4.1 Ionic, Covalent, Polar Covalent & Metallic Bonding

Ionic, Covalent, Polar Covalent & Metallic Bonding

Quick Summary: Chemical bonding is an electrostatic phenomenon minimizing potential energy between atomic nuclei and valence electrons. Across the electronegativity difference continuum, bonds transition from nonpolar covalent (equal sharing) to polar covalent (unequal sharing with bond dipoles) to ionic (discrete cation-anion electrostatic attraction in crystal lattices). Metallic bonding employs a delocalized electron fluid that enables mechanical plasticity and conductivity, while network covalent solids establish rigid macromolecular frameworks of exceptional hardness and thermal stability.

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1. Thermodynamic Nature of Bonds & Potential Energy Curves

A chemical bond minimizes the potential energy of interacting atoms:

• Long-Range Attraction ($r > r_0$): As isolated atoms approach from infinite distance (where $E=0$), electrostatic attraction between each nucleus and the other atom's electron cloud pulls them together, lowering potential energy.
• Energy Minimum ($r = r_0$): At the equilibrium bond length ($r_0$, $74\text{ pm}$ for $\text{H}_2$), attractive electrostatic forces balance electron-electron and nucleus-nucleus repulsions. The depth of this potential well defines the bond dissociation energy ($D_e$, $436\text{ kJ/mol}$ for $\text{H}_2$).
• Short-Range Repulsion ($r < r_0$): Compressing nuclei closer than $r_0$ triggers severe internuclear repulsion and Pauli core electron repulsion, causing potential energy to rise steeply.

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2. The Electronegativity Difference Continuum

Bonding spans a continuous spectrum dictated by electronegativity difference ($\Delta\text{EN}$) on the Pauling scale:

• Nonpolar Covalent ($\Delta\text{EN} \le 0.4$): Electrons are shared equally between identical or similar atoms (e.g., $\text{H}_2, \text{Cl}_2$, and $\text{C}-\text{H}$ with $\Delta\text{EN} = 0.4$), producing zero permanent dipole.
• Polar Covalent ($0.4 < \Delta\text{EN} \le 1.8$): Unequal sharing creates partial charges ($\delta^+, \delta^-$) and a permanent bond dipole moment ($\mu = q \times r$), as in $\text{H}-\text{Cl}$ ($\Delta\text{EN} = 0.9$).
• Ionic ($\Delta\text{EN} > 1.8$): Large electronegativity differences cause electron transfer, forming ions held by electrostatic lattice forces (e.g., $\text{NaCl}$, $\Delta\text{EN} = 2.1$).

Pauling estimated percent ionic character as $\text{Ionic\%} = (1 - e^{-0.25(\Delta\text{EN})^2}) \times 100\%$. Gray areas exist: gaseous $\text{HF}$ has $\Delta\text{EN} = 1.9$, but hydrogen's high ionization energy maintains polar covalent sharing rather than full ionic separation.

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3. Ionic Lattices, Coulomb's Law & Lattice Energy

Ionic solids crystallize into three-dimensional arrays maximizing cation-anion attraction. The electrostatic potential energy follows Coulomb's law:

$E_{\text{coulomb}} = \frac{k_e \cdot q_1 q_2}{r_0}$

Lattice energy ($U_{\text{lattice}}$) is the energy required to separate one mole of solid into gaseous ions ($U > 0$):

$\text{MX}(s) \longrightarrow \text{M}^{z+}(g) + \text{X}^{z-}(g) \quad U_{\text{lattice}} \propto \frac{|q_1 q_2|}{r_+ + r_-}$

Worked Lattice Energy Comparison

Ionic charge magnitude takes precedence over interionic radius:

• $\text{NaCl}$ vs. $\text{MgO}$: Both have similar spacing ($r_0 \approx 282\text{ pm}$ for $\text{NaCl}$ vs. $212\text{ pm}$ for $\text{MgO}$). However, $\text{NaCl}$ has $|(+1)(-1)| = 1$ ($U = 787\text{ kJ/mol}$), whereas $\text{MgO}$ has $|(+2)(-2)| = 4$ ($U = 3791\text{ kJ/mol}$). The fourfold charge factor explains why $\text{MgO}$ melts at $2852\text{ }^\circ\text{C}$ while $\text{NaCl}$ melts at $801\text{ }^\circ\text{C}$.
• Size Effect: At constant charge, smaller ions achieve closer contact, increasing lattice energy: $U(\text{NaF}, 923\text{ kJ/mol}) > U(\text{NaCl}, 787\text{ kJ/mol}) > U(\text{KCl}, 715\text{ kJ/mol})$.

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4. The Born-Haber Cycle

Because lattice energy cannot be measured directly, it is determined via the Born-Haber cycle using Hess's law:

$\Delta H_f^\circ = \Delta H_{\text{sub}} + \text{IE} + \frac{1}{2}\text{BDE} + \text{EA} - U_{\text{lattice}}$

For sodium chloride ($\text{NaCl}$):

1. Sublimation of $\text{Na}(s) \rightarrow \text{Na}(g)$ ($+107.3\text{ kJ/mol}$)
2. Ionization of $\text{Na}(g) \rightarrow \text{Na}^+(g) + e^-$ ($+495.8\text{ kJ/mol}$)
3. Dissociation of $\frac{1}{2}\text{Cl}_2(g) \rightarrow \text{Cl}(g)$ ($+121.3\text{ kJ/mol}$)
4. Electron affinity of $\text{Cl}(g) + e^- \rightarrow \text{Cl}^-(g)$ ($-348.6\text{ kJ/mol}$)
5. Lattice formation of $\text{Na}^+ + \text{Cl}^- \rightarrow \text{NaCl}(s)$ ($-U_{\text{lattice}}$)

With $\Delta H_f^\circ(\text{NaCl}) = -411.2\text{ kJ/mol}$, solving yields $U_{\text{lattice}} = +787.0\text{ kJ/mol}$.

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5. Metallic Bonding, Band Theory & Alloys

In metals, low ionization energies allow valence electrons to delocalize into a mobile sea of electrons surrounding cation cores. In band theory, overlapping valence orbitals create continuous bands where the valence band overlaps the conduction band (zero band gap), enabling electrical and thermal conductivity. Non-directional bonding allows cation planes to slide under shear stress without repulsion, providing ductility and malleability.

Alloys: Substitutional vs. Interstitial

• Substitutional Alloys: Solute atoms replace host metal atoms of comparable radius (within $15\%$, Hume-Rothery rule). Examples: brass ($\text{Cu}/\text{Zn}$), bronze ($\text{Cu}/\text{Sn}$), sterling silver.
• Interstitial Alloys: Small nonmetal atoms ($\text{C}, \text{B}, \text{H}$) occupy interstitial voids between larger metal atoms, distorting lattice planes and impeding dislocation glide. This makes carbon steel significantly harder and stronger than pure elemental iron.

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6. Network Covalent Solids

Network covalent solids consist of continuous covalent frameworks extending across macroscopic crystals:

• Diamond: Carbon atoms are $sp^3$ hybridized in a rigid tetrahedral framework. Extreme hardness (Mohs 10), melting point $> 3550\text{ }^\circ\text{C}$, electrical insulator.
• Graphite: Carbon atoms are $sp^2$ hybridized in planar hexagonal sheets with delocalized $\pi$ electrons providing electrical conductivity parallel to the sheets. Weak dispersion forces between sheets permit sliding (lubricant).
• Quartz ($\text{SiO}_2$) & Carborundum ($\text{SiC}$): Corner-sharing $\text{SiO}_4$ tetrahedra or diamond-like $\text{SiC}$ networks provide extreme thermal stability and abrasive hardness.

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7. Comparative Matrix of Bonding Types