Chemical Bonding and Molecular Structure: NEET notes

1. Kössel-Lewis approach and the octet rule

NCERT § "Kössel-Lewis Approach to Chemical Bonding"

• Kössel and Lewis explained bonding as atoms reaching a stable noble-gas-like octet, either by transferring electrons (ionic bond) or by sharing them (covalent bond).
• Lewis symbols show only the valence electrons of an atom as dots around its symbol; the group valence is usually either the number of dots or 8 minus that number.
• In a covalent bond each shared pair counts towards the octet of both atoms; one shared pair is a single bond, two a double bond and three a triple bond.
• Formal charge on an atom in a Lewis structure = (valence electrons in the free atom) − (non-bonding electrons) − ½(bonding electrons).
• When several Lewis structures can be drawn, prefer the one that keeps formal charges smallest, since it is normally the most stable; ozone, for example, carries formal charges of +1 and −1 on two of its oxygens.
• Limitation 1, incomplete octet: in LiCl, BeH₂ and BCl₃ the central atom has fewer than eight electrons.
• Limitation 2, odd-electron molecules: NO and NO₂ cannot give every atom an octet.
• Limitation 3, expanded octet: elements from period 3 onwards can use d orbitals and hold more than eight electrons, as in PF₅, SF₆ and H₂SO₄.
• The octet theory also fails to explain the shapes of molecules and their relative stability, and it ignores the fact that some noble gases (xenon, krypton) do form compounds.

2. Ionic bonding and lattice enthalpy

NCERT § "Ionic or Electrovalent Bond"

• An ionic bond forms more easily when one atom has a low ionisation enthalpy and the other has a large negative electron gain enthalpy.
• Forming isolated gaseous ions usually costs energy; the overall process becomes favourable because of the large energy released when the ions pack into a crystal lattice.
• Lattice enthalpy is the energy required to break one mole of a solid ionic compound fully apart into its gaseous ions; for NaCl it is 788 kJ mol⁻¹.
• The larger the lattice enthalpy, the more stable the ionic compound.
• Ionic solids are crystalline arrays with no discrete molecules, so 'NaCl' describes the ratio of ions, not a molecule.
• Electrovalence equals the number of unit charges on the ion formed.

3. Bond parameters: length, angle, enthalpy and order

NCERT § "Bond Parameters"

• Bond length is the separation of the nuclei of two bonded atoms at equilibrium; covalent radius is half the distance between two identical bonded atoms, while the van der Waals radius, measured between non-bonded atoms in contact, is larger.
• Typical carbon-carbon bond lengths are C–C 154 pm, C=C 134 pm and C≡C 120 pm; the H–H bond is 74 pm.
• Bond angle is measured at the central atom, between the orbitals that carry its bonding pairs; spectroscopy gives its experimental value, and it helps fix the shape.
• Bond enthalpy is the energy needed to break one mole of a given bond between two atoms in the gaseous state; the H–H value is 435.8 kJ mol⁻¹.
• For polyatomic molecules with several identical bonds (like the O–H bonds of water), an average bond enthalpy is used because each successive bond needs a different energy to break.
• Bond order in the Lewis picture is the number of bonds between two atoms: H₂ 1, O₂ 2, N₂ 3, CO 3.
• Isoelectronic species have the same bond order; F₂ and O₂²⁻ both have bond order 1, while N₂, CO and NO⁺ all have bond order 3.
• As bond order increases, bond enthalpy increases and bond length decreases.

4. Resonance structures

NCERT § "Resonance Structures"

• If no one Lewis structure can describe a molecule, several structures are drawn that share the same arrangement of nuclei but place the electrons differently; the real molecule is a hybrid of them.
• Ozone has two equal O–O bonds of 128 pm, between a single (148 pm) and a double (121 pm) O–O bond, which no single Lewis structure can show.
• The carbonate ion has three identical C–O bonds, and CO₂ is also described by resonance.
• The resonance hybrid has lower energy than any contributing structure, which stabilises the molecule.
• Resonance structures do not exist separately and the molecule does not flip between them; there is no equilibrium between the canonical forms.

5. Polarity of bonds and dipole moment

NCERT § "Polarity of Bonds"

• A bond between two identical atoms (H₂, O₂) is non-polar; when the atoms differ in electronegativity, the shared pair shifts towards the more electronegative atom and the bond becomes polar (as in HF).
• Dipole moment μ = charge × distance between the charge centres; it is a vector, drawn from the positive to the negative end in the convention chemists use (crossed arrow).
• The unit is the Debye: 1 D = 3.33564 × 10⁻³⁰ C m.
• A molecule's net dipole moment is the vector sum of its bond dipoles, so symmetry can cancel it: BeF₂, BF₃, CO₂, CH₄ and CCl₄ have zero dipole moment.
• Water is bent, so its two O–H bond dipoles add to a net value (about 1.85 D).
• NH₃ has a larger dipole moment than NF₃: in NH₃ the lone-pair moment adds to the N–H bond moments, while in NF₃ it opposes the N–F bond moments.
• Ionic bonds carry some covalent character too, and Fajans' rules say when it is larger: a small cation paired with a large anion, and a cation with a higher charge.
• Of two cations with the same size and charge, a transition-metal type cation with an (n−1)dⁿ ns⁰ configuration (for example Cu⁺, 3d¹⁰) polarises the anion more than one with a noble gas ns² np⁶ configuration.

6. VSEPR theory and molecular shapes

NCERT § "The Valence Shell Electron Pair Repulsion (VSEPR) Theory"

• The shape of a molecule is set by the number of electron pairs (bonding and lone) around the central atom, which arrange themselves as far apart as possible.
• A multiple bond is treated as a single electron-pair region (a 'super pair') when predicting shape.
• Repulsion order: lone pair-lone pair > lone pair-bond pair > bond pair-bond pair, because lone pairs are held by only one nucleus and spread out more.
• Without lone pairs: 2 pairs linear (BeCl₂, 180°), 3 trigonal planar (BF₃, 120°), 4 tetrahedral (CH₄, 109.5°), 5 trigonal bipyramidal (PCl₅), 6 octahedral (SF₆).
• With lone pairs and 4 regions: NH₃ (3 bond pairs, 1 lone pair) is trigonal pyramidal with about 107°; H₂O (2 bond pairs, 2 lone pairs) is bent with about 104.5°.
• With 5 regions, lone pairs take equatorial positions: SF₄ (4 bp, 1 lp) is see-saw and ClF₃ (3 bp, 2 lp) is T-shaped. Background from the Class 12 noble-gas chapter, not in this chapter's table: XeF₂ (2 bp, 3 lp) is linear by the same rule.
• With 6 regions: BrF₅ (5 bp, 1 lp) is square pyramidal and XeF₄ (4 bp, 2 lp) is square planar.
• SO₂ and O₃, each with 3 regions including one lone pair, are bent.
• Molecular shape names describe the positions of atoms only; lone pairs affect the shape but are not part of its name.

7. Valence bond theory and orbital overlap

NCERT § "Valence Bond Theory"

• Valence bond theory explains bond formation as the overlap of half-filled atomic orbitals holding electrons of opposite spin.
• As two H atoms approach, attractions between each nucleus and the other's electron start to outweigh repulsions; energy falls to a minimum at 74 pm, where the H₂ molecule forms.
• The greater the extent of overlap, the stronger the bond.
• Overlap is positive (in-phase, same sign) when a bond forms, negative (out of phase) when it does not, and zero when orbital symmetry prevents interaction.
• A sigma (σ) bond forms by end-to-end (head-on) overlap along the internuclear axis; it can involve s-s, s-p or p-p overlap.
• A pi (π) bond forms by sideways overlap of parallel p orbitals, above and below the internuclear axis.
• A σ bond is stronger than a π bond because head-on overlap is more extensive; a double bond is one σ plus one π, and a triple bond is one σ plus two π.
• Simple overlap of pure orbitals cannot explain the equal bonds and 109.5° angles in CH₄, which led to the idea of hybridisation.

8. Hybridisation

NCERT § "Hybridisation"

• Hybridisation is the mixing of atomic orbitals of similar energy on the same atom to form an equal number of equivalent hybrid orbitals.
• Only orbitals of similar energy hybridise; hybrid orbitals form σ bonds or hold lone pairs, never π bonds.
• sp: one s + one p, linear, 180°, 50% s character (BeCl₂; each carbon in ethyne).
• sp²: one s + two p, trigonal planar, 120°, 33% s character (BCl₃; each carbon in ethene).
• sp³: one s + three p, tetrahedral, 109.5° (109°28′), 25% s character (CH₄); NH₃ and H₂O are also sp³, with angles squeezed by lone pairs.
• In ethene each carbon uses sp² orbitals for σ bonds and the unhybridised p orbital for the π bond; in ethyne each carbon forms 2 σ bonds and 2 π bonds.
• sp³d (dz² orbital used) gives a trigonal bipyramid, as in PCl₅; the two axial P–Cl bonds are longer and weaker than the three equatorial bonds, which makes PCl₅ reactive.
• sp³d² (dz² and dx²−y² used) gives an octahedron, as in SF₆, with six equal S–F bonds at 90°.
• Quick rule: count σ bonds plus lone pairs on the central atom; 2, 3, 4, 5 and 6 correspond to sp, sp², sp³, sp³d and sp³d².

9. Molecular orbital theory

NCERT § "Molecular Orbital Theory"

• Atomic orbitals of the bonded atoms combine into molecular orbitals that belong to the whole molecule; the number of MOs formed equals the number of atomic orbitals combined.
• MOs form by linear combination of atomic orbitals (LCAO): addition gives a bonding MO of lower energy, subtraction gives an antibonding MO (marked *) of higher energy.
• Combining orbitals must have similar energy, the same symmetry about the molecular axis, and must overlap well.
• MOs are filled following the aufbau principle, Pauli's exclusion principle and Hund's rule.
• Energy order up to N₂: σ1s < σ*1s < σ2s < σ*2s < (π2px = π2py) < σ2pz < (π*2px = π*2py) < σ*2pz.
• For O₂ and F₂ the σ2pz orbital lies below the two π2p orbitals.
• Bond order = ½(Nb − Na); a positive value means a stable molecule, zero means the molecule does not exist, and higher bond order means shorter and stronger bonds.
• Unpaired electrons in MOs make a species paramagnetic; if all electrons are paired it is diamagnetic.

10. Homonuclear diatomic molecules

NCERT § "Bonding in Some Homonuclear Diatomic Molecules"

• H₂: bond order 1, diamagnetic. He₂: bond order 0, so it is not stable.
• Li₂: bond order 1, diamagnetic. B₂: bond order 1, paramagnetic because its two π2p electrons are unpaired.
• C₂: bond order 2, diamagnetic, and both bonds are π bonds in the MO picture.
• N₂: bond order 3, diamagnetic, with a very high bond enthalpy.
• O₂: bond order 2 with two unpaired electrons in the π* orbitals, so it is paramagnetic, which the Lewis structure cannot explain.
• Removing an antibonding electron raises bond order: O₂⁺ has 2.5; adding electrons lowers it: O₂⁻ has 1.5 and O₂²⁻ has 1.
• F₂: bond order 1, diamagnetic. Ne₂: bond order 0, not formed.

11. Hydrogen bonding

NCERT § "Hydrogen Bonding"

• An H atom attached to F, O or N is left with a partial positive charge, so it is pulled towards a lone pair on a nearby F, O or N atom; that pull is a hydrogen bond, drawn as a dotted line.
• A hydrogen bond is much weaker than a covalent bond.
• Intermolecular hydrogen bonds link different molecules, as in HF and water; they raise boiling points and account for the unusually high boiling point of water.
• Intramolecular hydrogen bonds form within one molecule, as in o-nitrophenol, where the H of –OH bonds to an O of the nearby –NO₂ group.
• HCl does not show significant hydrogen bonding; chlorine is less electronegative and larger than F, O or N.
• HF forms zig-zag chains held by F–H···F hydrogen bonds, and water molecules are linked through O–H···O hydrogen bonds.

Must-know facts

1. Octet exceptions: incomplete (BeH₂, BCl₃, LiCl), odd-electron (NO, NO₂), expanded (PF₅, SF₆, H₂SO₄).
2. Formal charge = V − L − ½S.
3. Lattice enthalpy of NaCl = 788 kJ mol⁻¹.
4. 1 D = 3.33564 × 10⁻³⁰ C m.
5. Zero dipole moment: BeF₂, BF₃, CO₂, CH₄, CCl₄; non-zero: H₂O, NH₃, NF₃.
6. Dipole moment of NH₃ > NF₃ because the lone-pair moment adds in NH₃ and opposes in NF₃.
7. Repulsion order: lp-lp > lp-bp > bp-bp.
8. Bond angles: CH₄ 109.5° > NH₃ ~107° > H₂O ~104.5°.
9. Shapes: SF₄ see-saw, ClF₃ T-shaped, XeF₂ linear, BrF₅ square pyramidal, XeF₄ square planar, SF₆ octahedral.
10. PCl₅: sp³d, axial bonds longer than equatorial bonds.
11. sp³d uses dz²; sp³d² uses dz² and dx²−y².
12. s character: sp 50%, sp² 33%, sp³ 25%.
13. σ bond is stronger than π bond; double bond = 1σ + 1π, triple bond = 1σ + 2π.
14. Bond order = ½(Nb − Na).
15. σ2pz lies above π2p up to N₂, and below π2p for O₂ and F₂.
16. O₂ is paramagnetic with bond order 2; N₂ is diamagnetic with bond order 3.
17. Bond orders: O₂⁺ 2.5, O₂ 2, O₂⁻ 1.5, O₂²⁻ 1.
18. B₂ is paramagnetic; C₂ is diamagnetic.
19. Hydrogen bonding needs H attached to F, O or N; o-nitrophenol shows intramolecular H-bonding.

Common traps

Formulas

Key terms

Octet rule

Tendency of atoms to reach eight valence electrons by losing, gaining or sharing electrons.

Formal charge

Charge assigned to an atom in a Lewis structure by assuming shared electrons are split equally.

Lattice enthalpy

Energy needed to break one mole of an ionic solid completely into gaseous ions.

Bond enthalpy

Energy needed to break one mole of a particular bond in gaseous molecules.

Resonance hybrid

The single real structure that several Lewis structures together approximate.

Dipole moment

Product of the separated charge and the distance between charge centres; a vector.

Sigma bond

Bond formed by head-on overlap of orbitals along the internuclear axis.

Pi bond

Bond formed by sideways overlap of parallel p orbitals.

Hybridisation

Mixing of atomic orbitals of similar energy on one atom into equivalent new orbitals.

LCAO

Building molecular orbitals by adding and subtracting atomic orbital wave functions.

Antibonding orbital

A molecular orbital higher in energy than the parent atomic orbitals, which weakens bonding when occupied.

Paramagnetic

Attracted into a magnetic field because of unpaired electrons.

Hydrogen bond

Attraction between an H atom bonded to F, O or N and a lone pair on another such atom.