1. Valence Shell Electron Pair Repulsion (VSEPR) Theory
- Core Principle: Electron pairs around the central atom arrange themselves in three-dimensional space to minimize electrostatic repulsion.
- Repulsion Magnitude Hierarchy:
$$\text{Lone Pair - Lone Pair} > \text{Lone Pair - Bond Pair} > \text{Bond Pair - Bond Pair}$$
- Lone pairs occupy more spatial volume than bonding pairs because they are attracted to only a single atomic nucleus.
- Steric Number Formula:
$$\text{Steric Number} = \text{Number of Bonded Atoms } (\sigma\text{ bonds}) + \text{Number of Lone Pairs on Central Atom}$$
| Steric Number | Bonding Pairs | Lone Pairs | Molecular Geometry | Ideal / Actual Bond Angle | Representative Example |
|---|---|---|---|---|---|
| 2 | 2 | 0 | Linear | $180^\circ$ | $\text{BeCl}_2, \text{CO}_2$ |
| 3 | 3 | 0 | Trigonal Planar | $120^\circ$ | $\text{BF}_3, \text{AlCl}_3$ |
| 3 | 2 | 1 | Bent / V-Shaped | $< 120^\circ \text{ (approx } 119^\circ\text{)}$ | $\text{SO}_2, \text{SnCl}_2$ |
| 4 | 4 | 0 | Tetrahedral | $109.5^\circ$ | $\text{CH}_4, \text{SiCl}_4, \text{NH}_4^+$ |
| 4 | 3 | 1 | Trigonal Pyramidal | $107.5^\circ \text{ (or } 107^\circ\text{)}$ | $\text{NH}_3, \text{PCl}_3, \text{H}_3\text{O}^+$ |
| 4 | 2 | 2 | Bent / Angular | $104.5^\circ$ | $\text{H}_2\text{O}, \text{H}_2\text{S}, \text{OF}_2$ |
| 5 | 5 | 0 | Trigonal Bipyramidal | $90^\circ \text{ (axial), } 120^\circ \text{ (equatorial)}$ | $\text{PCl}_5$ |
| 6 | 6 | 0 | Octahedral | $90^\circ$ | $\text{SF}_6$ |
| Parameter | PTB Standard | Federal / NBF Standard | PMDC Consensus Rule |
|---|---|---|---|
| Bond Angle in Ammonia ($\text{NH}_3$) | Gives $107.5^\circ$ due to single lone pair repulsion. | Lists $107^\circ$ as standard rounded angle. | Both $107^\circ$ and $107.5^\circ$ accepted (look for angle reduction from $109.5^\circ$). |
| Bond Angle in Water ($\text{H}_2\text{O}$) | Gives $104.5^\circ$ due to two lone pairs. | Gives $104.5^\circ$ as standard bent angle. | $104.5^\circ$ is standard. |
| Coordinate Covalent Bond | Defined as dative bond where one atom donates both electrons. | Emphasizes that once formed, dative bonds are indistinguishable from normal covalent bonds. | Chemically and physically identical to regular covalent bonds post-formation. |
2. Orbital Hybridisation and Intermolecular Forces
Hybridisation States and Molecular Geometry
Hybridisation involves the mixing of atomic orbitals of slightly different energies to produce entirely degenerate hybrid orbitals.
- $sp^3$ Hybridisation: 1 $s$ orbital $+ 3$ $p$ orbitals produce 4 equivalent $sp^3$ hybrid orbitals directed toward tetrahedral vertices ($25\% \text{ s-character}, 75\% \text{ p-character}$).
- $sp^2$ Hybridisation: 1 $s$ orbital $+ 2$ $p$ orbitals produce 3 equivalent $sp^2$ hybrid orbitals in a trigonal plane at $120^\circ$ ($33.3\% \text{ s-character}, 66.7\% \text{ p-character}$), leaving one unhybridized $p$ orbital for $\pi$-bonding.
- $sp$ Hybridisation: 1 $s$ orbital $+ 1$ $p$ orbital produce 2 linear $sp$ hybrid orbitals at $180^\circ$ ($50\% \text{ s-character}, 50\% \text{ p-character}$), leaving two unhybridized $p$ orbitals for two $\pi$-bonds.
- Bond Strengths and Lengths: As $s$-character increases ($sp^3 < sp^2 < sp$), electrons are held closer to the nucleus, making the bond shorter, stronger, and more electronegative.
Intermolecular Forces (Van der Waals Forces)
- Dipole-Dipole Attractions: Electrostatic attractions between permanent dipoles in polar molecules (such as $\text{HCl}$ or $\text{SO}_2$).
- Hydrogen Bonding: Exceptionally strong dipole-dipole attraction occurring when hydrogen is covalently bonded to highly electronegative, small atoms with lone pairs (specifically Fluorine, Oxygen, or Nitrogen).
- Explains the anomalous high boiling points of $\text{H}_2\text{O}$, $\text{HF}$, and $\text{NH}_3$ compared to their heavier group hydrides.
- London Dispersion Forces: Temporary, instantaneous induced dipole attractions present in all atoms and molecules. Strength scales directly with polarizability, molecular mass, and surface area.
The 15-Second Elimination Shortcut
Calculate the hybridisation index ($H$) of the central atom using the rapid valence formula:
$$H = \frac{1}{2}\left[V + M - C + A\right]$$
Where $V$ is valence electrons of the central atom, $M$ is number of monovalent surrounding atoms ($\text{H, F, Cl, Br, I}$), $C$ is positive charge on the cation, and $A$ is negative charge on the anion.
- If $H = 2 \implies sp$
- If $H = 3 \implies sp^2$
- If $H = 4 \implies sp^3$
- If $H = 5 \implies sp^3d$
For $\text{NH}_4^+$: $H = \frac{1}{2}[5 + 4 - 1 + 0] = \frac{8}{2} = 4 \implies sp^3$ hybridisation in under 10 seconds.
The Clinical White Coat Preview
In molecular genetics and clinical pathology, hydrogen bonding provides the precise structural stability required for the DNA double helix. Adenine pairs with Thymine via two hydrogen bonds, while Guanine pairs with Cytosine via three hydrogen bonds. In Sickle Cell Anemia, a single missense point mutation changes hydrophilic glutamic acid to hydrophobic valine at position 6 of the $\beta$-globin chain. This alters hydrophobic and hydrogen bonding interactions, causing mutant deoxygenated hemoglobin ($\text{HbS}$) to polymerize into rigid fibrous rods that distort red blood cells into sickle shapes, causing painful vaso-occlusive crises and splenic infarction.
Frequently Asked Questions
Q: Why is carbon dioxide nonpolar even though the carbon-oxygen bonds are polar?
Carbon dioxide ($\text{CO}_2$) possesses a linear geometry ($O=C=O$) with $sp$ hybridisation. The two equal carbon-oxygen bond dipoles point in opposite directions at $180^\circ$, canceling each other out and yielding a net molecular dipole moment of zero ($\mu = 0\text{ D}$).
Q: Why is water a liquid at room temperature while hydrogen sulfide is a gas?
Oxygen has a much higher electronegativity and smaller atomic radius than sulfur, allowing water molecules to form extensive three-dimensional intermolecular hydrogen bonding networks. Hydrogen sulfide ($\text{H}_2\text{S}$) forms only weak dipole-dipole attractions and London forces, existing as a gas at standard temperature.
Q: What is the hybridisation of xenon in xenon tetrafluoride (XeF4)?
Xenon has 8 valence electrons. In $\text{XeF}_4$, xenon forms 4 single covalent $\sigma$-bonds with four fluorine atoms and retains 2 lone pairs. The steric number is $4 + 2 = 6$, giving $sp^3d^2$ hybridisation with a square planar molecular geometry.
Start Retaining for Real: Master MDCAT Chemical Bonding: VSEPR, Hybridisation, and Dipole Moments with Active Recall
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