Chemical Bonding and Molecular Structure

Inorganic Chemistry Weightage: 4–5 Questions (16–20 Marks) NMC Unit 3

“Chemical bonding is the architectural grammar of chemistry. From the directional overlaps of hybrid orbitals to the delocalised contours of molecular orbital theory, mastering VSEPR geometries, bond orders, and dipole cancellations guarantees 16 to 20 marks on the NEET paper.”

— SCORECHEM ACADEMIC TEAM

1. Octet Rule, Lewis Dot Symbols & Formal Charge

Lewis Theory of Valence: Atoms combine either by electron transfer (electrovalent/ionic bond) or electron sharing (covalent bond) to achieve an outer octet ( $ns^2np^6$ ) mimicking noble gases.
Calculation of Formal Charge (F.C.):
$\text{F.C.} = V - L - \frac{1}{2}S$
Where $V$ $V$ is valence electrons of isolated atom, $L$ $L$ is lone pair (non-bonding) electrons, and $S$ $S$ is shared (bonding) electrons.
- Ozone ( $\text{O}_3$ ) Calculation:
  - Central Oxygen ( $\text{O}_1$ ): $6 - 2 - \frac{1}{2}(6) = \mathbf{+1}$
  - Double-bonded Oxygen ( $\text{O}_2$ ): $6 - 4 - \frac{1}{2}(4) = \mathbf{0}$
  - Single-bonded Oxygen ( $\text{O}_3$ ): $6 - 6 - \frac{1}{2}(2) = \mathbf{-1}$
Exceptions to the Octet Rule:
1. Incomplete Octet: Central atom has $<8$ electrons ( $\text{LiCl}, \text{BeH}_2, \text{BCl}_3, \text{BF}_3, \text{AlCl}_3$ ).
2. Odd-Electron Species: Unpaired valence electrons exist ( $\text{NO}, \text{NO}_2$ ).
3. Expanded Octet: Central atom from Period 3 onwards utilizes empty $d$ -orbitals to hold $>8$ electrons ( $\text{PF}_5$ [10e], $\text{SF}_6$ [12e], $\text{H}_2\text{SO}_4$ [12e]).

⚠️ NEET Trap: Limitations of Octet Theory The octet rule does not account for the shapes of molecules, relative thermodynamic stability, or the reactivity of noble gases like xenon and krypton ($\text{XeF}_2, \text{XeF}_4, \text{KrF}_2$).

2. Ionic Bonding, Lattice Enthalpy & Fajan's Rules

Formation Criteria: Favoured by low ionisation enthalpy of metal, high negative electron gain enthalpy of non-metal, and high lattice enthalpy of crystal.
Lattice Enthalpy ( $\Delta_{\text{lattice}}H$ ): Energy required to separate 1 mole of a crystalline ionic solid into gaseous constituent ions: $\text{NaCl}(s) \longrightarrow \text{Na}^+(g) + \text{Cl}^-(g) \quad (\Delta H = +788\text{ kJ mol}^{-1})$
Fajan's Rules (Covalent Character in Ionic Bonds):
1. Cation Size: Smaller cation $\implies$ greater polarising power $\implies$ higher covalent character ( $\text{LiCl} > \text{NaCl} > \text{KCl}$ ).
2. Anion Size: Larger anion $\implies$ more polarisable electron cloud $\implies$ higher covalent character ( $\text{LiI} > \text{LiBr} > \text{LiCl} > \text{LiF}$ ).
3. Charge on Ions: Higher positive or negative charge $\implies$ increased covalent character ( $\text{AlCl}_3 > \text{MgCl}_2 > \text{NaCl}$ ).
4. Electronic Configuration: Cations with pseudo-noble gas configurations ( $18e^-$ : $ns^2np^6nd^{10}$ , e.g., $\text{Cu}^+, \text{Ag}^+$ ) are more polarising than noble gas configurations ( $8e^-$ : $ns^2np^6$ , e.g., $\text{Na}^+, \text{K}^+$ ).

3. Bond Parameters, Resonance & Dipole Moments

Bond Parameters:
- Bond Order: $\text{BO} \propto \text{Bond Dissociation Enthalpy} \propto \frac{1}{\text{Bond Length}}$ .
- Resonance: Canonical forms have no independent physical existence. The actual molecule is a resonance hybrid possessing lower potential energy and averaged intermediate bond lengths (e.g., $\text{C}-\text{O}$ bond in $\text{CO}_3^{2-}$ is $1.33$ bond order; $\text{O}-\text{O}$ in $\text{O}_3$ is $128\text{ pm}$ ).
Dipole Moment ( $\mu$ ):
$\mu = Q \times r \quad (1\text{ D} = 3.33564 \times 10^{-30}\text{ C m})$
- Vector sum determines molecular polarity. Symmetrical geometries ( $\text{CO}_2, \text{BF}_3, \text{CH}_4, \text{CCl}_4, \text{SF}_6, \text{XeF}_4$ ) have $\mu = 0$ .
- The $\text{NH}_3$ vs $\text{NF}_3$ Distinction: In $\text{NH}_3$ , nitrogen's lone pair dipole reinforces the resultant $\text{N}-\text{H}$ bond dipoles ( $\mu = 1.47\text{ D}$ ). In $\text{NF}_3$ , the lone pair dipole opposes the resultant $\text{N}-\text{F}$ bond dipoles ( $\mu = 0.23\text{ D}$ ).

4. VSEPR Theory: Predicting Geometrical Shapes

Repulsion order: $\text{lp}-\text{lp} > \text{lp}-\text{bp} > \text{bp}-\text{bp}$ . Lone pairs occupy more spatial volume on the central atom than bonding pairs.

Type	Hybridisation	Bond Pairs	Lone Pairs	Ideal Angle	Actual Shape	High-Yield Examples
$\text{AB}_2$	$sp$	2	0	$180^\circ$	Linear	$\text{BeCl}_2, \text{CO}_2, \text{HCN}$
$\text{AB}_3$	$sp^2$	3	0	$120^\circ$	Trigonal Planar	$\text{BF}_3, \text{BCl}_3, \text{SO}_3$
$\text{AB}_2\text{E}$	$sp^2$	2	1	$<120^\circ$	Bent / Angular	$\text{SO}_2 (119.5^\circ), \text{O}_3$
$\text{AB}_4$	$sp^3$	4	0	$109.5^\circ$	Tetrahedral	$\text{CH}_4, \text{NH}_4^+, \text{CCl}_4$
$\text{AB}_3\text{E}$	$sp^3$	3	1	$<109.5^\circ$	Trigonal Pyramidal	$\text{NH}_3 (107^\circ), \text{PCl}_3, \text{ClO}_3^-$
$\text{AB}_2\text{E}_2$	$sp^3$	2	2	$<109.5^\circ$	Bent / V-Shaped	$\text{H}_2\text{O} (104.5^\circ), \text{H}_2\text{S}, \text{OF}_2$
$\text{AB}_5$	$sp^3d$	5	0	$90^\circ, 120^\circ$	Trigonal Bipyramidal	$\text{PCl}_5, \text{PF}_5$
$\text{AB}_4\text{E}$	$sp^3d$	4	1	$<90^\circ, <120^\circ$	See-Saw	$\text{SF}_4$
$\text{AB}_3\text{E}_2$	$sp^3d$	3	2	$<90^\circ$	T-Shaped	$\text{ClF}_3, \text{BrF}_3$
$\text{AB}_2\text{E}_3$	$sp^3d$	2	3	$180^\circ$	Linear	$\text{XeF}_2, \text{I}_3^-$
$\text{AB}_6$	$sp^3d^2$	6	0	$90^\circ$	Octahedral	$\text{SF}_6, [\text{CrF}_6]^{3-}$
$\text{AB}_5\text{E}$	$sp^3d^2$	5	1	$<90^\circ$	Square Pyramidal	$\text{BrF}_5, \text{IF}_5$
$\text{AB}_4\text{E}_2$	$sp^3d^2$	4	2	$90^\circ$	Square Planar	$\text{XeF}_4$

5. Valence Bond Theory & Hybridisation Mechanics

Sigma ( $\sigma$ ) vs Pi ( $\pi$ ) Bonds:
- $\sigma$ -bonds result from end-to-end (head-on) axial overlap ( $s-s, s-p_z, p_z-p_z$ ).
- $\pi$ -bonds result from lateral (sideways) overlap of parallel $p$ -orbitals perpendicular to the internuclear axis. $\sigma$ is stronger than $\pi$ due to larger overlap extent.
Steric Number Rule for Hybridisation: $\text{Steric Number} = (\text{Number of }\sigma\text{ bonds}) + (\text{Number of lone pairs on central atom})$
Involvement of $d$ -Orbitals:
- $sp^3d \implies s + p_x + p_y + p_z + d_{z^2}$ (axial bonds formed by $p_z + d_{z^2}$ ).
- $sp^3d^2 \implies s + p_x + p_y + p_z + d_{x^2-y^2} + d_{z^2}$ (octahedral geometries).
- $dsp^2 \implies d_{x^2-y^2} + s + p_x + p_y$ (square planar geometries, e.g., $[\text{Ni}(\text{CN})_4]^{2-}$ ).

6. Molecular Orbital Theory (MOT)

Linear Combination of Atomic Orbitals ( $\psi_{\text{MO}} = \psi_A \pm \psi_B$ ) yields lower-energy bonding MOs ( $\sigma, \pi$ ) and higher-energy antibonding MOs ( $\sigma^*, \pi^*$ ).

Energy Level Orders

For Light Diatomics ( $\le 14$ electrons: $\text{B}_2, \text{C}_2, \text{N}_2$ ) with $2s-2p$ mixing: $\sigma 1s < \sigma^* 1s < \sigma 2s < \sigma^* 2s < (\pi 2p_x = \pi 2p_y) < \sigma 2p_z < (\pi^* 2p_x = \pi^* 2p_y) < \sigma^* 2p_z$
For Heavy Diatomics ( $> 14$ electrons: $\text{O}_2, \text{F}_2$ ) without $2s-2p$ mixing: $\sigma 1s < \sigma^* 1s < \sigma 2s < \sigma^* 2s < \sigma 2p_z < (\pi 2p_x = \pi 2p_y) < (\pi^* 2p_x = \pi^* 2p_y) < \sigma^* 2p_z$

Calculation of Bond Order & Magnetic Character

\text{Bond Order} = \frac{N_b - N_a}{2}

$\text{N}_2$ ( $14e^-$ ): $\text{BO} = \frac{10-4}{2} = \mathbf{3}$ (Diamagnetic).
$\text{O}_2$ ( $16e^-$ ): $\text{BO} = \frac{10-6}{2} = \mathbf{2}$ (Paramagnetic with $2$ unpaired electrons in $\pi^* 2p_x, \pi^* 2p_y$ ).
$\text{O}_2^+$ ( $15e^-$ ): $\text{BO} = \frac{10-5}{2} = \mathbf{2.5}$ (Paramagnetic).
$\text{O}_2^-$ ( $17e^-$ ): $\text{BO} = \frac{10-7}{2} = \mathbf{1.5}$ (Paramagnetic).
$\text{O}_2^{2-}$ ( $18e^-$ ): $\text{BO} = \frac{10-8}{2} = \mathbf{1.0}$ (Diamagnetic).

7. Hydrogen Bonding Framework

Attractive dipole force where hydrogen is covalently linked to strongly electronegative atoms ( $\text{F}, \text{O}, \text{N}$ ).

Bond Strength Order: $\text{H}-\text{F}\dots\text{H} > \text{H}-\text{O}\dots\text{H} > \text{H}-\text{N}\dots\text{H}$ .
Types of Hydrogen Bonding:
1. Intermolecular: Between separate molecules ( $\text{HF}, \text{H}_2\text{O}, \text{C}_2\text{H}_5\text{OH}, p\text{-nitrophenol}$ ). Elevates boiling points, viscosity, and water miscibility.
2. Intramolecular: Within the same molecule between adjacent functional groups (e.g., ortho-nitrophenol, salicylaldehyde). Reduces boiling point and confers steam volatility.