Chemical Bonding

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Chemical bonding is the force that holds atoms together in compounds. Understanding why and how atoms bond — and predicting the shapes and properties of resulting molecules — is foundational to all of chemistry. Three primary types of bonding exist: ionic, covalent, and metallic, though most bonds exist on a spectrum between these ideal types.

Ionic Bonding:

Ionic bonds form when one atom completely transfers one or more electrons to another, creating oppositely charged ions held together by electrostatic attraction. This occurs between atoms with large electronegativity differences (typically > 1.7 on the Pauling scale).

Born-Haber cycle energy calculation for NaCl: $$\Delta H_f^\circ = \Delta H_{atom} + \frac{1}{2}\Delta H_{diss}(Cl_2) + I.E.(Na) + E.A.(Cl) + \Delta H_{lattice}$$ Where: atomisation energy of Na = 107 kJ/mol, bond dissociation of Cl₂ = 243 kJ/mol, ionisation energy of Na = 496 kJ/mol, electron affinity of Cl = -349 kJ/mol, lattice energy = -787 kJ/mol. Net $\Delta H_f = -411$ kJ/mol.

Covalent Bonding:

Covalent bonds form when atoms share electron pairs. The shared electrons contribute to the outer shells of both atoms, achieving stable octet configurations. Covalent bonds can be:

• Single bond (σ): One shared electron pair, bond length ~1.54 Å in C-C
• Double bond (σ + π): Two shared pairs, shorter and stronger (~1.34 Å)
• Triple bond (σ + π + π): Three shared pairs, shortest and strongest (~1.20 Å)

Electronegativity and Bond Polarity:

Electronegativity (Pauling scale) measures an atom’s ability to attract bonding electrons. Fluorine is the most electronegative element (EN = 3.98). A bond between atoms with electronegativity difference $\Delta EN$:

• $\Delta EN > 1.7$: predominantly ionic bond
• $0.4 < \Delta EN < 1.7$: polar covalent bond (dipole moment: $\mu = \delta \times d$)
• $\Delta EN < 0.4$: non-polar covalent bond

VSEPR Theory — Predicting Molecular Shapes:

The Valence Shell Electron Pair Repulsion theory states that electron pairs (bonding and non-bonding/lone pairs) around a central atom arrange themselves to minimise repulsion.

Steric Number	Arrangement	Bond Angles	Example
2	Linear	180°	BeCl₂, CO₂
3	Trigonal planar	120°	BF₃, AlCl₃
4	Tetrahedral	109.5°	CH₄, SiCl₄
3	Trigonal pyramidal	~107°	NH₃, PCl₃
2	Bent/V-shaped	~104.5°	H₂O
5	Trigonal bipyramidal	90°, 120°	PCl₅ (axial ≠ equatorial)
6	Octahedral	90°	SF₆

⚡ Exam Tip (MDCAT): In VSEPR, lone pairs exert greater repulsion than bonding pairs, so the H-N-H angle in ammonia (107°) is less than the ideal tetrahedral angle (109.5°), and the H-O-H angle in water (104.5°) is even smaller because oxygen has two lone pairs. This is a common MDCAT question. Also remember: PCl₅ has two types of chlorine — axial (longer bond, weaker) and equatorial (shorter bond, stronger). This is why PF₅ and PCl₅ exist but NF₅ does not (nitrogen cannot expand its octet due to lack of d-orbitals in the valence shell).

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🟡 Standard — Regular Study (2d–2mo)

For students who want genuine understanding and structural mastery.

Hybridisation:

Hybridisation is the mixing of atomic orbitals to form new hybrid orbitals with different shapes and energies, enabling better bonding description.

• sp³ (tetrahedral): One s + three p orbitals combine to form four equivalent sp³ orbitals directed to the corners of a tetrahedron (109.5° apart). Found in alkanes (methane CH₄, ethane C₂H₆), ammonia (NH₃), water (H₂O).
• sp² (trigonal planar): One s + two p orbitals mix, leaving one pure p orbital perpendicular to the plane. Found in alkenes (ethylene H₂C=CH₂), borane (BH₃), carbonyl groups (C=O).
• sp (linear): One s + one p orbital mix, leaving two pure p orbitals perpendicular to each other and to the bond axis. Found in alkynes (acetylene HC≡CH), BeCl₂, CO₂, cyanide ion (CN⁻).

sp³d and sp³d² Hybridisation:

Phosphorus pentachloride (PCl₅) uses sp³d hybridisation of phosphorus — the phosphorus atom promotes one 3s electron to 3d orbital, enabling five hybrid orbitals. The resulting trigonal bipyramidal shape has three equatorial (120° apart) and two axial (90° to equatorial) positions.

Sulphur hexafluoride (SF₆) uses sp³d² hybridisation — six equivalent orbitals directed to the corners of an octahedron. Both PCl₅ and SF₆ are hypervalent molecules (expand octet), which was historically explained by d-orbital participation, though modern computational chemistry suggests the bonding is more complex.

Dipole Moment and Polarity:

The dipole moment $\mu = Q \times r$ (charge × distance between centres) in Debye units (D). A molecule with polar bonds may still be non-polar overall if the bond dipoles cancel (e.g., CO₂ is linear, so the two C=O dipoles cancel; BF₃ is trigonal planar, three F dipoles cancel).

Water has a dipole moment of 1.85 D because it is bent (104.5°) — the dipoles do not cancel. This is why water is a polar molecule and an excellent solvent for ionic compounds.

Hydrogen Bonding:

A special type of dipole-dipole attraction between a hydrogen atom bonded to a highly electronegative element (F, O, or N) and a lone pair on another electronegative atom. Hydrogen bonds have bond energies of 10–40 kJ/mol — much weaker than covalent bonds (~200–400 kJ/mol) but much stronger than van der Waals forces.

Water’s hydrogen bonding explains:

• High boiling point (100°C, anomalously high for its molecular weight)
• High surface tension
• Ice being less dense than water (open cage-like structure in solid state)
• Capillary action in plants

⚡ Common MDCAT Mistake: Students confuse hydrogen bonding with ionic or covalent bonding. Hydrogen bonding is an intermolecular force (between molecules), not an intramolecular bond. It explains the physical properties of substances, not their chemical reactivity.

Valence Bond Theory vs Molecular Orbital Theory:

Valence Bond (VB) Theory: Bonds form when atomic orbitals on adjacent atoms overlap. Overlap can be sigma (head-on, maximum along the bond axis) or pi (sideways, above and below the bond axis).

MO Theory: Atomic orbitals combine mathematically to form molecular orbitals that are delocalised over the entire molecule. Bonding MOs are lower in energy than atomic orbitals; antibonding MOs are higher. Electrons fill from lowest to highest energy (Aufbau principle).

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

MO Theory for Diatomic Molecules:

For O₂ and beyond, the MO order is: $\sigma1s < \sigma^*1s < \sigma2s < \sigma^*2s < \pi2p_x = \pi2p_y < \sigma2p_z < \pi^*2p_x = \pi^*2p_y < \sigma^*2p_z$

For O₂ (16 electrons): Bond order = (8 bonding − 4 antibonding)/2 = 2. This matches the double bond (O=O). O₂ has two unpaired electrons in the $\pi^*$ orbitals — hence it is paramagnetic (attracted to magnetic fields), which VB theory cannot explain but MO theory correctly predicts.

For N₂ (14 electrons): Bond order = (8 bonding − 2 antibonding)/2 = 3. Triple bond: one sigma bond from $\sigma2p_z$ and two pi bonds from $\pi2p_x$ and $\pi2p_y$.

Bond order correlation with bond properties:

Bond Order	Bond Length (Å)	Bond Energy (kJ/mol)
1 (e.g., F₂)	~1.42	~159
2 (e.g., O₂)	~1.21	~498
3 (e.g., N₂)	~1.10	~945

Resonance Structures — Formal Charge Calculation:

Formal charge helps determine the most plausible resonance structure: $$\text{Formal charge} = \text{Valence electrons} - \text{Non-bonding electrons} - \frac{\text{Bonding electrons}}{2}$$

For ozone (O₃): The central oxygen has formal charge +1, the terminal oxygens have formal charges 0 and -1. The resonance structures show the O-O bonds as having bond order 1.5, explaining why O₃ has a bond angle of 117° (greater than the 104.5° of water, because lone pair repulsion is less with formal positive charge on the central O).

For nitrate ion (NO₃⁻): Three equivalent resonance structures with N having formal charge +1 and each O having formal charge -2/3 (averaged). The N-O bond has bond order 1.33.

Coordinate/Dative Bond:

A covalent bond where both electrons come from the same atom. Once formed, it is indistinguishable from a regular covalent bond. Examples: CO (carbon monoxide), H₃O⁺ (hydronium ion), NH₄⁺ (ammonium ion), SO₂ (one dative bond between S and each O).

⚡ MDCAT Advanced Note: Fajan’s Rules for ionic vs covalent character: A small cation with high positive charge and an anion with large size and high negative charge gives maximum covalent character. For example, AlCl₃ is covalent (small Al³⁺ polarises the large Cl⁻ ion), while NaCl is highly ionic. This is the basis of the HSAB (Hard-Soft Acid-Base) concept: hard acids prefer to bond with hard bases; soft acids prefer soft bases.

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