4.2 Chemical Bonding, Molecular Geometry & Intermolecular Forces

4.2 Chemical Bonding, Molecular Geometry & Intermolecular Forces

Chemical bonding explains how atoms combine to form stable compounds. For the AMC exam, mastering VSEPR theory, hybridization, Molecular Orbital Theory (MOT), dipole moments, and intermolecular forces is essential.

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Primary Chemical Bonds & Lattice Energy

1. Ionic Bonding: Complete transfer of valence electrons from a electropositive metal to an electronegative non-metal. Ionic compounds form 3D crystalline lattices held by electrostatic forces.
   • Lattice Energy ($\Delta H_{lattice}$): Energy released when 1 mole of an ionic crystal is formed from its gaseous ions: $\text{Na}^+_{(g)} + \text{Cl}^-_{(g)} \rightarrow \text{NaCl}_{(s)} \quad \Delta H_{lattice} = -787 \text{ kJ/mol}$
   • Lattice energy increases with higher ionic charge ($Q_1 Q_2$) and smaller ionic radii ($r_+ + r_-$).
2. Covalent Bonding: Mutual sharing of electron pairs. Exceptions to the Octet Rule include electron-deficient molecules (e.g., $\text{BF}_3$, 6 valence $e^-$) and expanded octet molecules (e.g., $\text{PCl}_5$ with 10 $e^-$, $\text{SF}_6$ with 12 $e^-$).
3. Coordinate Covalent (Dative) Bond: A covalent bond where both shared electrons are provided by a single donor atom possessing a lone pair (e.g., ammonium ion $\text{NH}_4^+$, hydronium ion $\text{H}_3\text{O}^+$, and Lewis acid-base adduct $\text{BF}_3\cdot\text{NH}_3$).

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Valence Shell Electron Pair Repulsion (VSEPR) Theory

VSEPR theory dictates that valence electron pairs around a central atom arrange themselves to minimize electrostatic repulsion and maximize mutual distance.

Order of Repulsive Forces

$\text{Lone Pair - Lone Pair (LP-LP)} > \text{Lone Pair - Bond Pair (LP-BP)} > \text{Bond Pair - Bond Pair (BP-BP)}$

VSEPR Molecular Geometry Summary Table

• Note on Angle Distortions: In $\text{NH}_3$, 1 lone pair compresses the tetrahedral angle from $109.5^\circ$ to $107.5^\circ$. In $\text{H}_2\text{O}$, 2 lone pairs compress it further to $104.5^\circ$.

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Valence Bond Theory (VBT) & Hybridization

VBT explains covalent bond formation through atomic orbital overlap:

• $\sigma$ (Sigma) Bond: Formed by head-on (axial) overlap along the internuclear axis. Stronger bond with free rotation.
• $\pi$ (Pi) Bond: Formed by sideways (lateral/parallel) overlap of unhybridized $p$-orbitals. Weaker bond, restricted rotation.
  • Single bond = $1 \sigma$
  • Double bond = $1 \sigma + 1 \pi$
  • Triple bond = $1 \sigma + 2 \pi$

Types of Hybridization

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Molecular Orbital Theory (MOT)

MOT describes electrons over the entire molecule using bonding and antibonding molecular orbitals formed by Linear Combination of Atomic Orbitals (LCAO).

• Bonding MOs ($\sigma, \pi$): Lower energy, higher stability, constructive interference.
• Antibonding MOs ($\sigma^, \pi^$): Higher energy, lower stability, destructive interference.

Key Formulas & Rules

• Bond Order: $\text{Bond Order} = \frac{N_b - N_a}{2}$ where $N_b$ is the number of bonding electrons and $N_a$ is the number of antibonding electrons.
• Higher bond order signifies greater bond energy, shorter bond length, and higher molecular stability.
• Paramagnetism: Unpaired electrons in MOs (attracted to magnetic field). Example: $\text{O}_2$ has 2 unpaired electrons in $\pi^* 2p_y$ and $\pi^* 2p_z$ (Bond Order = 2).
• Diamagnetism: All electrons paired (repelled by magnetic field). Example: $\text{N}_2$ (Bond Order = 3).

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Dipole Moments & Intermolecular Forces (IMFs)

Dipole Moment ($\mu$)

Vector product of electric charge ($q$) and distance ($d$): $\mu = q \times d$.

• Measured in Debye ($D$); $1 D = 3.336 \times 10^{-30} \text{ C}\cdot\text{m}$.
• Symmetrical molecules have net dipole moment $\mu = 0 \text{ D}$ due to vector cancellation (e.g., $\text{CO}_2, \text{BF}_3, \text{CCl}_4, \text{CH}_4, \text{trans-1,2-dichloroethene}$).
• Unsymmetrical polar molecules have $\mu > 0$ (e.g., $\text{H}_2\text{O} = 1.85 \text{ D}, \text{NH}_3 = 1.47 \text{ D}, \text{CHCl}_3 = 1.04 \text{ D}, \text{cis-1,2-dichloroethene}$).

Intermolecular Forces (van der Waals Forces)

1. Dipole-Dipole Forces: Electrostatic attraction between polar molecules (e.g., $\text{HCl} \cdots \text{HCl}$).
2. Dipole-Induced Dipole Forces (Debye Forces): Polar molecule induces a temporary dipole in a non-polar molecule.
3. London Dispersion Forces (LDF): Temporary dipole-induced dipole attraction present in all atoms and molecules, dominant in non-polar species (e.g., $\text{He, N}_2, \text{CH}_4$). LDF increases with molar mass, polarizability, and molecular surface area.
4. Hydrogen Bonding: Exceptionally strong electrostatic attraction between a Hydrogen atom bonded to a highly electronegative atom ($\text{F, O, N}$) and a lone pair on another electronegative atom.
   • Anomalous Properties of Water: Maximum density of liquid water occurs at $4^\circ\text{C}$. Ice has an open 3D cage-like hexagonal structure with lower density than liquid water, causing ice to float.

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Worked Numerical Examples

Example 1: Molecular Orbital Bond Order Calculation

Problem: Determine the bond order and magnetic character of the dioxygen cation $\text{O}_2^+$.

Solution:

1. Total valence electrons for $\text{O}_2^+$ (15 electrons): Configuration: $\sigma 1s^2 \sigma^* 1s^2 \sigma 2s^2 \sigma^* 2s^2 \sigma 2p_z^2 \pi 2p_x^2 \pi 2p_y^2 \pi^* 2p_x^1 \pi^* 2p_y^0$.
2. Bonding electrons $N_b = 10$, Antibonding electrons $N_a = 5$.
3. $\text{Bond Order} = \frac{10 - 5}{2} = 2.5$.
4. Because it contains 1 unpaired electron in $\pi^* 2p_x$, $\text{O}_2^+$ is paramagnetic.

Example 2: Counting $\sigma$ and $\pi$ Bonds

Problem: Calculate the number of $\sigma$ and $\pi$ bonds in a molecule of Ethyne (Acetylene, $\text{H-C}\equiv\text{C-H}$).

Solution:

• $2 \times \text{C-H}$ single bonds $= 2 \sigma$ bonds.
• $1 \times \text{C}\equiv\text{C}$ triple bond $= 1 \sigma + 2 \pi$ bonds.
• Total: $3 \sigma$ bonds and $2 \pi$ bonds.