Chemical Bonding and Molecular Structure — NEET notes

Ionic Bond

Formed by complete transfer of electrons from a metal to a non-metal, creating oppositely charged ions held together by electrostatic attraction. Lattice energy stabilizes the crystal, and Born-Haber cycle connects formation enthalpy to individual energy steps.

Lattice Energy q^+ q^- r^+ + r^-

Ionic Bond Formation

An ionic bond forms when an electropositive atom transfers one or more electrons to an electronegative atom. The resulting cation and anion attract each other via strong electrostatic (Coulombic) forces.

The ionic bond is the simplest type of chemical bond to understand: one atom loses electrons, another gains them. The atom that loses becomes a cation (positive), and the atom that gains becomes an anion (negative). The electrostatic attraction between these opposite charges IS the ionic bond.

Na(g) arrow Na^+(g) + e^- (IE_1 = 496 kJ/mol)

Cl(g) + e^- arrow Cl^-(g) (EA = -349 kJ/mol)

• Ionic bonds form between atoms with large electronegativity difference (typically > 1.7 )
• Metals from Group 1 and 2 (low IE) are the best electron donors
• Non-metals from Group 16 and 17 (high EA) are the best electron acceptors
• Ionic bond is non-directional — electrostatic attraction acts equally in all directions
• No discrete 'molecule' exists in ionic compounds — it's a 3D lattice of alternating ions

Lattice Energy

Lattice energy is the energy released when gaseous cations and anions combine to form one mole of an ionic solid. It determines the stability, melting point, and solubility of ionic compounds.

Lattice energy ( U ) is the energy released when one mole of an ionic compound is formed from its gaseous ions. Alternatively, it's the energy required to completely separate one mole of a solid ionic compound into gaseous ions. Higher lattice energy = stronger ionic bond = more stable crystal.

U q^+ q^- r^+ + r^-

• Higher charges → higher lattice energy: MgO ( q = +2, -2 ) has MUCH higher U than NaCl ( q = +1, -1 )
• Smaller ions → higher lattice energy: LiF > NaF > KF > RbF > CsF
• High lattice energy → high melting point, high hardness, low solubility in water (usually)
• Lattice energy cannot be measured directly — it's calculated using the Born-Haber cycle

Quick recall

Arrange in order of increasing lattice energy: NaCl, KCl, MgO, CaO.

KCl < NaCl < CaO < MgO . KCl has larger ions than NaCl. MgO and CaO have double charges, but Mg²⁺ is smaller than Ca²⁺, so MgO wins.

Born-Haber Cycle

The Born-Haber cycle applies Hess's law to calculate lattice energy indirectly by breaking ionic compound formation into measurable steps: sublimation, ionization, dissociation, electron affinity, and lattice formation.

Since lattice energy can't be measured directly, we use the Born-Haber cycle — a clever application of Hess's law. We break the formation of an ionic compound from its elements into individual steps, each with a known energy. The lattice energy is the 'missing piece' that makes the cycle close.

H_f = H_ sub + IE + 1 2 H_ diss + EA + U

Plugging in for NaCl: -411 = 108 + 496 + 121 + (-349) + U , so U = -411 - 376 = -787 kJ/mol.

• Born-Haber cycle is just Hess's law applied to ionic compounds
• Endothermic steps: sublimation, dissociation, ionization energy
• Exothermic steps: electron affinity (usually), lattice energy (always)
• All quantities except lattice energy can be measured experimentally

Properties of Ionic Compounds

Ionic compounds have high melting and boiling points, are hard and brittle, conduct electricity in molten/dissolved state but not as solids, and are generally soluble in polar solvents.

The properties of ionic compounds are a direct consequence of the strong, non-directional electrostatic forces holding the ions in a 3D crystal lattice. Every property traces back to one fact: it takes a LOT of energy to pull these ions apart.

• High m.p. and b.p. — strong electrostatic forces need lots of energy to overcome (NaCl: 801°C, MgO: 2852°C)
• Hard but brittle — hard because ions resist displacement; brittle because any shift brings like charges together → repulsion → crack
• Electrical conductivity — zero as solid (ions locked in place), high when molten or dissolved (ions free to move)
• Soluble in polar solvents — water's high dielectric constant weakens ion-ion attraction; hydration energy compensates for lattice energy
• Insoluble in non-polar solvents — benzene, CCl₄ can't stabilize free ions

Quick recall

Why does solid NaCl not conduct electricity, but molten NaCl does?

In solid NaCl, ions are locked in fixed lattice positions — they can't move. In molten NaCl, ions are free to migrate toward electrodes, carrying charge → electrical conductivity.

Covalent Bond & Lewis Structures

Covalent bonds form by sharing electron pairs between atoms. Lewis dot structures show this sharing visually. Formal charge identifies the best structure, and exceptions to the octet rule (incomplete octet, expanded octet, odd electrons) are crucial for NEET.

Formal Charge = V - N - B 2

Covalent Bond

When two atoms have similar electronegativities, neither can steal the other's electron. Instead, they SHARE electron pairs to achieve noble gas configurations. The shared pair is attracted by both nuclei simultaneously.

A covalent bond forms when two atoms share one or more electron pairs. Unlike ionic bonds (transfer), covalent bonds involve mutual sharing. Each shared pair constitutes one bond. The driving force is the same as ionic bonds — atoms want noble gas configurations.

• Single bond: 1 shared pair (e.g., H–H, Cl–Cl) → bond
• Double bond: 2 shared pairs (e.g., O=O, C=O) → 1 + 1 bond
• Triple bond: 3 shared pairs (e.g., N N, C O) → 1 + 2 bonds
• Covalent bonds are directional (unlike ionic bonds) — this gives molecules definite shapes
• Formed between atoms with small electronegativity difference (typically < 1.7 )

Lewis Dot Structures

Lewis structures show valence electrons as dots and shared pairs as lines. Follow the systematic method: count valence electrons, identify the central atom, distribute electrons to satisfy octets, and check.

Lewis structures are diagrams that show how valence electrons are distributed in a molecule. Each bonding pair is shown as a line (or two dots), and each lone pair as two dots on a single atom.

Example: CO₂ — Total valence e⁻ = 4 + 6 + 6 = 16. Put C in center, connect two O's with single bonds (uses 4e⁻). Place 12e⁻ on oxygens (6 each). C has only 4e⁻ in bonds — needs 4 more. Convert one lone pair from each O into a bond → O=C=O. Each O has 2 lone pairs, C has 0 lone pairs. All octets satisfied.

• Central atom = least electronegative atom (C in CO₂, N in NH₃, S in SO₃)
• Hydrogen and fluorine are ALWAYS terminal (outer) atoms
• Carbon ALWAYS forms 4 bonds in stable molecules
• Oxygen typically forms 2 bonds + 2 lone pairs
• Nitrogen typically forms 3 bonds + 1 lone pair

Quick recall

Draw the Lewis structure of NO_3^- . How many valence electrons?

N has 5, each O has 6, plus 1 for the negative charge = 5 + 18 + 1 = 24 e⁻. Structure: N is central, one N=O double bond and two N–O single bonds with one extra electron on each terminal O. Three resonance structures exist (the double bond rotates among the three O atoms).

Formal Charge

When multiple valid Lewis structures exist, formal charge helps pick the most stable one. The best structure has formal charges closest to zero, with negative formal charge on the more electronegative atom.

Formal charge is the charge an atom WOULD have if all bonding electrons were shared equally. It's a bookkeeping tool to evaluate which Lewis structure best represents the actual electron distribution.

FC = V - N - B 2

Where V = valence electrons of the free atom, N = non-bonding (lone pair) electrons, B = bonding electrons.

Example: CO₂ — For O=C=O: FC on C = 4 - 0 - 8 2 = 0 . FC on each O = 6 - 4 - 4 2 = 0 . All zeros — this is the best structure!

• Formal charge is NOT the actual charge on an atom — it's a theoretical assignment
• Sum of all formal charges = net charge of the species (0 for neutral molecules)
• FC = 0 on all atoms → ideal structure
• If FC 0, place negative FC on the more electronegative atom

Exceptions to the Octet Rule

Three types of molecules violate the octet rule: incomplete octet (BF₃, BeCl₂), odd-electron species (NO, NO₂), and expanded octet (PCl₅, SF₆) using d-orbitals for elements in period 3 and beyond.

The octet rule works beautifully for most molecules, but several important compounds break it. Understanding these exceptions is essential — NEET loves testing them.

• Incomplete octet: Central atom has < 8 electrons. Examples: BeCl_2 (4e⁻ on Be), BF_3 (6e⁻ on B), AlCl_3 (6e⁻ on Al)
• Odd-electron species: Total valence electrons is odd → at least one atom can't have a complete octet. Examples: NO (11e⁻), NO_2 (17e⁻), ClO_2 (19e⁻)
• Expanded octet: Central atom has > 8 electrons using empty d -orbitals. Only possible for Period 3 and beyond. Examples: PCl_5 (10e⁻ on P), SF_6 (12e⁻ on S), IF_7 (14e⁻ on I)

Coordinate (Dative) Bond

A special type of covalent bond where BOTH shared electrons come from the same atom (the donor). Once formed, a coordinate bond is indistinguishable from a regular covalent bond.

In a normal covalent bond, each atom contributes one electron to the shared pair. In a coordinate bond (also called dative bond), one atom provides BOTH electrons. The donor atom must have a lone pair, and the acceptor must have an empty orbital.

Donor(:) + Acceptor arrow Donor arrow Acceptor

• Represented by an arrow arrow pointing from donor to acceptor
• Donor = Lewis base (has lone pair): NH_3 , H_2O , CO
• Acceptor = Lewis acid (has empty orbital): H^+ , BF_3 , AlCl_3 , metal ions
• Once formed, coordinate bond is identical in properties to a normal covalent bond
• Examples: NH_4^+ (NH₃ donates to H⁺), H_3O^+ (H₂O donates to H⁺), CO (C donates to O), O_3

Quick recall

In NH_4^+ , how many coordinate bonds and how many covalent bonds are there?

1 coordinate bond (N donates lone pair to H⁺) + 3 normal covalent bonds (N–H). But once formed, ALL FOUR N–H bonds are identical — you can't tell which one was coordinate. Bond length and strength are the same for all four.

VSEPR Theory

Valence Shell Electron Pair Repulsion theory predicts molecular shapes by minimizing repulsion between electron pairs around the central atom. Lone pairs take more space than bonding pairs, distorting ideal geometries into actual molecular shapes.

Repulsion order: lp-lp > lp-bp > bp-bp

VSEPR Basics

The central idea of VSEPR: electron pairs (both bonding and lone pairs) around a central atom repel each other and arrange themselves to minimize repulsion. This arrangement determines the geometry.

VSEPR (Valence Shell Electron Pair Repulsion) theory is beautifully simple: electron pairs around a central atom repel each other and arrange themselves as far apart as possible. The geometry depends on the total number of electron pairs — both bonding pairs (bp) and lone pairs (lp).

• Electron pair geometry = arrangement of ALL electron pairs (bp + lp) around the central atom
• Molecular geometry = arrangement of only the ATOMS (ignores lone pairs in naming the shape)
• These two are the SAME only when there are zero lone pairs on the central atom
• A double or triple bond counts as a single electron pair region (called a 'super pair') for geometry prediction
• Repulsion order: lp–lp > lp–bp > bp–bp (lone pairs are 'fatter' — they spread out more)

Shapes with No Lone Pairs

When the central atom has ONLY bonding pairs and zero lone pairs, the electron pair geometry and molecular geometry are identical. These are the 'parent' shapes from which all distorted shapes derive.

When there are no lone pairs on the central atom, the molecular shape equals the electron pair geometry. These are the five fundamental shapes you MUST memorize:

• In TBP geometry, there are two distinct positions: axial (top/bottom, 90° to equatorial) and equatorial (middle plane, 120° apart)
• Multiple bonds count as ONE electron pair for geometry: CO₂ has 2 double bonds → 2 'super pairs' → linear
• All 5 shapes above are 'ideal' — they only occur when the central atom has zero lone pairs

Shapes with Lone Pairs

Lone pairs occupy more space than bonding pairs, compressing bond angles and creating shapes like bent, trigonal pyramidal, seesaw, T-shaped, and square pyramidal from their parent geometries.

When lone pairs are present, they occupy space but are invisible in the molecular shape (we only 'see' atoms). The molecular shape is named based on the positions of the ATOMS, not the electron pairs. Each lone pair distorts the ideal geometry.

• Each lone pair reduces bond angle by ~2-2.5° from the ideal
• NH₃: 1 lp compresses 109.5° → 107°. H₂O: 2 lps compress further → 104.5°
• In TBP geometry, lone pairs always go to equatorial positions (more room, less 90° interactions)
• In octahedral geometry, lone pairs go on opposite sides (trans) when there are 2 lps

The seesaw, T-shape, and square pyramidal shapes are rare in NEET questions, but XeF₂ (linear from TBP), XeF₄ (square planar from octahedral), and XeO₃ (trigonal pyramidal) appear frequently.

Hybridization

Hybridization is the mixing of atomic orbitals on the same atom to form new, equivalent hybrid orbitals with specific geometries. sp gives linear (180°), sp² gives trigonal planar (120°), sp³ gives tetrahedral (109.5°), sp³d gives TBP, and sp³d² gives octahedral.

Hybridization = 1 2 [V + M - C + A]

What is Hybridization?

Hybridization is the mathematical mixing of atomic orbitals (s, p, d) on the same atom to produce a new set of equivalent hybrid orbitals that are better oriented for bonding.

Here's the problem hybridization solves: carbon has the electron configuration 1s^2 2s^2 2p^2 . The 2s orbital is spherical, and the two 2p orbitals are at 90°. If carbon used these directly, CH₄ would have two types of bonds at 90° — but experimentally, all four C–H bonds are identical at 109.5°. Hybridization explains this by proposing that the 2s and three 2p orbitals mix to form four identical sp^3 hybrids.

• Number of hybrid orbitals = number of atomic orbitals mixed (conservation of orbitals)
• Hybrid orbitals are equivalent in energy and shape (unlike the original s and p orbitals)
• Only bonds and lone pairs use hybrid orbitals — bonds use unhybridized p orbitals
• Hybridization is a concept of the central atom — terminal atoms are usually not discussed
• Hybrid orbitals have one large lobe (for bonding) and one small lobe — better overlap than pure orbitals

Types of Hybridization

Each type of hybridization involves mixing a specific number of orbitals and produces a characteristic geometry. The type depends on the number of sigma bonds + lone pairs on the central atom.

• sp^3d and sp^3d^2 are possible only for Period 3 and beyond (need empty d orbitals)
• 2 unhybridized p orbitals remain in sp hybridization → available for 2 bonds
• 1 unhybridized p orbital remains in sp^2 hybridization → available for 1 bond
• 0 unhybridized p orbitals remain in sp^3 → no bonds possible

Diamond ( sp^3 , 3D network) is the hardest natural substance. Graphite ( sp^2 , layered sheets) is a lubricant. Same element, different hybridization, opposite properties!

How to Predict Hybridization

Count the number of sigma bonds + lone pairs on the central atom (called steric number). This directly gives the hybridization: 2→sp, 3→sp², 4→sp³, 5→sp³d, 6→sp³d².

You don't need to draw the full electronic configuration to predict hybridization. Just use the steric number — the total count of bonds + lone pairs on the central atom. Multiple bonds (double/triple) count as just ONE bond for this purpose.

Simpler method: Just count bonds + lone pairs on the central atom. - CO₂: C has 2 double bonds = 2 bonds + 0 lp → steric number 2 → sp - NH₃: N has 3 N–H bonds + 1 lp → steric number 4 → sp³ - SF₆: S has 6 S–F bonds + 0 lp → steric number 6 → sp³d²

Quick recall

What is the hybridization of Xe in XeF₄?

Xe has 8 valence e⁻. It forms 4 bonds (to 4 F) using 4 e⁻ for bonding. Remaining 4 e⁻ = 2 lone pairs. Steric number = 4 bonds + 2 lp = 6 → sp³d² → octahedral electron geometry → square planar molecular shape.

Hybridization in Organic Molecules

In organic chemistry, carbon switches between sp³ (single bonds, tetrahedral), sp² (one double bond, planar), and sp (triple bond, linear). Identifying hybridization at each carbon is a critical NEET skill.

Carbon is unique — it readily adopts all three common hybridizations. Each carbon atom in a molecule can have its OWN hybridization. In CH_2=CH–C , the four carbons are sp^2 , sp^2 , sp , sp from left to right.

• sp³ carbon: 4 single bonds, tetrahedral, 109.5° — ethane ( C_2H_6 ), methane, cyclohexane
• sp² carbon: 1 double bond + remaining single bonds, trigonal planar, 120° — ethene ( C_2H_4 ), benzene, CO_3^ 2-
• sp carbon: 1 triple bond or 2 double bonds, linear, 180° — ethyne ( C_2H_2 ), CO₂, C_3O_2
• Each C–C single bond allows free rotation; C=C double bond does NOT (restricted by bond)
• In benzene, all 6 carbons are sp^2 with delocalized electrons above and below the ring

Quick recall

In CH_3–CHO (acetaldehyde), what is the hybridization of each carbon?

Carbon-1 (CH₃): 4 bonds + 0 lp → steric number 4 → sp³. Carbon-2 (CHO): 3 bonds (1 to C, 1 to H, 1 to O in the part of C=O) + 0 lp → steric number 3 → sp². The C=O has one (hybrid orbital) + one (unhybridized p ).

Molecular Orbital Theory

MOT treats electrons as belonging to the entire molecule, not individual atoms. Atomic orbitals combine to form bonding (lower energy) and antibonding (higher energy) molecular orbitals. Bond order = ½(bonding - antibonding) determines stability and magnetic behavior.

Bond Order = N_b - N_a 2

MOT Basics

Unlike VBT (which keeps electrons localized between atoms), MOT says electrons in a molecule occupy molecular orbitals that spread over the entire molecule. Atomic orbitals combine to form bonding MOs (constructive interference) and antibonding MOs (destructive interference).

Molecular Orbital Theory (MOT) is a more sophisticated approach than Lewis structures or VBT. The key idea: when atoms combine, their atomic orbitals merge to form molecular orbitals (MOs) that belong to the entire molecule. Electrons fill these MOs according to the same rules as atomic orbitals (Aufbau, Pauli, Hund's).

• When 2 atomic orbitals combine → 2 molecular orbitals form (conservation of orbitals)
• Bonding MO ( , ): lower energy than parent AOs, electron density concentrated BETWEEN nuclei → stabilizes the molecule
• Antibonding MO ( ^* , ^* ): higher energy than parent AOs, electron density concentrated OUTSIDE the internuclear region → destabilizes the molecule
• Bonding MO = constructive interference (in-phase overlap) of wavefunctions
• Antibonding MO = destructive interference (out-of-phase overlap), has a node between nuclei

MO Energy Level Diagram

The order of filling MOs differs for molecules with Z ≤ 7 (like N₂) versus Z > 7 (like O₂, F₂). This difference in ordering is the most tested aspect of MOT in NEET.

Molecular orbitals are filled in order of increasing energy, just like atomic orbitals. But the energy ordering of MOs changes depending on the atomic number:

• The ONLY difference: for Z 7, _ 2p_z is ABOVE _ 2p (s-p mixing pushes it up)
• For Z > 7, _ 2p_z is BELOW _ 2p (normal order)
• This ordering difference determines whether B₂ and O₂ are paramagnetic or diamagnetic
• Both _ 2p_x and _ 2p_y have the SAME energy (degenerate) — fill them by Hund's rule

Bond Order & Magnetic Properties

Bond order = ½(bonding electrons - antibonding electrons). It predicts bond stability, bond strength, and bond length. Unpaired electrons in MOs make the molecule paramagnetic.

Bond Order = N_b - N_a 2

Where N_b = number of electrons in bonding MOs, N_a = number of electrons in antibonding MOs.

• Bond order > 0 → molecule is stable (exists)
• Bond order = 0 → molecule does NOT exist (e.g., He₂, Be₂, Ne₂)
• Higher bond order → shorter bond length and higher bond energy (stronger bond)
• Paramagnetic: has unpaired electrons in MOs (attracted to magnetic field) — O₂, B₂, NO
• Diamagnetic: all electrons paired (weakly repelled by magnetic field) — N₂, F₂, CO

Quick recall

Arrange in order of increasing bond length: N_2 , N_2^+ , N_2^- .

Bond orders: N₂ = 3, N₂⁺ = 2.5 (lost 1 bonding electron), N₂⁻ = 2.5 (gained 1 antibonding electron). Bond length order: N₂ < N₂⁺ = N₂⁻. Higher bond order → shorter bond.

Resonance

When a single Lewis structure cannot adequately represent a molecule's electron distribution, multiple structures (resonance structures) are drawn. The actual molecule is a weighted average (resonance hybrid) of all valid structures. Resonance stabilizes the molecule by delocalizing electrons.

Resonance Energy = E_ actual - E_ most stable contributing structure

Resonance

Some molecules cannot be accurately represented by a single Lewis structure because electrons are delocalized over multiple atoms. We draw multiple structures connected by double-headed arrows (↔), and the real molecule is a blend of all of them.

Consider ozone ( O_3 ). We can draw O=O–O (double bond on the left) or O–O=O (double bond on the right). Experiments show BOTH O–O bonds are identical (128 pm) — intermediate between a single bond (148 pm) and double bond (121 pm). Neither Lewis structure alone is correct. The real molecule is a resonance hybrid — a blend of both structures.

• Resonance structures are connected by a double-headed arrow rightarrow (NOT a regular arrow arrow , which means a reaction)
• The actual molecule is a resonance hybrid — NOT a mixture and NOT alternating between structures
• Only electrons move between resonance structures — atoms stay in the same positions
• More resonance structures → more delocalization → greater stability (lower energy)
• Resonance is a limitation of Lewis structure theory, not a real physical phenomenon

Rules for Drawing Resonance Structures

Resonance structures must have the same atom arrangement, same total electrons, and follow certain rules. Not all resonance structures contribute equally — equivalent structures contribute most.

Drawing valid resonance structures requires following strict rules. Break any of these, and the structure isn't a valid resonance form.

• Rule 1: All structures must have the same arrangement of atoms (only electrons move, not atoms)
• Rule 2: All structures must have the same number of total electrons
• Rule 3: All structures must have the same number of unpaired electrons (same multiplicity)
• Rule 4: Equivalent resonance structures contribute equally to the hybrid (e.g., all three structures of CO_3^ 2- )
• Rule 5: Structures with more covalent bonds and fewer formal charges are more stable → contribute more

Resonance Energy

The difference between the actual energy of the molecule and the energy of the most stable single resonance structure is the resonance energy. Greater resonance energy means the molecule is much more stable than any single Lewis structure suggests.

Resonance energy (also called delocalization energy) is always negative (stabilizing). It measures how much MORE stable the actual molecule is compared to the best single Lewis structure. The more equivalent resonance structures a molecule has, the larger the resonance energy.

Resonance Energy = E_ actual - E_ most stable resonance structure

• Benzene has a resonance energy of ~150 kJ/mol — this is why it's exceptionally stable and undergoes substitution rather than addition reactions
• More equivalent resonance structures → greater resonance energy → greater stability
• Resonance energy cannot be measured directly — it's calculated as the difference between experimental and theoretical (single-structure) values
• Resonance stabilization explains: stability of carboxylate ion ( RCOO^- ), acidity of carboxylic acids, basicity differences among amines

Quick recall

Which is more stable: CO_3^ 2- or CO_2 ? Why?

CO_3^ 2- has 3 equivalent resonance structures (all C–O bonds identical), giving it significant resonance stabilization. CO_2 has only one dominant structure (O=C=O) with no real resonance (the two bonds are already equivalent by symmetry). However, stability comparison depends on context — CO_3^ 2- is more 'resonance-stabilized' per bond.

Bond Parameters

Bond parameters — bond length, bond energy, bond angle, and bond order — are measurable properties that characterize chemical bonds. They are interconnected: higher bond order means shorter bond length, higher bond energy, and different bond angles depending on hybridization.

Bond Order Bond Length Bond Energy

Bond Length

Bond length is the equilibrium distance between the nuclei of two bonded atoms. It depends on atomic size, bond order, hybridization, and resonance. Shorter bonds are stronger bonds.

Bond length is the distance between the centers (nuclei) of two bonded atoms when the molecule is in its equilibrium (lowest energy) state. It's measured in picometers (pm) or angstroms (A, where 1 A = 100 pm).

• Atomic size ↑ → bond length ↑ (larger atoms are farther apart): H–F (92 pm) < H–Cl (127 pm) < H–Br (141 pm) < H–I (161 pm)
• Bond order ↑ → bond length ↓ (more shared electrons pull atoms closer): C–C (154 pm) > C=C (134 pm) > C C (120 pm)
• Hybridization: sp bonds are shortest, sp^3 bonds are longest: sp –H < sp^2 –H < sp^3 –H because s -character increases → orbital is closer to nucleus
• Resonance makes all equivalent bonds equal length: all C–C bonds in benzene = 139 pm (between 154 and 134 pm)

Quick recall

Arrange in increasing bond length: C–C in ethane, C–C in ethene, C–C in benzene, C–C in ethyne.

Ethyne (C C, 120 pm) < Ethene (C=C, 134 pm) < Benzene (C–C, 139 pm, bond order 1.5) < Ethane (C–C, 154 pm). Higher bond order → shorter length.

Bond Energy

Bond energy (or bond dissociation energy) is the energy required to break one mole of a particular bond in gaseous molecules. Higher bond energy = stronger bond = harder to break.

Bond dissociation energy is the energy needed to break one mole of a specific bond in a gaseous molecule into gaseous fragments (atoms or radicals). For polyatomic molecules, we often use the average bond energy — the mean of all bond dissociation energies of the same type of bond.

• Bond order ↑ → bond energy ↑: C–C (347 kJ/mol) < C=C (614) < C C (839)
• N N has one of the highest bond energies: 941 kJ/mol (explains N₂'s extreme inertness)
• Bond length ↓ → bond energy ↑ (shorter bonds are stronger bonds)
• Bond energy is always positive (energy must be input to break bonds)
• Average bond energy of O–H in H₂O: first O–H takes 502 kJ/mol, second takes 427 kJ/mol → average = 464 kJ/mol

Bond Angle

Bond angle is the angle between two adjacent bonds at the same central atom. It depends on hybridization, lone pairs, electronegativity of substituents, and multiple bonds.

Bond angle is the angle formed between two covalent bonds that share a common atom. It's determined primarily by the hybridization of the central atom, but lone pairs and substituent electronegativity cause deviations from ideal values.

Classic comparison: NH₃ (107°) vs NF₃ (102°). Both are sp^3 with 1 lone pair. But F is more electronegative than H → pulls bonding electrons away from N → less bp-bp repulsion → smaller angle in NF₃.

• Ideal angles: linear (180°), trigonal planar (120°), tetrahedral (109.5°), TBP (90°, 120°), octahedral (90°)
• Each lone pair reduces the angle by approximately 2–2.5° from the ideal
• CH₄ (109.5°) > NH₃ (107°) > H₂O (104.5°) — progressive increase in lone pairs
• Lone pair–lone pair repulsion > lone pair–bond pair > bond pair–bond pair

Bond Order

Bond order is the number of chemical bonds between a pair of atoms. It can be a whole number (1, 2, 3) for simple molecules or a fraction (1.33, 1.5) for resonance structures. It connects to both bond length and bond energy.

Bond order is the number of electron pairs shared between two atoms. For simple molecules: single bond = 1, double bond = 2, triple bond = 3. For resonance structures, bond order can be fractional.

Bond Order (in resonance) = Total number of bonds between two atoms across all structures Number of resonance structures

• Higher bond order → shorter bond length → higher bond energy → higher bond stretching frequency (IR)
• Bond order can be fractional: benzene C–C = 1.5, CO_3^ 2- C–O = 1.33, SO_3 S–O = 1.67
• In MOT: Bond order = N_b - N_a 2 (can predict non-integer values and zero values)
• Bond order = 0 → molecule does not exist (e.g., He₂, Be₂)

Quick recall

What is the bond order of S–O in SO_3 ?

S forms 3 bonds to 3 oxygen atoms across 3 equivalent resonance structures. In each structure, one S=O is a double bond and two S–O are single bonds (with coordinate character). Total bonds per S–O position across 3 structures = 2+1+1 = 4. Structures = 3. Bond order = 5/3 ≈ 1.67.

Hydrogen Bonding

Hydrogen bonding is an especially strong intermolecular force that occurs when H bonded to a highly electronegative atom (F, O, N) interacts with a lone pair on another electronegative atom. It explains the anomalously high boiling points of water, HF, and NH₃, and is crucial for DNA structure and protein folding.

X–H Y (where X, Y = F, O, or N)

Nature of Hydrogen Bond

A hydrogen bond forms when a hydrogen atom covalently bonded to F, O, or N is attracted to a lone pair on a nearby F, O, or N atom. It has about 10-40 kJ/mol strength — roughly 1/10th of a covalent bond.

A hydrogen bond is an attractive interaction between a hydrogen atom bonded to a highly electronegative atom (F, O, or N) and a lone pair on another electronegative atom (F, O, or N) — either in the same molecule or in a different molecule. It's written as X–H···Y, where the dashed line represents the hydrogen bond.

• H-bond strength: 10–40 kJ/mol (vs covalent bond: 200–400 kJ/mol, vs van der Waals: 1–10 kJ/mol)
• H-bond is mainly electrostatic but has a small covalent component (~10%)
• The H-bond is directional — strongest when X–H···Y is linear (180°)
• F forms the strongest H-bonds, followed by O, then N: H-bond strength F > O > N
• Hydrogen bond is NOT a true bond — it's an intermolecular force (but the strongest type of intermolecular force)

Types

Intermolecular H-bonds occur between different molecules (increasing boiling point). Intramolecular H-bonds occur within the same molecule (decreasing boiling point relative to intermolecular H-bonded isomers).

Hydrogen bonds come in two varieties based on whether the donor and acceptor are on the same molecule or different molecules. This distinction has dramatic effects on physical properties.

• Intramolecular H-bonds form when donor and acceptor groups are close together (5-7 membered ring preferred)
• Intramolecular H-bonding 'locks up' the H-bond donors/acceptors → fewer sites available for intermolecular interaction
• This is why ortho-isomers often have lower b.p. than para-isomers in substituted phenols and benzoic acids

Effects of H-Bonding

Hydrogen bonding explains anomalous boiling points (H₂O > H₂S), ice floating on water, DNA double helix stability, protein folding, and the solubility of polar molecules in water.

Hydrogen bonding is responsible for many of water's unusual properties and is the single most important intermolecular force in biology.

• Anomalous boiling points: H₂O (100°C) >> H₂S (–60°C), even though H₂S has higher molecular mass. Same trend: HF >> HCl, NH₃ >> PH₃
• Ice floats on water: H-bonds in ice create an open hexagonal structure (less dense than liquid water). This is why lakes freeze top-down, and aquatic life survives in winter.
• DNA double helix: A–T base pairs connected by 2 H-bonds, G–C pairs by 3 H-bonds. This is why GC-rich DNA is harder to denature (higher melting temp).
• Protein structure: -helix and -sheet secondary structures are stabilized by N–H···O=C hydrogen bonds between amino acid backbone atoms
• Water as universal solvent: H-bonds with polar solutes (sugars, alcohols, amino acids) → excellent dissolution

Quick recall

Why does H₂O have a higher boiling point than HF, even though F is more electronegative than O?

Each H₂O molecule can form 4 H-bonds (2 as donor via 2 O–H bonds, 2 as acceptor via 2 lone pairs on O). HF can form only 2 H-bonds (1 donor H, and F has 3 lone pairs but only 1 H to donate). Water forms an extensive 3D H-bond network → much more energy needed to break → higher b.p.

Dipole Moment & Polarity

Dipole moment measures the polarity of a bond or molecule. It equals charge times distance (μ = q × d) and is a vector quantity. The net dipole moment of a molecule depends on both individual bond polarities AND molecular geometry — symmetric molecules can have zero net dipole despite having polar bonds.

= q d (unit: Debye, D)

Dipole Moment

Dipole moment (μ) is the product of charge magnitude (q) and distance of separation (d). It's a vector pointing from positive to negative end. The unit is Debye (D), where 1 D = 3.336 × 10⁻³⁰ C·m.

When two bonded atoms have different electronegativities, the shared electrons are pulled toward the more electronegative atom, creating a partial negative charge ( ^- ) on that atom and a partial positive charge ( ^+ ) on the other. This separation of charge creates a dipole moment.

= q d

Where q = magnitude of partial charge on either atom, d = distance between the charges (bond length). Unit: Debye (D), where 1 D = 3.336 10^ -30 C m.

• Dipole moment is a vector — it has both magnitude and direction
• Direction convention: the arrow points from ^+ to ^- (in chemistry; physics uses the opposite convention)
• Greater electronegativity difference → greater dipole moment of the bond
• Pure covalent bonds (H–H, Cl–Cl) have = 0 (no charge separation)
• 100% ionic bond would have = e d (where e = electronic charge). Actual is always less → gives % ionic character

% ionic character = _ observed _ if 100 % ionic 100

Molecular Dipole Moment

The net dipole moment of a molecule is the vector sum of all individual bond dipoles. Symmetric molecules like CO₂, BF₃, CCl₄, and SF₆ have zero net dipole despite having polar bonds, because the bond dipoles cancel perfectly.

Individual bonds may be polar, but the MOLECULE can still be non-polar if the bond dipoles cancel by vector addition. This happens when the molecule has a symmetric geometry.

• Symmetric molecules with identical substituents → = 0 : CO₂, BF₃, CH₄, CCl₄, SF₆, XeF₂, XeF₄
• Any molecule with lone pair(s) on central atom → usually 0 (lone pair contributes a dipole)
• Exception: XeF₂ (linear, 3 lp) and XeF₄ (square planar, 2 lp) have = 0 because lone pairs cancel by symmetry
• For diatomic molecules: _ molecule = _ bond (there's only one bond)

Applications of Dipole Moment

Dipole moment measurements reveal molecular geometry, distinguish between cis and trans isomers, determine percent ionic character, and predict solubility and intermolecular forces.

Dipole moment is not just a number — it's a powerful diagnostic tool that reveals the structure and properties of molecules.

• Determining geometry: (H_2O) = 1.85 D proves water is bent (if linear, would be 0)
• cis vs trans: cis-1,2-dichloroethene has 0 (dipoles add), trans has = 0 (dipoles cancel) → used to distinguish isomers
• % ionic character: comparing observed with theoretical 100% ionic gives the ionic character of the bond
• Predicting solubility: like dissolves like — polar molecules ( 0 ) dissolve in polar solvents (water), non-polar ( = 0 ) dissolve in non-polar solvents (hexane)
• Intermolecular forces: higher → stronger dipole-dipole interactions → higher boiling point (among molecules of similar size)

Quick recall

Which has a higher dipole moment: NH₃ or NF₃? Why is this surprising?

NH₃ ( = 1.47 D) > NF₃ ( = 0.24 D). Surprising because F is MORE electronegative than H! In NH₃, the lone pair dipole and bond dipoles point in the SAME direction (both away from N). In NF₃, bond dipoles point TOWARD F (away from N) but the lone pair points away from N → they OPPOSE each other, nearly canceling.