other side.
• Consequences
  • Very low electrical resistance (e.g., copper wiring).
  • High thermal conductivity—heat transfer requires frequent particle collisions; mobile electrons increase collision rate.

Electrical & Thermal Conductivity in Metals

• Heat-conduction model
  • Hot region: particles (ions + delocalized electrons) move faster.
  • Cold region: particles move slower.
  • Rapid electron motion across the lattice equalizes kinetic energy quickly.
• Electricity conduction
  • Current = flow of charge; delocalized electrons serve as mobile charge carriers.
  • No need to break any bonds to move; lattice remains intact.

Polyatomic Ions & Coordinate (Dative/Heterolytic) Bonds

• Final bonding type in Chapter 12.
• Terminology
  • Coordinate (dative) bond ≡ heterolytic bond: both bonding electrons supplied by one atom.
  • Alternative name: coordination bond (common when metals have vacant d-orbitals).
• In polyatomic ions, multiple non-metals bond covalently inside the ion; the entire ion then participates in ionic bonding outside with counter-ions.

Formation of Ammonium Ion ( $\text{NH}_4^+$ )

• Start with ammonia ($\text{NH}_3$):
  • N has 5 valence e⁻; each H supplies 1 e⁻ ⇒ $8$ valence e⁻ satisfy octet.
  • Nitrogen retains one lone pair.
• In aqueous solution, abundant $\text{H}^+$ (protons) are attracted to the lone pair.
• Coordinate bond creation
  • Lone pair donates both electrons to bond with $\text{H}^+$.
  • Resulting ion: brackets + charge shown to emphasize charge is spread across all atoms.
• Lewis representation (charge outside the brackets):
  $[\;\text{H}\,–\,\text{N}\,(\text{H})_3\;]^+$

Charge Dispersal (Hypochondriacion)

• Surplus or deficiency of charge is not isolated on one atom.
• Hypochondriacion (advanced term)
  • Charge density is redistributed evenly over the entire polyatomic ion.
  • Lowers potential energy → stabilization.
• Mechanistic analogy: many atoms each “donate a few strands of hair” to cover a bald spot (electropositive center).
• Final full stabilization achieved when the ion pairs with an oppositely charged ion (e.g., $\text{NH}<em>4^+ + \text{Cl}^- \rightarrow \text{NH}</em>4\text{Cl}$).

Additional Example – Nitrate / Nitric Acid

• Nitric acid: $\text{HNO}<em>3$; polyatomic portion is $\text{NO}</em>3^-$ (nitrate).
• Inside nitrate
  • Mixture of homolytic (normal covalent) and heterolytic (coordinate) bonds.
• Overall charge $-1$ is delocalized over all O atoms and N according to resonance structures.

Polyatomic-Ion Summary (add to study notes)

• Non-metals bond covalently inside the ion.
• Resulting electron count creates net surplus (+) or deficit (–) of electrons.
• Charge is spread (hypochondriacion) → stabilizes the ion.
• Ion can then form an ionic salt with an oppositely charged partner.

Comparative Radii: Atomic, Ionic, Covalent & van der Waals

• All radii measure distance between a nucleus (+) and an electron cloud (–), but contexts differ.

Atomic Radius

• Single, isolated atom (often noble gas in solid form).
• Distance from nucleus to outermost electron.

Ionic Radius

• Same concept applied to an ion.
• Size depends on ion type:
  • $\text{Na}^+$ ≈ $102\ \text{pm}$ (smaller—lost an e⁻ shell).
  • $\text{Cl}^-$ ≈ $181\ \text{pm}$ (larger—added e⁻, increased e⁻–e⁻ repulsion).
• $1\ \text{pm} = 10^{-12}\ \text{m}$.

Covalent Radius

• Half the internuclear distance in a homonuclear diatomic molecule.
  $r<em>{\text{cov}} = \dfrac{d</em>{\text{nuc–nuc}}}{2}$
  Example: $\text{Cl}_2$.

van der Waals Radius

• Intermolecular, not intramolecular.
• Half the closest approach distance between non-bonded nuclei of adjacent molecules.
  $r<em>{\text{vdW}} = \dfrac{d</em>{\text{mol1–mol2}}}{2}$
• Useful for modeling molecular packing/crystal structures.

Connections, Implications & Exam Tips

• Metallic bonding → explains conductivity & malleability (electrons move, ions slide without breaking bonds).
• Polyatomic ions blend covalent (internal) and ionic (external) bonding; memorize common ion formulas, charges, and bonding nature.
• Charge delocalization lowers energy analogously to resonance; expect questions on stability and reactivity.
• Radii trends:
  • Cation radius < neutral atom; anion radius > neutral atom.
  • van der Waals > covalent ≈ atomic (general guideline).
• Always specify units (pm) and whether distances are intra- vs. intermolecular.