Bonding — Concepts, Formulas & Examples

Bonding is how atoms hold together to form molecules, crystals and metals. CBSE Class 11 and NEET test ionic, covalent and hydrogen bonding extensively. This is the conceptual foundation for all of chemistry — every reaction is just bonds breaking and new ones forming.

Why do atoms bond at all? A lone sodium atom has one electron sitting in a half-empty 3s orbital, energetically restless. A lone chlorine atom is one electron short of a stable octet. When Na gives that electron to Cl, both reach noble gas configurations and the resulting electrostatic attraction locks them into a crystal lattice. That drive toward lower energy and greater stability is the engine behind every bond.

Core Concepts

Types of chemical bonds

Ionic — transfer of electrons, forms cations and anions held by electrostatic attraction. Covalent — sharing of electron pairs. Metallic — delocalised electrons in a lattice of positive ions. Hydrogen bonds — weak attraction between H bonded to N/O/F and another electronegative atom. Coordinate (dative) — a special covalent bond where both electrons come from a single atom, as in $\text{NH}_4^+$ where the lone pair of nitrogen bonds to $\text{H}^+$ .

Ionic bonding in detail

Typically between metal and non-metal with large electronegativity difference (greater than 1.7 as a rough guide). NaCl is the textbook example. High melting and boiling points, conduct when molten or dissolved, brittle crystal lattices.

The energy cycle that governs ionic bond formation is the Born-Haber cycle. It ties together ionisation energy of the metal, electron affinity of the non-metal, and lattice energy of the crystal. The net energy must be negative (exothermic) for the compound to be stable.

U \propto \frac{q^+ \cdot q^-}{r^+ + r^-}

Higher charges and smaller ions give stronger lattice energy. That is why MgO (2+, 2-) has a much higher melting point than NaCl (1+, 1-).

Covalent bonding in detail

Between non-metals sharing electrons. Can be single ( $\sigma$ ), double ( $\sigma + \pi$ ) or triple ( $\sigma + 2\pi$ ). Gives molecules with specific shapes. Low melting points for molecular covalent compounds, poor conductors, soluble in non-polar solvents (for non-polar molecules).

Bond parameters worth knowing:

Parameter	What it measures	Trend
Bond length	Distance between nuclei	Decreases with bond order
Bond energy	Energy to break one mole of bonds	Increases with bond order
Bond order	Number of shared electron pairs	Single < Double < Triple
Bond angle	Angle between two bonds	Depends on hybridisation and lone pairs

Metallic bonding

Metal atoms release valence electrons into a shared ‘electron sea’. The positive ion cores sit in a lattice held together by attraction to the delocalised electrons. This explains electrical conductivity (electrons move freely), malleability (layers can slide without breaking directional bonds) and lustre (free electrons absorb and re-emit light).

VSEPR theory

Valence shell electron pair repulsion. Pairs repel each other and arrange themselves to minimise repulsion. Predicts molecular shapes — linear ( $\text{CO}_2$ ), trigonal planar ( $\text{BF}_3$ ), tetrahedral ( $\text{CH}_4$ ), trigonal pyramidal ( $\text{NH}_3$ ), bent ( $\text{H}_2\text{O}$ ).

The order of repulsion is: lone pair-lone pair > lone pair-bond pair > bond pair-bond pair. This is why lone pairs compress bond angles — in water, two lone pairs push the $\text{H-O-H}$ angle down to 104.5° from the ideal tetrahedral 109.5°.

Hydrogen bonding

Hydrogen attached to a very electronegative atom (N, O, F) develops a strong partial positive charge and attracts lone pairs on other electronegative atoms. Responsible for water’s high boiling point, DNA base pairing and protein folding.

Two types: intramolecular (within the same molecule, as in ortho-nitrophenol) and intermolecular (between different molecules, as in water and alcohols). Intramolecular H-bonding generally lowers boiling point relative to the intermolecular type because it reduces the molecule’s ability to bond with neighbours.

Fajan’s rules — when ionic becomes covalent

Small cations with high charge polarise large anions, pulling electron density back toward the cation. The bond develops covalent character. Fajan’s rules predict this:

Small cation, large anion — more covalent
High charge on cation — more covalent
Cation with pseudo-noble-gas configuration (like $\text{Cu}^+$ , $\text{Ag}^+$ ) — more covalent than a true noble-gas cation of similar size

This is why LiCl is more covalent than KCl — $\text{Li}^+$ is much smaller and polarises $\text{Cl}^-$ more effectively.

Worked Examples

Oxygen is electronegative enough for H-bonding; sulphur is not. Water molecules hold each other tightly through a network of hydrogen bonds. H2S molecules interact only through weaker van der Waals forces. The extra energy needed to break hydrogen bonds accounts for water’s much higher boiling point.

Both have 4 electron pairs around the central atom. CH4 has 4 bonded pairs — perfect tetrahedron, 109.5°. NH3 has 3 bonded plus 1 lone pair — the lone pair repels more than a bonding pair, compressing the bond angle to 107°, giving a trigonal pyramidal shape.

Consider $\text{AlCl}_3$ . Electronegativity difference between Al (1.5) and Cl (3.0) is 1.5 — borderline. Applying Fajan’s rules, $\text{Al}^{3+}$ is small and triply charged, so it heavily polarises the large $\text{Cl}^-$ ions. Result: $\text{AlCl}_3$ is predominantly covalent. It has a low melting point (190°C) and exists as a dimer $\text{Al}_2\text{Cl}_6$ — very un-ionic behaviour.

Diamond has every carbon $sp^3$ hybridised with four strong covalent bonds in a 3D network — no weak direction. Graphite has $sp^2$ carbons in flat sheets with strong in-plane bonds but only weak van der Waals forces between layers. The layers slide over each other, making graphite soft and a good lubricant.

In $\text{O}_3$ , the central oxygen forms one double bond and one coordinate bond. Formal charge on the central O: $6 - 2 - \frac{1}{2}(6) = +1$ . On the singly bonded terminal O: $6 - 6 - \frac{1}{2}(2) = -1$ . On the doubly bonded terminal O: $6 - 4 - \frac{1}{2}(4) = 0$ . The two resonance structures average out, giving each terminal O a charge of $-\frac{1}{2}$ and the central O a charge of $+1$ .

Key Formulas

\mu = q \times d

where $q$ is the magnitude of charge separation and $d$ is the distance between the charges. Measured in Debye (D). A higher dipole moment means a more polar molecule. For polyatomic molecules, the net dipole is the vector sum of individual bond dipoles.

\text{Bond Order} = \frac{N_b - N_a}{2}

where $N_b$ is the number of electrons in bonding MOs and $N_a$ is the number in antibonding MOs. For $\text{O}_2$ : $\text{BO} = \frac{10 - 6}{2} = 2$ (double bond).

Common Mistakes

Saying ionic bonds are stronger than covalent. Not always — the C-C bond is about 350 kJ/mol, stronger than many ionic bonds. Compare within the same framework, not across.

Confusing hydrogen bond with covalent bond involving hydrogen. A hydrogen bond is an intermolecular (or intramolecular) attraction, much weaker (about 10-40 kJ/mol) than a covalent O-H bond (about 460 kJ/mol).

Writing that VSEPR predicts bond energies. It predicts shapes only. For bond energies, look at bond order and orbital overlap.

Forgetting that electronegativity difference is a spectrum, not a switch. A difference of 1.7 is a guideline, not a law. Many real bonds have mixed ionic-covalent character.

Assuming all molecules with polar bonds are polar. $\text{CO}_2$ has two polar C=O bonds, but they cancel out due to the linear geometry. Net dipole moment is zero — the molecule is non-polar.

Exam Weightage and Strategy

Chemical bonding carries 6-8 marks in CBSE Class 11 boards. NEET typically has 2-3 questions from this chapter every year, covering VSEPR shapes, hydrogen bonding and molecular orbital theory. JEE Main goes deeper into MO diagrams and bond parameters.

CBSE board questions split into three types: (a) define and give examples (2 marks), (b) explain a phenomenon like why HF has a higher boiling point than HCl (3 marks), and (c) draw a MO diagram or predict shape and polarity (5 marks). PYQs repeat the same concepts with different molecules.

For NEET, the favourite questions are:

Which of the following has the highest bond angle? (VSEPR application)
Arrange in order of increasing ionic character (Fajan’s rules)
Which species is paramagnetic? (MO theory — count unpaired electrons)

Learn five molecular shapes with examples. Those five cover 90% of VSEPR questions. For MO theory, memorise the MO diagram for $\text{O}_2$ and $\text{N}_2$ — most JEE questions are variations on these two.

Practice Questions

Q1. Arrange NaF, NaCl, NaBr, NaI in order of decreasing lattice energy. Explain why.

NaF > NaCl > NaBr > NaI. Lattice energy depends on $\frac{q^+ \cdot q^-}{r^+ + r^-}$ . Since all have the same charges, the smaller the anion, the higher the lattice energy. $\text{F}^-$ is the smallest halide ion.

Q2. Why is $\text{BF}_3$ planar but $\text{NF}_3$ is pyramidal?

$\text{BF}_3$ has 3 bond pairs and no lone pairs on B — $sp^2$ hybridised, trigonal planar, 120°. $\text{NF}_3$ has 3 bond pairs plus 1 lone pair on N — $sp^3$ hybridised, trigonal pyramidal, about 102°. The lone pair on N pushes the bond pairs closer.

Q3. $\text{O}_2$ is paramagnetic. Explain using MO theory.

The MO configuration of $\text{O}_2$ fills the $\pi^*_{2p}$ antibonding orbitals with two electrons, one in each (Hund’s rule). These two unpaired electrons make $\text{O}_2$ paramagnetic. Lewis structure incorrectly predicts it to be diamagnetic — this was a triumph of MO theory.

Q4. Why does ice float on water?

In ice, each water molecule forms four hydrogen bonds in a tetrahedral arrangement, creating an open crystalline structure with empty space. This makes ice less dense than liquid water, where the H-bond network is partly broken and molecules pack more closely. Ice density is about 0.92 g/cm³ versus water at 1.00 g/cm³.

Q5. Predict the shape and bond angle of $\text{XeF}_4$ .

Xe has 4 bond pairs and 2 lone pairs — total 6 electron pairs, so $sp^3d^2$ hybridised. Electron pair geometry is octahedral. The two lone pairs occupy opposite positions (to minimise lp-lp repulsion), giving a square planar molecular shape with 90° bond angles.

FAQs

What is the difference between polar and non-polar covalent bonds?

In a polar covalent bond, electrons are shared unequally because the atoms have different electronegativities (e.g., H-Cl). In a non-polar covalent bond, electrons are shared equally (e.g., H-H, Cl-Cl). A bond between atoms with an electronegativity difference less than about 0.4 is usually considered non-polar.

Can a molecule with polar bonds be non-polar?

Yes. If the bond dipoles cancel due to symmetry, the net dipole moment is zero. Examples: $\text{CO}_2$ (linear), $\text{CCl}_4$ (tetrahedral), $\text{BF}_3$ (trigonal planar). The geometry matters as much as the bond polarity.

What is resonance?

When a single Lewis structure cannot represent the actual electron distribution, we draw two or more structures that differ only in the placement of electrons (not atoms). The real molecule is a weighted average of all resonance structures. Benzene with its two Kekule structures is the classic example — each C-C bond is neither single nor double but an intermediate 1.5 bond.

Why is bond length of C-C in benzene shorter than a single bond but longer than a double bond?

Benzene has resonance — each C-C bond has a bond order of 1.5. A pure single C-C bond is 1.54 angstrom, a pure double C=C is 1.34 angstrom, and benzene’s C-C is 1.39 angstrom, right between the two.

What is the octet rule and when does it fail?

The octet rule states that atoms tend to gain, lose or share electrons to achieve eight electrons in their valence shell (like noble gases). It fails for: (a) electron-deficient species like $\text{BF}_3$ (6 electrons on B), (b) odd-electron species like NO, (c) expanded octets like $\text{SF}_6$ (12 electrons on S) possible only for period 3 and beyond elements that have d orbitals available.

Bonding is the language of chemistry. Once you know why atoms come together, every reaction is just a conversation between bonds breaking and forming.