Exam Master Review Sheet - Chemical Bonding

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EXAM MASTER FORMULA SHEET

Chemical Bonding & Molecular Structure

Ultimate Revision for JEE Main, Advanced & NEET

1. Ionic Bonding, Lattice Energy & Fajan's Rules

Lattice Energy (\(U\)):

\[ U \propto \frac{|z^+ \cdot z^-|}{r^+ + r^-} \]

Energy released when 1 mole of solid ionic crystal is formed from isolated gaseous ions.

Charge dominates over size!

Born-Haber Cycle:

\(\Delta H_f = \Delta H_{sub} + \frac{1}{2}\Delta H_{diss} + IE + EA + U\)

Solubility Criteria: An ionic compound is generally soluble in water if:
Hydration Energy > Lattice Energy

Fajan's Rules (Covalent Character in Ionic Bonds):

No ionic bond is 100% ionic. Covalent character arises due to polarization of the anion by the cation.

High Polarizing Power (Cation):

• High charge on cation (e.g., \(Al^{3+} > Mg^{2+} > Na^+\))
• Small size of cation (e.g., \(Li^+ > Na^+ > K^+\))
• Pseudo-inert gas configuration (\(ns^2np^6nd^{10}\)) polarizes more than inert gas config (\(ns^2np^6\)). E.g., \(CuCl\) is more covalent than \(NaCl\).

High Polarizability (Anion):

• High negative charge on anion
• Large size of anion (e.g., \(I^- > Br^- > Cl^- > F^-\))

As Covalent Character \(\uparrow \implies\) M.P., B.P., & Solubility in water \(\downarrow\)

2. Hybridization & VSEPR Theory (Shapes)

Steric Number (\(Z\)) Calculation:

\[ Z = \frac{1}{2} [V + M - C + A] \]

V: Valence \(e^-\) of central atom

M: Monovalent atoms (H, F, Cl, Br, I) attached

C: Charge of Cation (-)

A: Charge of Anion (+)

VSEPR Repulsion Order:

Lone Pair - Lone Pair
>
Lone Pair - Bond Pair
>
Bond Pair - Bond Pair

Note: Multiple bonds act as a single super-pair for geometry but exert stronger repulsion than single bonds.

\(Z\)	Hybridization	Lone Pairs (lp)	Molecular Shape (Geometry)	Examples
2	\(sp\)	0	Linear (180°)	\(BeCl_2, CO_2, HCN\)
3	\(sp^2\)	0	Trigonal Planar (120°)	\(BF_3, SO_3, NO_3^-\)
		1	V-shape / Bent (< 120°)	\(SO_2, O_3, SnCl_2\)
4	\(sp^3\)	0	Tetrahedral (109°28')	\(CH_4, NH_4^+, SO_4^{2-}\)
		1	Trigonal Pyramidal (< 109.5°)	\(NH_3, PCl_3, H_3O^+\)
		2	V-shape / Bent (<< 109.5°)	\(H_2O, H_2S, OF_2\)
5	\(sp^3d\)	0	Trigonal Bipyramidal (TBP)	\(PCl_5, PF_5\)
		1	See-saw	\(SF_4\)
		2	T-shape	\(ClF_3, BrF_3\)
		3	Linear	\(XeF_2, I_3^-, ICl_2^-\)
6	\(sp^3d^2\)	0	Octahedral / Sq. Bipyramidal	\(SF_6\)
		1	Square Pyramidal	\(IF_5, BrF_5\)
		2	Square Planar	\(XeF_4, [Ni(CN)_4]^{2-}\)

3. Dipole Moment (\(\mu\)) & Formal Charge

Dipole Moment (\(\mu\)):

\[ \mu = q \times d \]

Units: Debye (D). \(1 \text{ D} = 3.3356 \times 10^{-30} \text{ C}\cdot\text{m}\) = \(10^{-18} \text{ esu}\cdot\text{cm}\)

% Ionic Character: \[ \% \text{ I.C.} = \frac{\mu_{\text{observed (experimental)}}}{\mu_{\text{calculated (100\% ionic)}}} \times 100 \]

Formal Charge (F.C.):

Apparent charge on an atom in a molecule/ion.

\[ F.C. = V - L - \frac{S}{2} \]

• V: Total valence electrons in free atom
• L: Total non-bonding (lone pair) electrons
• S: Total shared (bonding) electrons

The most stable Lewis structure has formal charges closest to zero.

4. Molecular Orbital Theory (MOT)

Bond Order (B.O.):

\[ \text{B.O.} = \frac{N_b - N_a}{2} \]

\(N_b\) = bonding \(e^-\), \(N_a\) = antibonding \(e^-\)

Key Relations:

• B.O. \(\propto\) Bond Dissociation Energy (Strength)
• B.O. \(\propto \frac{1}{\text{Bond Length}}\)
• If B.O. = 0 or negative, the molecule does not exist (e.g., \(He_2, Ne_2\)).
• Resonance Shortcut: \( \text{B.O.} = 1 + \frac{\text{Number of } \pi \text{ bonds}}{\text{Number of } \sigma \text{ bonds}} \) (e.g., \(CO_3^{2-}\) has B.O. = 1.33)

Energy Level Diagrams (Homonuclear Diatomics):

1. For \(\le 14\) electrons (\(B_2, C_2, N_2\)) — s-p mixing occurs:

\(\sigma 1s < \sigma^* 1s < \sigma 2s < \sigma^* 2s < \mathbf{(\pi 2p_x = \pi 2p_y) < \sigma 2p_z} < (\pi^* 2p_x = \pi^* 2p_y) < \sigma^* 2p_z\)

2. For \(> 14\) electrons (\(O_2, F_2\)) — No s-p mixing:

\(\sigma 1s < \sigma^* 1s < \sigma 2s < \sigma^* 2s < \mathbf{\sigma 2p_z < (\pi 2p_x = \pi 2p_y)} < (\pi^* 2p_x = \pi^* 2p_y) < \sigma^* 2p_z\)

Magnetic Nature: Unpaired electrons \(\implies\) Paramagnetic (e.g., \(O_2, B_2\)). All paired \(\implies\) Diamagnetic (e.g., \(N_2, C_2\)).

\(O_2\) is paramagnetic (2 unpaired \(e^-\) in \(\pi^*\)).

5. Hydrogen Bonding & Weak Van der Waals Forces

Intermolecular H-bond

Formed between two different molecules (same or different compounds).

Effects: Increases Boiling Point, Viscosity, Surface Tension, and Solubility in water.

Examples: \(H_2O, NH_3, HF\), Alcohols, Carboxylic acids (dimer formation).

Intramolecular H-bond

Formed within the same molecule (results in ring formation / Chelation).

Effects: Decreases Boiling Point (more volatile), prevents association, lowers solubility.

Examples: o-Nitrophenol, Salicylaldehyde.

Van der Waals Forces (Distance Dependency):

• Ion-Dipole Interaction: \(\propto 1/r^2\) (Strongest weak force, causes hydration).
• Dipole-Dipole (Keesom): \(\propto 1/r^3\) (Stationary polar molecules) or \(\propto 1/r^6\) (Rotating polar molecules).
• Ion-Induced Dipole: \(\propto 1/r^4\).
• Dipole-Induced Dipole (Debye): \(\propto 1/r^6\) (Polar + Non-polar).
• London Dispersion Forces: \(\propto 1/r^6\) (Non-polar + Non-polar). Depends on polarizability and molecular mass/surface area.

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