Chemical Bonding Formula Sheet
All key Chemical Bonding formulas: lattice energy, Born-Haber, formal charge, hybridization, bond order, VSEPR shapes & H-bonding for JEE quick revision.
Last-minute revision for Chemical Bonding and Molecular Structure. Every formula, key relation, and high-yield fact below is pulled straight from the chapter topics — ionic bonding, covalent bonding, VSEPR, hybridization, MOT, and hydrogen bonding.
Ionic Bonding
Lattice Energy
Energy released when one mole of an ionic solid forms from gaseous ions:
$$M^+(g) + X^-(g) \rightarrow MX(s) + \text{Lattice Energy}$$Born-Landé equation (theoretical lattice energy):
$$\boxed{U = -\frac{N_A M z^+ z^- e^2}{4\pi\epsilon_0 r_0}\left(1 - \frac{1}{n}\right)}$$- $N_A$ = Avogadro’s number; $M$ = Madelung constant (geometry dependent)
- $z^+, z^-$ = charges on cation and anion; $r_0$ = interionic distance
- $n$ = Born exponent (8-12, usually 9)
Simplified proportionality for JEE:
$$\boxed{U \propto \frac{z^+ \times z^-}{r_0}}$$Same anion, different cations: smaller cation wins. Same cation, different anions: smaller anion wins. Different charges: higher charge wins (charge dominates over size). Worked order: Al₂O₃ > MgO > LiF > NaCl; and MgO > NaCl > KCl.
Born-Haber Cycle
Hess’s Law applied to find lattice energy (for NaCl-type MX):
$$\boxed{\Delta H_f = \Delta H_{sub} + \frac{1}{2}D + IE + EA + U}$$Rearranged for lattice energy:
$$\boxed{U = \Delta H_f - \Delta H_{sub} - \frac{1}{2}D - IE - EA}$$| Symbol | Meaning | Notes |
|---|---|---|
| $\Delta H_f$ | Enthalpy of formation | Negative for stable compounds |
| $\Delta H_{sub}$ | Sublimation energy of metal | — |
| $D$ | Bond dissociation energy of non-metal | Use ½D for diatomic (Cl₂, O₂) |
| $IE$ | Ionization energy of metal | — |
| $EA$ | Electron affinity of non-metal | Negative |
| $U$ | Lattice energy | Negative (formation) / positive (dissociation) |
Fajan’s Rules — Covalent Character
Covalent character increases when:
- Cation is small (high charge density): Li⁺ > Na⁺ > K⁺
- Cation has high charge: Al³⁺ > Mg²⁺ > Na⁺ (Fe³⁺ > Fe²⁺)
- Anion is large (polarizable): I⁻ > Br⁻ > Cl⁻ > F⁻
- Cation has pseudo noble gas config (18e⁻ or 18+2e⁻): Ag⁺, Cu⁺, Hg²⁺ highly polarizing
Mnemonic: “Small Cation, Large Anion → Covalent fashion!”
Ionic vs covalent cutoff: $\Delta EN > 1.7 \Rightarrow$ ionic; $\Delta EN < 1.7 \Rightarrow$ covalent.
Key Lattice Energy Values
| Compound | Lattice Energy (kJ/mol) |
|---|---|
| KCl | 717 |
| RbF | 785 |
| NaCl | 788 |
| KF | 821 |
| NaF | 923 |
| LiF | 1037 |
| CaO | 3520 |
| MgO | 3850 |
| Al₂O₃ | ~15,000 |
Covalent Bonding
Formal Charge
$$\boxed{\text{Formal Charge} = V - L - \frac{B}{2}}$$- $V$ = valence electrons in free atom; $L$ = lone-pair electrons; $B$ = bonding (shared) electrons
Alternative: $\text{FC} = V - (\text{lone pairs} + \text{number of bonds})$.
Most stable structure → lowest formal charges, negative FC on the more electronegative atom, no like charges on adjacent atoms.
| Atom | Bonds | Lone pairs | FC |
|---|---|---|---|
| C | 4 | 0 | 0 |
| N | 3 | 1 | 0 |
| N | 4 | 0 | +1 |
| O | 2 | 2 | 0 |
| O | 1 | 3 | −1 |
Bond Order (Lewis / Resonance)
$$\text{Single} = 1,\quad \text{Double} = 2,\quad \text{Triple} = 3$$For resonance:
$$\boxed{\text{Bond Order} = \frac{\text{Total bonds between two atoms}}{\text{Number of resonance structures}}}$$Examples: CO₃²⁻ → 4/3 ≈ 1.33; benzene C–C → 1.5; O₃ O–O → 1.5.
Bond Parameters
| Effect | Higher bond order | Larger atomic size | More s-character |
|---|---|---|---|
| Bond length | Shorter | Longer | Shorter |
| Bond energy | Higher | — | Higher |
Correlation: stronger bond = shorter bond = higher bond energy = higher bond order.
s-character order: sp (50%) < sp² (33%) < sp³ (25%) → decreasing s-character, increasing length.
Dipole Moment
$$\boxed{\mu = q \times d}$$- Units: Debye (D), $1\,\text{D} = 3.34 \times 10^{-30}\ \text{C·m}$
- Vector quantity; net molecular dipole = vector sum of bond dipoles.
Symmetrical molecules cancel bond dipoles → net $\mu = 0$: CO₂ (linear), BF₃ / BCl₃ (trigonal planar), CCl₄ (tetrahedral), PCl₅ (TBP), SF₆ (octahedral). Polar despite polar bonds (asymmetric): H₂O (μ = 1.85 D), NH₃, CHCl₃ (μ = 1.04 D).
Polarity by Electronegativity Difference
| ΔEN | Bond type | Example |
|---|---|---|
| ≈ 0 | Nonpolar covalent | H–H, Cl–Cl, O₂ |
| 0.1 – 0.4 | Weakly polar | C–H |
| 0.4 – 1.7 | Polar covalent | H–Cl (ΔEN = 0.9), C–O, C–N |
| > 1.7 | Ionic | NaCl, MgO |
Electronegativity Scale (Pauling)
$$\boxed{\text{F (4.0)} > \text{O (3.5)} > \text{N} \approx \text{Cl (3.0)} > \text{Br (2.8)} > \text{C (2.5)} > \text{H} \approx \text{P (2.1)}}$$Trends: increases across a period (→), decreases down a group (↓). Mnemonic: “FONCl Brings Charges.”
Bond Length and Energy Values
| Bond | Length (pm) | Energy (kJ/mol) |
|---|---|---|
| C–C | 154 | 348 |
| C=C | 134 | 614 |
| C≡C | 120 | 839 |
| C–H | 109 | 413 |
| O–H | — | 463 |
| O=O | 121 | 498 |
| N≡N | 110 | 946 (strongest!) |
Halide bond lengths: C–F (138) < C–Cl (177) < C–Br (194) < C–I (214) pm.
Octet Rule Exceptions
- H, He: 2 electrons (duet)
- Be, B: fewer than 8 (BeCl₂ = 4, BF₃ = 6 on central atom)
- Period 3+ (P, S, Cl, Br, I): expanded octet — PCl₅ (10), SF₆ (12), IF₇ (14)
VSEPR Theory
Core Principles
$$\boxed{\text{Electron pairs repel and arrange to minimize repulsion}}$$$$\boxed{\text{LP-LP} > \text{LP-BP} > \text{BP-BP}}$$Steric Number: $\text{SN} = \text{bonding pairs} + \text{lone pairs}$ (multiple bonds count as one region).
Each lone pair reduces bond angle by ~2.5° (tetrahedral base): CH₄ 109.5° → NH₃ 107° → H₂O 104.5°.
Geometry Master Table
| SN | Type | BP | LP | Electron geometry | Molecular geometry | Bond angle | Example |
|---|---|---|---|---|---|---|---|
| 2 | AX₂ | 2 | 0 | Linear | Linear | 180° | CO₂, BeCl₂ |
| 3 | AX₃ | 3 | 0 | Trigonal planar | Trigonal planar | 120° | BF₃, CO₃²⁻ |
| 3 | AX₂E | 2 | 1 | Trigonal planar | Bent | ~120° (≈119° SO₂) | SO₂, NO₂⁻ |
| 4 | AX₄ | 4 | 0 | Tetrahedral | Tetrahedral | 109.5° | CH₄, NH₄⁺ |
| 4 | AX₃E | 3 | 1 | Tetrahedral | Trigonal pyramidal | ~107° | NH₃, PCl₃ |
| 4 | AX₂E₂ | 2 | 2 | Tetrahedral | Bent | ~104.5° | H₂O, H₂S |
| 5 | AX₅ | 5 | 0 | TBP | Trigonal bipyramidal | 90°, 120° | PCl₅ |
| 5 | AX₄E | 4 | 1 | TBP | See-saw | <90°, <120° | SF₄ |
| 5 | AX₃E₂ | 3 | 2 | TBP | T-shaped | ~90° | ClF₃, BrF₃ |
| 5 | AX₂E₃ | 2 | 3 | TBP | Linear | 180° | XeF₂, I₃⁻ |
| 6 | AX₆ | 6 | 0 | Octahedral | Octahedral | 90° | SF₆ |
| 6 | AX₅E | 5 | 1 | Octahedral | Square pyramidal | ~90° | BrF₅, IF₅ |
| 6 | AX₄E₂ | 4 | 2 | Octahedral | Square planar | 90° | XeF₄, ICl₄⁻ |
For 5 EP (TBP): lone pairs always fill equatorial positions first (less repulsion).
Electron geometry ≠ molecular geometry — JEE asks for the molecular shape (atoms only).
Multiple bonds count as one region (CO₂ → 2 regions → linear).
Hybridization
Steric Number Formula
$$\boxed{H = \frac{1}{2}[V + M - C + A]}$$- $V$ = valence electrons of central atom
- $M$ = number of monovalent atoms (H, Cl, Br, I, …)
- $C$ = charge on cation (positive); $A$ = charge on anion (negative)
| H | Hybridization | Geometry | Bond angle |
|---|---|---|---|
| 2 | sp | Linear | 180° |
| 3 | sp² | Trigonal planar | 120° |
| 4 | sp³ | Tetrahedral | 109.5° |
| 5 | sp³d | Trigonal bipyramidal | 90°, 120° |
| 6 | sp³d² | Octahedral | 90° |
| 7 | sp³d³ | Pentagonal bipyramidal | 72°, 90° |
Quick check (count σ bonds): 2σ → sp, 3σ → sp², 4σ → sp³.
Hybridization, Orbitals and Examples
| Hybridization | Orbitals mixed | s-character | Example |
|---|---|---|---|
| sp | s + p | 50% | BeCl₂, C₂H₂ |
| sp² | s + 2p | 33.3% | BF₃, C₂H₄ |
| sp³ | s + 3p | 25% | CH₄, NH₃ |
| sp³d | s + 3p + d | 20% | PCl₅, SF₄ |
| sp³d² | s + 3p + 2d | 16.7% | SF₆, XeF₄ |
| sp³d³ | s + 3p + 3d | — | IF₇ |
s-Character Effects
More s-character → shorter, stronger bonds and higher electronegativity (s-orbitals are closer to the nucleus).
- C≡C (sp-sp) 120 pm < C=C (sp²-sp²) 134 pm < C–C (sp³-sp³) 154 pm
- Acidity: HC≡CH (sp C–H, pKₐ ≈ 25) more acidic than CH₄ (sp³ C–H, pKₐ ≈ 50)
sp³d and sp³d² need Period 3+ elements (accessible 3d/4d/5d). Period 2 (C, N, O, F) maxes out at sp³ — that’s why SF₆ exists but OF₆ does not.
Molecular Orbital Theory (MOT)
Bond Order
$$\boxed{\text{Bond Order} = \frac{1}{2}(N_b - N_a)}$$- $N_b$ = electrons in bonding MOs; $N_a$ = electrons in antibonding MOs
- BO = 0 → molecule does not exist (e.g., He₂)
- Higher BO → stronger, shorter, more stable bond, lower reactivity
MO Energy Order
For N₂, C₂, B₂ (Z ≤ 7) — π below σ₂pz:
$$\sigma_{1s} < \sigma^*_{1s} < \sigma_{2s} < \sigma^*_{2s} < \pi_{2p_x} = \pi_{2p_y} < \sigma_{2p_z} < \pi^*_{2p_x} = \pi^*_{2p_y} < \sigma^*_{2p_z}$$For O₂, F₂ (Z > 7) — σ₂pz below π:
$$\sigma_{1s} < \sigma^*_{1s} < \sigma_{2s} < \sigma^*_{2s} < \sigma_{2p_z} < \pi_{2p_x} = \pi_{2p_y} < \pi^*_{2p_x} = \pi^*_{2p_y} < \sigma^*_{2p_z}$$Mnemonic: “Nitrogen and Lighter: π comes Lower.”
Homonuclear Diatomics Quick Reference
| Molecule | Electrons | Bond Order | Magnetic |
|---|---|---|---|
| H₂ | 2 | 1 | Diamagnetic |
| He₂ | 4 | 0 | Does not exist |
| B₂ | 10 | 1 | Paramagnetic |
| C₂ | 12 | 2 | Diamagnetic |
| N₂ | 14 | 3 | Diamagnetic |
| O₂ | 16 | 2 | Paramagnetic |
| F₂ | 18 | 1 | Diamagnetic |
O₂ Family (Bond Order vs Bond Length)
| Species | Electrons | Bond Order | Bond Length (pm) | Magnetic |
|---|---|---|---|---|
| O₂²⁺ | 14 | 3 | shortest | Diamagnetic |
| O₂⁺ | 15 | 2.5 | 112 | Paramagnetic (1 unpaired) |
| O₂ | 16 | 2 | 121 | Paramagnetic (2 unpaired) |
| O₂⁻ | 17 | 1.5 | 126 | Paramagnetic (1 unpaired) |
| O₂²⁻ | 18 | 1 | 149 | Diamagnetic |
Any species with odd total electrons is always paramagnetic.
Among common diatomics, only O₂ and B₂ are paramagnetic — memorize this.
Count all electrons (including core 1s) for the full diagram; magnetism comes from unpaired electrons, not from being diamagnetic = stable (stability tracks bond order).
Hydrogen Bonding
Definition and Requirements
$$\boxed{X-H \cdots Y \quad (X, Y = \text{F, O, N})}$$Three requirements: high electronegativity, small size, and an available lone pair. This is why only F, O, N (with H) qualify — Cl has EN ≈ 3.0 but is too large.
| Interaction | Strength (kJ/mol) |
|---|---|
| Covalent bond | 200–600 |
| Hydrogen bond | 10–40 |
| Van der Waals | 1–10 |
Strongest H-bond is F–H···F (shortest, 1.5–1.8 Å); strongest when linear (180°).
Intermolecular vs Intramolecular
| Property | Intermolecular | Intramolecular |
|---|---|---|
| Location | Between molecules | Within one molecule |
| Boiling point | Increases | Decreases |
| Solubility (water) | Increases | Decreases |
| Volatility | Decreases | Increases |
| Example | H₂O, p-nitrophenol | o-nitrophenol, salicylic acid |
With H-bonding > without H-bonding (for similar molecules).
CH₄ < NH₃ < CH₃OH < H₂O.
First member of a hydride group (HF, H₂O, NH₃) has the highest BP in its group — a tell-tale sign of H-bonding.
o-isomer (intramolecular) is more volatile / lower BP than p-isomer (intermolecular).
Anomalous Properties of Water
| Property | Value / fact |
|---|---|
| Boiling point | 100°C (vs ≈ −60°C expected) |
| Heat of vaporization | 40.7 kJ/mol (high) |
| Surface tension | 72.8 mN/m at 20°C |
| Density of ice | ≈ 0.92 g/cm³ → ice floats |
| Density of liquid | ≈ 1.00 g/cm³ |
| Maximum density at | 4°C (not 0°C) |
DNA base pairing: A=T (2 H-bonds), G≡C (3 H-bonds, stronger).
One-Glance Boxed Formula Recall
| Quantity | Formula |
|---|---|
| Lattice energy (proportionality) | $U \propto \dfrac{z^+ z^-}{r_0}$ |
| Born-Haber (lattice energy) | $U = \Delta H_f - \Delta H_{sub} - \frac{1}{2}D - IE - EA$ |
| Formal charge | $\text{FC} = V - L - \frac{B}{2}$ |
| Dipole moment | $\mu = q \times d$ |
| Hybridization number | $H = \frac{1}{2}[V + M - C + A]$ |
| Resonance bond order | $\dfrac{\text{total bonds}}{\text{resonance structures}}$ |
| MOT bond order | $\frac{1}{2}(N_b - N_a)$ |