Chemistry Class 11 Chapter 3: Chemical Bonding Notes

Chemical bonding explains why substances have the properties they do, and this chapter builds a full toolkit for understanding it. It starts with the three core Lewis-theory bond types, ionic, covalent, and dative, and with polyatomic ions whose central atoms expand beyond a normal octet, before turning to electronegativity as the single quantity that predicts whether a bond will be nonpolar covalent, polar covalent, or ionic, and to dipole moment as the measurable consequence of that polarity.

The second half develops three complementary models used to explain and predict molecular structure and bonding: Valence Bond Theory, which describes covalent bonds as the overlap of atomic orbitals into sigma and pi bonds, often after hybridization into sp, sp2, or sp3 orbitals; the VSEPR model, which predicts a molecule's three-dimensional shape and bond angles purely from the number of bonding and lone electron pairs around its central atom, with real applications in drug design; and Molecular Orbital Theory, which explains subtler effects such as oxygen's paramagnetism that simpler theories cannot, using the concept of bond order.

Learning Objectives

• Analyze the formation of dative bonds in CO, ozone, and the H3O+ ion
• Recognize that polyatomic ions such as sulfate and nitrate can have expanded octets
• Use electronegativity differences to predict whether a bond is ionic or covalent
• Use electronegativity to explain bond polarity and the dipole moments of molecules
• Describe the shapes and bond angles of molecules and ions using VSEPR theory, including its role in drug design
• Explain valence bond theory and describe covalent bonding using sp, sp2, and sp3 hybridization
• Explain the salient features of molecular orbital theory and the paramagnetic nature of the oxygen molecule
• Calculate the bond order of N2, O2, F2, and He2
• Describe van der Waals forces and hydrogen bonding, and use hydrogen bonding to explain the anomalous properties of water
• Use bond energy and bond length values to compare the reactivity and strength of covalent molecules

Key Concepts

3.1 Types of Chemical Bonds: Ionic, Covalent, and Dative

According to Lewis theory, atoms bond to complete their outermost shell with a noble-gas-like configuration, usually an octet. An ionic bond forms by the complete transfer of one or more electrons from an atom of low ionization energy to an atom of high electron affinity, as when sodium (2,8,1) loses its outer electron to become Na+ (2,8), matching neon's configuration, while chlorine (2,8,7) gains that electron to become Cl- (2,8,8), matching argon's; the oppositely charged ions then attract each other strongly in the crystal lattice. A covalent bond, by contrast, forms by the mutual sharing of an electron pair between two atoms, each completing its own valence shell; the bond is nonpolar when the two atoms have identical electronegativity, as in Cl2, and polar when they differ, as in H-Cl.

A dative, or coordinate covalent, bond forms when one atom alone supplies both electrons of the shared pair: an electron-rich donor atom with a lone pair bonds to an electron-deficient acceptor. In the hydronium ion, H3O+, a lone pair on the oxygen of water is donated to a bare proton; in carbon monoxide, oxygen forms a normal double bond to carbon and then donates a further lone pair to satisfy carbon's octet; and in ozone, O3, one oxygen atom donates a lone pair to a second oxygen atom, bonded as a free radical, forming a coordinate bond that leaves the donor atom with a formal positive charge and the acceptor atom a formal negative charge.

3.2 Expanded Octets in Polyatomic Ions

Polyatomic ions are composed of more than one type of atom and mostly carry a negative charge, common examples being carbonate, sulfate, and nitrate. In some of these ions, such as sulfate (SO4 2-), the central atom exceeds the normal octet by using its available d orbitals to accommodate extra electron density; the number of valence electrons around the central atom can be counted directly from its Lewis structure as 2 times the number of double-bond electron pairs plus 2 times the number of single-bond electron pairs or lone pairs, and for sulfate this comes to 12 electrons, four more than a normal octet. This expansion, seen also in ions such as ClO4- and the tri-iodide ion I3- which expands to 10 electrons around its central iodine, is only possible for elements from period 3 onward, since period 2 elements have no accessible d orbitals to expand into.

3.3 Electronegativity, Bond Type, and Bond Polarity

The difference in electronegativity between two bonded atoms is a reliable predictor of bond type: a difference below about 0.4 gives a nonpolar covalent bond, a difference between 0.4 and 1.8 gives a polar covalent bond, and a difference above 1.8 gives an ionic bond. This scale is illustrated by the electronegativity differences of H-H (0, nonpolar), H-Cl (0.9, polar covalent), and NaCl (2.1, ionic) — exactly matching their observed bonding character.

3.4 Dipole Moment and Molecular Polarity

When two bonded atoms differ in electronegativity, the shared electron density shifts toward the more electronegative atom, leaving a partial positive charge on one atom and a partial negative charge on the other; a molecule with this separation of charge is called a dipole, and the size of the separation is its dipole moment, measured in Debye units, with a higher value indicating greater polarity. For molecules of more than two atoms, the overall dipole moment depends on molecular geometry: water's V-shaped structure gives it a net dipole moment of 1.85 D directed from the hydrogen end toward the oxygen end, and the fact that this value is nonzero is itself evidence that water is bent rather than linear.

Some molecules have individually polar bonds yet a net dipole moment of zero, because their symmetric geometry causes the individual bond moments to cancel exactly: BeCl2 is linear with its two Be-Cl moments pointing in opposite directions, BF3 is trigonal planar with its three B-F moments cancelling, and CCl4 is perfectly tetrahedral with its four C-Cl moments cancelling, making all three molecules nonpolar overall despite having polar bonds. As a general rule, a molecule with identical ligands arranged in a regular, symmetric geometry around the central atom will have zero net dipole moment.

3.5 Bond Energy, Bond Length, and Relative Bond Strengths

Bond energy is the average energy required to break one mole of a particular bond, and it measures both bond strength and reactivity; it rises with increasing electronegativity difference between the bonded atoms, for example H-F at 565 kJ/mol is far stronger than H-I at 295 kJ/mol, and multiple bonds are always stronger than single bonds between the same two atoms (C triple-bond C is stronger than C=C, which is stronger than C-C). Bond length, the distance between two bonded nuclei, generally increases with the size of the bonded atoms, C-Cl at 180 pm is longer than C-F at 135 pm, and decreases as electronegativity difference increases, since the resulting ionic character pulls the atoms closer together.

Comparing bond energies across bond types confirms that true chemical bonds are far stronger than intermolecular forces: the ionic bond in NaCl (760 kJ/mol) and the covalent O-H bond in water (464 kJ/mol) both dwarf hydrogen bonding (20-50 kJ/mol), permanent dipole-dipole forces (5-20 kJ/mol), and London dispersion forces (1-20 kJ/mol); the metallic bond, at around 100-150 kJ/mol, sits between these two groups, its relative weakness attributed to the extensive delocalization of electrons throughout the metallic crystal.

3.6 Valence Bond Theory: Sigma and Pi Bonds

Valence Bond Theory (VBT) explains covalent bond formation, not just molecular shape: a bond forms when two half-filled atomic orbitals of similar energy, one from each atom, overlap along the line joining their nuclei, and a greater degree of overlap produces a stronger, more directional bond. A sigma bond forms by this kind of head-on, linear overlap, s-s overlap as in H2, s-p overlap as in HCl, or p-p overlap along the same axis as in Cl2, and is the only type of bond present in every single covalent bond, single or multiple.

A pi bond forms differently: when two p orbitals on adjacent atoms are aligned parallel to each other rather than head-on, their sideways overlap creates two regions of electron density, one above and one below the line joining the nuclei. A double bond, such as in O2, therefore consists of one sigma bond, from head-on overlap of one pair of p orbitals, plus one pi bond, from sideways overlap of a second, perpendicular pair; a triple bond, such as in N2, consists of one sigma bond plus two pi bonds, using all three p orbitals on each atom.

3.7 Atomic Orbital Hybridization

Hybridization is the mixing of atomic orbitals of comparable energy within a single atom to form a new set of equivalent orbitals of identical energy and shape, with the number of hybrid orbitals produced always equal to the number of atomic orbitals mixed. In sp hybridization, one s and one p orbital mix to give two sp orbitals arranged linearly at 180 degrees, explaining the linear geometry of BeCl2; in sp2 hybridization, one s and two p orbitals mix to give three sp2 orbitals arranged in a trigonal plane at 120 degrees, explaining the shape of BF3.

In sp3 hybridization, one s and three p orbitals mix to give four sp3 orbitals arranged tetrahedrally, explaining the shape of methane, CH4, where each of the four sp3 orbitals of carbon overlaps with a hydrogen 1s orbital to form a sigma bond directed toward a corner of a regular tetrahedron. In every case, hybrid orbitals have lower energy than the unhybridized atomic orbitals they replace, and the resulting hybrid-orbital geometry, linear for sp, trigonal planar for sp2, tetrahedral for sp3, directly matches the electron-pair geometry predicted independently by the VSEPR model.

3.8 VSEPR Theory: Predicting Molecular Shapes

The Valence Shell Electron Pair Repulsion (VSEPR) model, proposed by Sidgwick and Powell, predicts a molecule's shape from the idea that all electron pairs around a central atom, bonding and lone pairs alike, arrange themselves as far apart as possible to minimize repulsion. Because lone pairs occupy more space than bond pairs, the strength of repulsion follows the order lone pair-lone pair greater than lone pair-bond pair greater than bond pair-bond pair, so a lone pair always compresses the bond angles around it below the ideal geometric value: ammonia's bond angle is compressed from the ideal 109.5 degrees to 107 degrees by one lone pair, and water's is compressed further, to 104.5 degrees, by two.

The total number of electron pairs around the central atom sets the electron-pair geometry, 2 pairs give linear, 3 give trigonal planar, 4 give tetrahedral, 5 give trigonal bipyramidal, and 6 give octahedral, while the molecule's actual shape is this same geometry with any lone-pair positions left out of the description — so four electron pairs give a tetrahedral shape with zero lone pairs (CH4), a pyramidal shape with one lone pair (NH3), and a bent, V-shaped molecule with two lone pairs (H2O). A double or triple bond, despite containing two or three electron pairs, is still treated as a single region of electron density for VSEPR purposes.

3.9 VSEPR in Drug Design

Drugs act on specific biological targets, such as enzyme active sites, through bioactive molecules called ligands, and a drug's effectiveness depends heavily on its molecular shape fitting its target the way a key fits a lock, a property called specificity. Because VSEPR theory predicts the three-dimensional shape and bond angles of a molecule directly from its structure, it is a practical tool in drug design for judging whether a candidate ligand's shape is compatible with a target's active site; aspirin, for example, binds to and blocks the enzyme cyclooxygenase (COX) because the shape of its acetyl group is complementary to the shape of COX's active site.

3.10 Molecular Orbital Theory: Bond Order and Paramagnetism

Molecular Orbital Theory (MOT) treats a molecule's electrons as occupying molecular orbitals belonging to the whole molecule, formed when atomic orbitals of matching sign overlap. Two atomic orbitals always combine to give two molecular orbitals: a lower-energy bonding orbital, sigma or pi, when same-sign lobes overlap, and a higher-energy antibonding orbital, sigma-star or pi-star, when opposite-sign lobes overlap. Bond order, a measure of the number of bonds between two atoms, is calculated as half the difference between the number of electrons in bonding orbitals and the number in antibonding orbitals; a bond order of zero, as calculated for He2, means the molecule does not form at all.

Applying this method to N2 gives a bond order of 3, one sigma and two pi bonds, consistent with its known triple bond and very high bond energy, while O2 gives a bond order of 2, one sigma and one pi bond, a double bond, but MOT reveals something VBT cannot: oxygen's molecular orbital diagram places two of its electrons singly, with parallel spins, in two separate antibonding pi-star orbitals. These two unpaired electrons make O2 paramagnetic, meaning it is attracted into a magnetic field, a real, experimentally observed property, liquid oxygen visibly clings between the poles of a strong magnet, that simpler bonding theories fail to predict.

Important Definitions

Key Facts and Relations

Topic	Key Fact / Relation
Bond-type prediction by electronegativity difference	Below 0.4: nonpolar covalent | 0.4-1.8: polar covalent | above 1.8: ionic
Valence electrons around a central atom (Lewis structure)	2 x (double-bond electron pairs) + 2 x (single-bond pairs or lone pairs)
Bond order (MOT)	Bond order = (bonding electrons – antibonding electrons) / 2
Bond order of N2	3 (one sigma + two pi bonds)
Bond order of O2	2 (one sigma + one pi bond); paramagnetic, 2 unpaired electrons in pi* orbitals
Bond order of He2	0 (molecule does not form)
VSEPR: 4 pairs, 0 lone pairs	Tetrahedral shape, 109.5 degrees, e.g. CH4
VSEPR: 4 pairs, 1 lone pair	Pyramidal shape, about 107 degrees, e.g. NH3
VSEPR: 4 pairs, 2 lone pairs	Bent/V-shaped, about 104.5 degrees, e.g. H2O
Relative bond strength (kJ/mol)	Ionic (NaCl, 760) > covalent (O-H, 464) > hydrogen bond (20-50) > dipole-dipole (5-20) > London dispersion (1-20)

Diagrams

VSEPR Molecular Shapes: A comparison of five VSEPR shapes, linear (BeCl2), trigonal planar (BF3), tetrahedral (CH4), pyramidal (NH3), and bent (H2O), showing how lone pairs progressively compress the bond angle

sp, sp2, and sp3 Hybrid Orbital Geometries: Three panels showing the linear arrangement of sp orbitals in BeCl2, the trigonal planar arrangement of sp2 orbitals in BF3, and the tetrahedral arrangement of sp3 orbitals in CH4

Molecular Orbital Diagram of Oxygen (O2): An energy-level diagram showing bonding and antibonding molecular orbitals of O2, with two unpaired electrons in the pi* orbitals responsible for its paramagnetism

Short Questions & Answers

Long Questions & Answers

Explain how Valence Bond Theory and orbital hybridization together account for the shapes and bonding of covalent molecules such as BeCl2, BF3, and CH4.

What does Valence Bond Theory say about how a covalent bond forms?

VBT states that a covalent bond forms when two half-filled atomic orbitals of similar energy, one from each atom, overlap along the axis joining their nuclei; greater orbital overlap produces a stronger bond, and the bond's direction is fixed by the shape and orientation of the overlapping orbitals.

What is the difference between a sigma bond and a pi bond?

A sigma bond forms by head-on, linear overlap of two orbitals along the internuclear axis and is present in every covalent bond; a pi bond forms by sideways overlap of two parallel p orbitals, giving electron density above and below the internuclear axis, and appears only in double and triple bonds alongside a sigma bond.

What is hybridization, and why is it needed to explain molecular shapes?

Hybridization is the mixing of atomic orbitals of comparable energy within a single atom into a new set of equivalent orbitals of the same energy and shape; it is needed because the shapes of pure, unmixed atomic orbitals, spherical s, dumbbell p, cannot by themselves account for the observed bond angles of real molecules.

How does sp hybridization explain the linear shape of BeCl2?

Beryllium's one 2s and one 2p orbital mix to form two sp hybrid orbitals arranged at 180 degrees; each overlaps with a half-filled p orbital of a chlorine atom to form a sigma bond, so BeCl2 adopts the same 180-degree linear arrangement as the hybrid orbitals themselves.

How do sp2 and sp3 hybridization explain the shapes of BF3 and CH4?

In BF3, boron's one 2s and two 2p orbitals mix to form three sp2 orbitals arranged in a trigonal plane at 120 degrees, matching BF3's trigonal planar shape; in CH4, carbon's one 2s and three 2p orbitals mix to form four sp3 orbitals arranged tetrahedrally at 109.5 degrees, matching methane's tetrahedral shape, with each hybrid orbital overlapping a hydrogen 1s orbital to form a sigma bond.

Describe the postulates of the VSEPR model and explain, using molecular orbital theory, why simple bonding theories fail to predict the paramagnetism of oxygen.

What are the key postulates of the VSEPR model?

Both lone pairs and bond pairs around a central atom determine molecular geometry; electron pairs arrange themselves as far apart as possible to minimize repulsion; lone pairs occupy more space and repel more strongly than bond pairs, so repulsion strength follows lone pair-lone pair greater than lone pair-bond pair greater than bond pair-bond pair; and a multiple bond, despite containing more than one electron pair, is treated as a single region of electron density.

How does the number of electron pairs around a central atom determine electron-pair geometry?

Two electron pairs give a linear geometry, three give trigonal planar, four give tetrahedral, five give trigonal bipyramidal, and six give octahedral; this electron-pair geometry is then adjusted for the molecule's actual shape by considering only the positions of the bonded atoms, excluding any lone pairs.

What are the postulates of molecular orbital theory?

Atomic orbitals of the combining atoms overlap to form new molecular orbitals belonging to the whole molecule; same-sign orbital overlap produces a lower-energy bonding orbital, while opposite-sign overlap produces a higher-energy antibonding orbital; and bond order, a measure of the number of bonds formed, equals half the difference between the number of electrons in bonding and antibonding orbitals.

What does the molecular orbital diagram of O2 show about its electron arrangement?

Filling O2's molecular orbitals in order of increasing energy leaves two electrons to occupy the degenerate pi-star (2py) and pi-star (2pz) antibonding orbitals; following Hund's rule, these two electrons occupy the two orbitals singly, with parallel spins, rather than pairing up in one.

Why can Valence Bond Theory not explain oxygen's paramagnetism, while molecular orbital theory can?

VBT depicts the oxygen-oxygen double bond simply as one sigma and one pi bond, formed from fully-paired shared electrons, and provides no way to represent unpaired electrons within that picture; MOT, by contrast, explicitly tracks how many electrons occupy each individual bonding and antibonding orbital, correctly revealing the two unpaired electrons in oxygen's antibonding pi-star orbitals that are directly responsible for its observed paramagnetism.

Multiple Choice Questions (MCQs)

Quick Revision Summary

• Ionic bond: complete electron transfer, low-IE metal + high-EA nonmetal (e.g. NaCl)
• Covalent bond: mutual electron sharing; nonpolar if electronegativities equal, polar if different
• Dative (coordinate) bond: both shared electrons donated by one atom (e.g. H3O+, CO, O3)
• Expanded octet: central atom exceeds 8 valence electrons using d orbitals, period 3 or later only, e.g. SO4 2-, I3-
• Electronegativity difference predicts bond type: below 0.4 nonpolar covalent | 0.4-1.8 polar covalent | above 1.8 ionic
• Dipole moment measures charge separation (Debye units); symmetric molecules (BeCl2, BF3, CCl4) can have polar bonds but zero net dipole moment
• Bond energy rises with electronegativity difference and bond multiplicity; bond length rises with atom size, falls with electronegativity difference
• Bond strength order: ionic > covalent > hydrogen bonding > dipole-dipole > London dispersion
• VBT: sigma bond = head-on overlap; pi bond = sideways overlap of parallel p orbitals; double bond = 1 sigma + 1 pi; triple bond = 1 sigma + 2 pi
• Hybridization: sp = linear (180 degrees), sp2 = trigonal planar (120 degrees), sp3 = tetrahedral (109.5 degrees)
• VSEPR: electron pairs arrange to minimize repulsion; lp-lp > lp-bp > bp-bp; lone pairs compress bond angles
• VSEPR shapes: 2 pairs = linear, 3 = trigonal planar, 4 = tetrahedral/pyramidal/bent, 5 = trigonal bipyramidal, 6 = octahedral
• MOT bond order = (bonding electrons – antibonding electrons) / 2; bond order 0 means no molecule (He2)
• MOT explains O2 paramagnetism, 2 unpaired electrons in pi* orbitals, something VBT cannot show

Exam Tips

• When predicting bond type, always compute the electronegativity difference first — most 'ionic vs covalent' exam questions reduce to comparing this single number against 0.4 and 1.8
• For dipole moment questions, check symmetry before anything else: a molecule with identical ligands in a fully symmetric geometry (linear, trigonal planar, tetrahedral) always has zero net dipole moment even if every bond is polar
• Count electron pairs first, then look up the geometry, then subtract lone pairs for the actual shape — this three-step VSEPR method avoids most shape-prediction errors
• Match hybridization to geometry directly: sp = linear, sp2 = trigonal planar, sp3 = tetrahedral — if you know one, you know the other
• For MOT bond-order questions, write out the molecular orbital filling order first (sigma2s, sigma*2s, then the 2p orbitals) before counting bonding vs antibonding electrons
• Remember that MOT, not VBT, is the theory that explains paramagnetism — if a question asks why a substance is attracted to a magnet, look for unpaired electrons in antibonding orbitals