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Chemical Bonding & VSEPR Formulas

VSEPR molecular geometries, steric number hybridization, bond order from MOT, dipole moments, and hydrogen bonding.

7 Formulas•698+ Questions in Bank

Concept Diagram

VSEPR Molecular Geometries & Hybridization
sp LinearAngle: 180°e.g., BeCl₂, C₂H₂sp² TrigonalAngle: 120°e.g., BF₃, C₂H₄sp³ TetrahedralAngle: 109.5°e.g., CH₄, CCl₄Steric No = (Valence e⁻ + Monovalent - Charge) / 2SN 2=sp, 3=sp², 4=sp³, 5=sp³d, 6=sp³d²
Key orbital hybridizations: sp (Linear 180°), sp² (Trigonal Planar 120°), sp³ (Tetrahedral 109.5°), and sp³d (Trigonal Bipyramidal).

Core Formulas & Mathematical Identities

7
01

Steric Number & Hybridization

Steric No=12[V+M−C+A]=σ-bonds+lone pairs\text{Steric No} = \frac{1}{2}[V + M - C + A] = \sigma\text{-bonds} + \text{lone pairs}

V: valence e⁻, M: monovalent atoms (H, F, Cl), C: positive charge, A: negative charge.

Examiner Tip: SN: 2 = sp (180°), 3 = sp² (120°), 4 = sp³ (109.5°), 5 = sp³d, 6 = sp³d².
02

Molecular Orbital Theory (MOT) Bond Order

Bond Order=Nb−Na2,Bond Length∝1Bond Order\text{Bond Order} = \frac{N_b - N_a}{2}, \quad \text{Bond Length} \propto \frac{1}{\text{Bond Order}}
Diagram Reference:Molecular Orbital Theory (MOT) Bond Order

N_b: bonding electrons, N_a: antibonding electrons.

Examiner Tip: 14 electrons (N₂) has BO = 3. Each added or removed electron changes BO by ±0.5.
03

Dipole Moment & Percentage Ionic Character

μ=q×d,% Ionic Character=μobservedμtheoretical×100%\mu = q \times d, \quad \% \text{ Ionic Character} = \frac{\mu_{\text{observed}}}{\mu_{\text{theoretical}}} \times 100\%

Measures molecular bond polarity (1 Debye = 3.336 × 10⁻³⁰ C m).

Examiner Tip: Symmetric molecules with no lone pairs (like CCl₄, BF₃, CO₂) have net μ = 0.
04

Formal Charge Calculation

Formal Charge=V−L−12S\text{Formal Charge} = V - L - \frac{1}{2}S

V: valence electrons in free atom, L: lone pair non-bonding electrons, S: shared bonding electrons.

Examiner Tip: Lowest formal charge configuration represents the most stable Lewis resonance structure.
05

Fajan's Rules (Covalent Character in Ionic Bonds)

Polarizing Power∝ChargeCation Radius,Polarizability∝Anion Radius\text{Polarizing Power} \propto \frac{\text{Charge}}{\text{Cation Radius}}, \quad \text{Polarizability} \propto \text{Anion Radius}

Covalent character increases with: (1) high charge on cation/anion, (2) smaller cation, (3) larger anion, and (4) pseudo-inert gas electron configuration 18e⁻ (Cu⁺, Ag⁺) over 8e⁻ (Na⁺, K⁺).

Examiner Tip: Higher covalent character lowers melting point and increases solubility in non-polar organic solvents (e.g. AgI is yellow/covalent, AgF is white/ionic).
06

Bond Angle Hierarchy Rules

Hybridization (sp>sp2>sp3)→No. of Lone Pairs ↓→EN of Central Atom ↑→EN of Surrounding Atoms ↓\text{Hybridization } (sp > sp^2 > sp^3) \to \text{No. of Lone Pairs } \downarrow \to \text{EN of Central Atom } \uparrow \to \text{EN of Surrounding Atoms } \downarrow

Systematic order for comparing bond angles across molecules.

Examiner Tip: Drago's Rule: In PH₃, AsH₃, H₂S, H₂Se, no hybridization occurs; bond angles are close to 90° pure p-orbital angles.
07

Back-Bonding & 3-Center-2-Electron Bonds

pπ−pπ  (in BF3),pπ−dπ  (in N(SiH3)3),B2H6  (Banana 3c−2e− bridge bonds)p\pi - p\pi \; (\text{in } BF_3), \quad p\pi - d\pi \; (\text{in } N(SiH_3)_3), \quad B_2H_6 \; (\text{Banana } 3c-2e^- \text{ bridge bonds})

Transfer of lone pair electrons from filled orbital into adjacent empty p or d orbital increases bond order and reduces Lewis acidity.

Examiner Tip: N(CH₃)₃ is pyramidal with sp³ N, whereas N(SiH₃)₃ is planar with sp² N due to pπ-dπ back-donation into empty d-orbitals of Si.

Top Examiner Traps & Pitfalls

Frequently tested misconceptions in Chemical Bonding & VSEPR

  • •Ignoring lone pairs when naming shape: lone pairs distort geometry (e.g. H₂O has steric number 4, sp³ hybridization, but BENT shape).
  • •Applying 14-electron MOT configuration to O₂ or F₂ (>14 electrons have σ₂p_z lower in energy than π₂p_x, π₂p_y).

Fundamental Theory & Core Concepts

4 Topics

1Kossel-Lewis Approach & Formal Charge

  • ›Octet Rule: Atoms combine either by transfer or by sharing of valence electrons to attain an 8-electron stable noble gas configuration.
  • ›Octet Rule Exceptions: (1) Incomplete octet (LiCl, BeH₂, BF₃); (2) Odd-electron species (NO, NO₂); (3) Expanded octet with available empty d-orbitals (PF₅, SF₆, H₂SO₄).
  • ›Formal Charge: FC = V - L - (1/2)S (where V = valence e⁻ of free atom, L = total lone pair e⁻, S = total shared/bonding e⁻). Lowest energy Lewis structure has minimum formal charges on atoms and negative charge on the most electronegative atom.

2VSEPR Theory & Molecular Geometry

  • ›Core Postulate: Electron pairs (both bond pairs and lone pairs) around the central atom repel one another and arrange themselves in space to minimize electrostatic repulsion.
  • ›Repulsion hierarchy: (Lone Pair - Lone Pair) > (Lone Pair - Bond Pair) > (Bond Pair - Bond Pair). Lone pairs occupy more space because they are held by only one atomic nucleus.
  • ›Crucial distinction between Geometry and Shape: Geometry refers to the spatial arrangement of ALL electron pairs (steric number). Shape/Structure describes the arrangement of ATOMS only, ignoring lone pairs (e.g. NH₃ has tetrahedral geometry, but trigonal pyramidal shape).

3Hybridization Concepts & Rules

  • ›Hybridization is the mathematical mixing of atomic orbitals of comparable energies on the SAME central atom to form equivalent hybrid orbitals with identical shape and energy.
  • ›Only σ-bonds and lone pairs participate in hybridization; π-bonds are formed by unhybridized pure p or d orbitals via lateral (sideways) overlap.
  • ›Hybrid orbital directional characteristics: sp (linear, 50% s-character, 180°), sp² (trigonal planar, 33.3% s, 120°), sp³ (tetrahedral, 25% s, 109.5°), sp³d (trigonal bipyramidal: equatorial bonds shorter 120°, axial bonds longer 90°), sp³d² (octahedral, all 90°).

4Molecular Orbital Theory (MOT) & Magnetism

  • ›Linear Combination of Atomic Orbitals (LCAO): Wavefunctions add constructively to form lower-energy Bonding Molecular Orbitals (BMO: σ, π) and destructively to form higher-energy Antibonding Molecular Orbitals (ABMO: σ*, π*).
  • ›Energy Ordering for ≤ 14 electrons (Li₂, Be₂, B₂, C₂, N₂): Due to 2s-2p mixing, σ₂p_z is pushed above π₂p_x = π₂p_y: σ1s < σ*1s < σ2s < σ*2s < (π2p_x = π2p_y) < σ2p_z < (π*2p_x = π*2p_y) < σ*2p_z.
  • ›Energy Ordering for > 14 electrons (O₂, F₂): No significant 2s-2p mixing, normal order: σ1s < σ*1s < σ2s < σ*2s < σ2p_z < (π2p_x = π2p_y) < (π*2p_x = π*2p_y) < σ*2p_z.
  • ›Magnetic Character: Paramagnetic if one or more unpaired electrons exist (e.g. O₂ has 2 unpaired electrons in π*2p_x and π*2p_y, correctly predicted by MOT unlike Lewis theory); Diamagnetic if all electrons are paired.
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