Chapter Review

Chemical Bonding

VSEPR, Hybridization and Molecular Shape · Sigma/Pi Bonds, Polarity and Bond Energy

VSEPR Theory

Electron pairs around a central atom arrange at maximum distance apart to minimise repulsion, determining molecular geometry. Both lone pairs and bond pairs participate in shaping the molecule.

Key Points

  • •
    Lone pairs occupy more space than bond pairs because they are attracted by only one nucleus, spreading the charge cloud further
  • •
    Multiple bonds (double/triple) have higher charge density and occupy more space but count as one region for geometry
  • •
    Molecular shape considers only atom positions (ignoring lone pairs); electron pair geometry includes lone pairs
  • •
    Bond angles compress progressively with more lone pairs: 0 lp → 109.5°, 1 lp → 107.5°, 2 lp → 104.5°
  • •
    Electronegative substituents pull bonding electrons away, reducing bp-bp repulsion and further compressing angles
Formula

Molecular Shapes from Electron Pair Arrangements

The number of electron pair regions around the central atom dictates the geometry. The same number of regions can produce different shapes depending on how many are lone pairs.

Key Points

  • •
    AB₂ (2 pairs, 0 lp): Linear, 180° — BeCl₂, CO₂, HgCl₂
  • •
    AB₃ (3 pairs, 0 lp): Trigonal planar, 120° — BF₃, AlCl₃, SO₃
  • •
    AB₂E (3 pairs, 1 lp): Bent/angular, <120° — SnCl₂, SO₂
  • •
    AB₄ (4 pairs, 0 lp): Tetrahedral, 109.5° — CH₄, CCl₄, SiCl₄, NH₄⁺
  • •
    AB₃E (4 pairs, 1 lp): Trigonal pyramidal, ~107.5° — NH₃, PH₃, NF₃
  • •
    AB₂E₂ (4 pairs, 2 lp): Bent/angular, ~104.5° — H₂O, H₂S, H₂Se

sp³ Hybridization

One s and three p orbitals mix to form four equivalent sp³ hybrid orbitals arranged tetrahedrally at 109.5°. Explains bonding in CH₄ (tetrahedral), NH₃ (trigonal pyramidal), and H₂O (bent).

Key Points

  • •
    Carbon promotes one 2s electron to 2p, then hybridizes all four valence orbitals into sp³
  • •
    In NH₃, one sp³ orbital holds a lone pair — lone pair repulsion compresses angle to 107.5°
  • •
    In H₂O, two sp³ orbitals hold lone pairs — strong lp-lp and lp-bp repulsion compresses angle to 104.5°
  • •
    NH₂⁻ (2 lp, 105°) < NH₃ (1 lp, 107.5°) < NH₄⁺ (0 lp, 109.5°) — demonstrates lone pair effect
  • •
    All sp³ hybridized atoms have 25% s-character in their hybrid orbitals
Formula

sp² Hybridization

One s and two p orbitals form three equivalent sp² orbitals at 120° in a plane, with one unhybridized p orbital perpendicular for pi bond formation. Explains trigonal planar geometries and double bonds.

Key Points

  • •
    BF₃: boron promotes one electron then hybridizes to three sp² orbitals — trigonal planar, 120°, no lone pairs
  • •
    Ethene: each carbon forms three sp² orbitals; C=C double bond = one sigma (sp²-sp²) + one pi (p-p sideways)
  • •
    The unhybridized p orbital is essential — without it, only sigma bonds (single bonds) can form
  • •
    33% s-character — bonds are shorter and stronger than sp³ bonds of the same element
  • •
    Pi bond prevents free rotation around double bonds, creating planar geometry
Formula

sp Hybridization

One s and one p orbital form two sp orbitals at 180°, with two unhybridized p orbitals for two pi bonds. Explains linear geometries and triple bonds.

Key Points

  • •
    BeCl₂: beryllium promotes one electron, hybridizes to two sp orbitals — linear, 180°
  • •
    Ethyne: each carbon is sp hybridized; C≡C triple bond = one sigma (sp-sp) + two pi bonds (py-py and pz-pz)
  • •
    Two pi bonds form in perpendicular planes, creating a cylindrical electron cloud around the sigma bond
  • •
    50% s-character — shortest and strongest bonds for a given element (sp < sp² < sp³ in length)
  • •
    Quick identification: steric number = sigma bonds + lone pairs on central atom (2 → sp, 3 → sp², 4 → sp³)
Formula

Sigma and Pi Bonds

Sigma bonds form from head-on overlap along the internuclear axis (strongest type); pi bonds form from sideways overlap of parallel p orbitals (weaker, requires a pre-existing sigma bond).

Key Points

  • •
    Sigma: head-on overlap, electron density along the axis, allows free rotation in single bonds
  • •
    Pi: sideways overlap, electron density above/below axis with nodal plane, prevents rotation
  • •
    Single bond = 1 sigma; double bond = 1 sigma + 1 pi; triple bond = 1 sigma + 2 pi
  • •
    Sigma bonds form first — pi bonds can only form between atoms already sharing a sigma bond
  • •
    Pi bonds are more reactive than sigma bonds due to less effective overlap and exposed electron density

Bond Polarity and Molecular Polarity

Bond polarity arises from unequal electron sharing due to electronegativity differences. Molecular polarity depends on the vector sum of all bond dipoles, which is determined by molecular geometry.

Key Points

  • •
    Non-polar bond: identical atoms, equal sharing (H₂, Cl₂, F₂)
  • •
    Polar bond: different atoms, δ⁺ on less EN atom, δ⁻ on more EN atom (H-F, C-O, C-Cl)
  • •
    Non-polar molecules with polar bonds: CO₂ (linear), BF₃ (trigonal planar), CH₄/CCl₄ (tetrahedral) — symmetry cancels dipoles
  • •
    Polar molecules: H₂O (angular, μ=1.85 D), NH₃ (pyramidal, μ=1.49 D), SO₂ (angular, μ=1.61 D)
  • •
    Replacing one atom in a symmetric molecule breaks cancellation (CH₃Cl is polar, CCl₄ is not)
Formula

Ionic Character of Covalent Bonds

No covalent bond is purely covalent — ionic character increases with electronegativity difference. The extra bond energy beyond the pure covalent estimate directly measures ionic attraction.

Key Points

  • •
    ΔEN ≥ 1.7: predominantly ionic (NaCl ~72%, CsF ~92% — no bond is 100% ionic)
  • •
    Ionic character adds electrostatic attraction, increasing bond energy beyond the pure covalent value
  • •
    H-X trend: HF (extra 274 kJ/mol) > HCl (95) > HBr (55) > HI (8) — decreasing EN difference
  • •
    Bond energy of H-X: HF (567) > HCl (431) > HBr (366) > HI (299) kJ/mol
  • •
    Ionic character can be calculated from dipole moment data using % ionic = μ_obs/μ_ionic × 100
Formula

Bond Energy and Bond Length

Bond energy is the average energy to break one mole of bonds in the gas phase (kJ/mol). Bond energy and bond length are inversely related — shorter bonds are stronger.

Key Points

  • •
    Bond energy: C—C (348) < C=C (614) < C≡C (839) kJ/mol — but not in simple multiples (pi bonds are weaker than sigma)
  • •
    Bond length: C—C (154) > C=C (133) > C≡C (120) pm — shorter = stronger
  • •
    Higher s-character in hybrid orbitals produces shorter bonds: sp (50% s) < sp² (33%) < sp³ (25%) in length
  • •
    Ionic character shortens bonds below the sum of covalent radii (Si-F: predicted 181 pm, actual 154-159 pm)
  • •
    Bond length ≈ sum of covalent radii for similar atoms (C-Cl: 77 + 99 = 176 pm, actual 177 pm)
Formula

Dipole Moment

The dipole moment (μ = q × r) quantifies charge separation as a vector from δ⁺ to δ⁻, measured in Debye. It reveals both ionic character of bonds and molecular geometry through vector addition.

Key Points

  • •
    Defined as μ = q × r, where q is the partial charge and r is the charge separation distance
  • •
    Unit: 1 Debye = 3.336 × 10⁻³⁰ mC; a full electron charge at 100 pm gives 4.8 D
  • •
    Net dipole = vector sum of all bond dipoles — direction matters for polyatomic molecules
  • •
    Zero dipole confirms symmetric geometry; non-zero dipole confirms asymmetric/bent geometry
  • •
    H-X dipole trend: HF (1.90 D) > HCl (1.03) > HBr (0.78) > HI (0.38) — decreasing EN difference
Formula

Formulas

Electron Pair Repulsion Order

Lone pair repulsion is strongest, bond pair repulsion is weakest — this hierarchy determines bond angle compression by lone pairs.

Steric Number to Hybridization

Steric number = sigma bonds + lone pairs on central atom. 2 → sp (180°), 3 → sp² (120°), 4 → sp³ (109.5°).

sp³ Hybridization

One s + three p orbitals form four tetrahedral hybrid orbitals at 109.5°.

sp² Hybridization

One s + two p orbitals form three planar hybrid orbitals at 120°, leaving one unhybridized p for pi bonding.

sp Hybridization

One s + one p orbital form two linear hybrid orbitals at 180°, leaving two unhybridized p orbitals for two pi bonds.

Dipole Moment

Product of partial charge and separation distance. Vector from δ⁺ to δ⁻. Units: Debye (D).

Percentage Ionic Character

Observed dipole moment as a percentage of fully ionic dipole moment. No bond is 100% ionic.

Net Molecular Dipole

Vector sum of all individual bond dipole moments. Zero means non-polar; non-zero means polar.