Bond parameters, resonance and polarity

What are bond parameters?

In plain words: once you know which atoms are bonded, you can ask how far apart they sit, at what angles, how hard the bond is to break and how many electron pairs it holds. For comparable bonds between the same kinds of atoms, higher bond order usually means a shorter, stronger bond. And when two atoms share electrons unequally, one end of the bond becomes slightly negative and the other slightly positive.

Bond length

Bond length is defined as the equilibrium distance between the nuclei of two bonded atoms in a molecule.

NCERT Chemistry Part I (Class 11), Section 4.3.1, page 107

Bond lengths are measured by spectroscopic, X-ray diffraction and electron diffraction methods. Each atom contributes to the bond length: for a covalent bond A–B, approximately R = r_A + r_B, where r_A and r_B are the covalent radii (NCERT Fig. 4.1, page 107). The covalent radius is half the distance between two similar atoms joined by a covalent bond. The van der Waals radius is the overall size of an atom, including its valence shell, when it is not bonded: half the distance between two similar atoms in separate molecules in a solid (page 107). For chlorine, the covalent radius is 99 pm and the van der Waals radius 180 pm (NCERT Fig. 4.2).

(Average values from NCERT Table 4.2, page 108. Molecules: H₂ 74, F₂ 144, Cl₂ 199, N₂ 109, O₂ 121, HCl 127 pm, from NCERT Table 4.3. NCERT’s 144 pm for F₂ is high: the measured equilibrium bond length is 141 pm.)

Bond angle

The bond angle is the angle between the lines joining a central nucleus to two bonded nuclei in a molecule or complex ion. It is measured in degrees by spectroscopic methods and indicates how the orbitals are arranged, and so the shape of the molecule (NCERT Section 4.3.2, page 108). The H–O–H angle in water is 104.5°.

Bond enthalpy

Bond enthalpy is the energy needed to break one mole of bonds of a particular type between two atoms in the gaseous state, in kJ mol⁻¹ (NCERT Section 4.3.3, page 108). The larger the bond dissociation enthalpy, the stronger the bond:

In a polyatomic molecule, equal bonds need different energies to break one after another, because the chemical environment changes. In water (page 109):

So the mean (average) bond enthalpy is used: the total dissociation enthalpy divided by the number of bonds broken, (502 + 427) ÷ 2 = 464.5 kJ mol⁻¹ for O–H in water. The same O–H bond also differs slightly between molecules, such as water and ethanol (page 109). Mean bond enthalpies are used to estimate reaction enthalpies (see bond enthalpy in thermodynamics).

Bond order

In the Lewis description of covalent bond, the Bond Order is given by the number of bonds between the two atoms in a molecule.

NCERT Chemistry Part I (Class 11), Section 4.3.4, page 109

H₂, O₂ and N₂ have bond orders 1, 2 and 3; CO (a triple bond) has 3. N₂, with bond order 3, has a dissociation enthalpy of 946 kJ mol⁻¹, one of the highest for a diatomic molecule (page 109). The following isoelectronic diatomic examples have the same elementary bond order: F₂ and O₂²⁻ have 1; N₂, CO and NO⁺ have 3.

A general correlation useful for understanding the stablities of molecules is that: with increase in bond order, bond enthalpy increases and bond length decreases.

NCERT Chemistry Part I (Class 11), Section 4.3.4, page 109

Carbon–carbon bonds show it: C–C 154 pm, C=C 133 pm, C≡C 120 pm.

Resonance structures

Sometimes no single Lewis structure matches the measured properties. Ozone can be drawn as structure I or II, each with one O–O single bond (normally 148 pm) and one O=O double bond (normally 121 pm). But both O–O bonds in O₃ are measured at 128 pm: in between, and equal (NCERT Section 4.3.5, page 109).

According to the concept of resonance, whenever a single Lewis structure cannot describe a molecule accurately, a number of structures with similar energy, positions of nuclei, bonding and non-bonding pairs of electrons are taken as the canonical structures of the hybrid which describes the molecule accurately.

NCERT Chemistry Part I (Class 11), Section 4.3.5, page 109

The real structure, the resonance hybrid, is more stable than any canonical form, and resonance averages out the bond properties (page 110). Other examples are the carbonate ion and carbon dioxide (Examples 2 and 3). NCERT lists common misconceptions to avoid (page 110):

• the canonical forms have no real existence;
• the molecule does not spend part of its time in one form and part in another;
• there is no equilibrium between canonical forms, unlike the keto and enol forms of tautomerism;
• the molecule has a single structure, the hybrid, which no single Lewis structure can show.

Polarity of bonds and dipole moment

Ionic and covalent descriptions are limiting models, and many bonds have mixed character (NCERT Section 4.3.6, page 110). When two identical atoms share a pair, as in H₂, Cl₂ or N₂, the electron density is shared symmetrically: a nonpolar covalent bond. In HF, fluorine is far more electronegative than hydrogen, so the shared pair shifts towards fluorine: a polar covalent bond (page 111).

The polarity gives the molecule a dipole moment, μ, the product of the charge and the distance between the centres of positive and negative charge (page 111):

Dipole moments are usually given in debye (D), after Peter Debye. A dipole moment is a vector. In chemistry it is drawn as a crossed arrow (+→) on the Lewis structure: the cross at the positive end, the head at the negative end, showing the shift of electron density (page 111). This is opposite to the conventional dipole-moment vector, which runs from the negative to the positive centre (NCERT page 111).

In a useful approximate decomposition, the molecular dipole is the vector sum of bond and lone-pair contributions; bond dipoles alone often suffice for symmetric examples, so it depends on the shape (pages 111–112):

• H₂O, bent at 104.5°: the two O–H dipoles add to 1.85 D = 1.85 × 3.33564 × 10⁻³⁰ = 6.17 × 10⁻³⁰ C m.
• BeF₂ (linear) and BF₃ (trigonal planar, bonds at 120°): the bond dipoles cancel, so μ = 0.
• NH₃ and NF₃ are both pyramidal with a lone pair on N. In NH₃ the lone-pair (orbital) dipole points the same way as the resultant of the N–H bond dipoles, so the moment is large: 1.47 D (4.90 × 10⁻³⁰ C m). In NF₃ it points the opposite way and largely cancels the N–F resultant, though F is more electronegative than N: 0.23 D (page 112).

NCERT’s Table 4.5 (page 112) lists, among others, HF 1.78, HCl 1.07, HBr 0.79, HI 0.38, H₂S 0.95 and CHCl₃ 1.04 D, and zero for H₂, CO₂, BF₃, CH₄ and CCl₄. (Its text and figure give NF₃ as 0.8 × 10⁻³⁰ C m, which is 0.24 D; the table’s 0.23 D is 0.77 × 10⁻³⁰ C m.)

Fajans’ rules: covalent character of ionic bonds

Just as all the covalent bonds have some partial ionic character, the ionic bonds also have partial covalent character.

NCERT Chemistry Part I (Class 11), Section 4.3.6, page 112

Fajans explained this partial covalent character with three rules (page 112):

• the smaller the cation and the larger the anion, the greater the covalent character;
• the greater the charge on the cation, the greater the covalent character;
• for cations of the same size and charge, one with an (n − 1)dⁿ ns⁰ configuration, typical of transition metals, polarises more than one with a noble gas configuration, ns² np⁶, typical of the alkali and alkaline earth metals.

So LiI is more covalent than LiF, AlCl₃ more than MgCl₂ and MgCl₂ more than NaCl, and CuCl (Cu⁺, 3d¹⁰) more than NaCl (Na⁺, 2s² 2p⁶), though the two cations are similar in size.

The cation polarises the anion, pulling its electron cloud towards itself and building up electron density between the nuclei, as in a covalent bond. The polarising power of the cation, the polarisability of the anion and the extent of distortion decide the percentage of covalent character (page 112).

Solved examples

Common mistakes to avoid

Quick revision summary

• Bond length R = r_A + r_B (covalent radii); van der Waals radius is larger (Cl: 99 and 180 pm).
• Bond angle: H–O–H in water 104.5°. Bond enthalpy: energy to break one mole of bonds in the gas phase; use the mean for polyatomic molecules (O–H in water 464.5 kJ mol⁻¹).
• Bond order = number of bonds; higher bond order, higher bond enthalpy and shorter bond (C–C 154, C=C 133, C≡C 120 pm). Comparable valence-isoelectronic diatomics often have the same elementary bond-order count.
• Resonance: the hybrid of canonical forms is the real, more stable structure (O₃, CO₃²⁻, CO₂).
• Polar bonds and dipole moment μ = Q × r (1 D = 3.33564 × 10⁻³⁰ C m); the molecular moment is the vector sum of bond dipoles (CO₂, BF₃ zero; H₂O 1.85 D; NH₃ > NF₃).
• Fajans’ rules: small, highly charged cations and large anions give ionic bonds more covalent character.

Questions students ask

What is the SI unit of dipole moment?

The SI unit of dipole moment is the coulomb metre (C m), but molecular dipole moments are usually given in debye (D), where 1 D = 3.33564 × 10^⁻³⁰ C m. The debye suits molecules because their moments are tiny: charges of ±e (1.602 × 10^⁻¹⁹ C) just 100 pm apart would give μ = 1.602 × 10^⁻²⁹ C m, or 4.80 D. Measured values are usually smaller, such as 1.85 D for water, because the charges on bonded atoms are only partial.

What is the difference between resonance and tautomerism?

Resonance structures differ only in the arrangement of electrons, have no separate existence and together describe one real molecule, the resonance hybrid, while tautomers are real isomers that differ in the position of an atom, usually hydrogen, and exist together in equilibrium. Propanone, CH₃COCH₃ (the keto form), is in equilibrium with a tiny amount of its enol, CH₂=C(OH)CH₃, a different compound with the hydrogen on oxygen; the canonical forms of ozone are not separate compounds at all. Resonance is shown with a double-headed arrow (↔) and tautomerism with equilibrium arrows (⇌).

What is the difference between dipole moment and polarisability?

Dipole moment measures a permanent separation of charge in a molecule (μ = Q × r), while polarisability measures how easily an electron cloud is distorted by an electric field or a nearby ion, which creates an induced dipole. HF has a permanent dipole moment of 1.78 D; an argon atom has none, but its electron cloud can still be polarised. In Fajans’ rules the polarisability of the anion works together with the polarising power of the cation: the large I⁻ ion is far more polarisable than F⁻, which is why AgI is much more covalent, and much less soluble in water, than AgF.

Are Fajans’ rules in the JEE Main 2027 and NEET (UG) 2026 syllabuses?

Yes, Fajans’ rules are in both syllabuses: JEE Main 2027 and NEET (UG) 2026 list ‘Fajan’s rule’ under Unit 3, Chemical Bonding and Molecular Structure, next to electronegativity and dipole moment. In the NCERT Class 11 book they are a short passage at the end of Section 4.3.6 (Polarity of bonds, page 112) rather than a section of their own; they are named after Kazimierz Fajans, so ‘Fajans’ rules’ is the correct spelling. The rules compare covalent character, for example SnCl₄ against SnCl₂ or LiCl against KCl (the first of each pair is more covalent).

Practice questions

Try each question first, then open the answer to check your working.

1. Q1. How do you express the bond strength in terms of bond order (NCERT Exercise 4.9, page 134)?

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   The higher the bond order, the stronger the bond: bond enthalpy increases and bond length decreases. N≡N (order 3, 946 kJ mol⁻¹) is stronger than O=O (order 2, 498 kJ mol⁻¹).

2. Q2. Although CO₂ and H₂O are both triatomic, H₂O is bent and CO₂ linear. Explain this on the basis of dipole moment (NCERT Exercise 4.15, page 134).

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   CO₂ has zero dipole moment although its C=O bonds are polar, so the two bond dipoles must cancel: the molecule is linear. H₂O has a dipole moment of 1.85 D, so its O–H dipoles do not cancel: the molecule is bent.

3. Q3. Which of NH₃ and NF₃ has the higher dipole moment, and why (NCERT Exercise 4.23, page 134)?

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   NH₃ (1.47 D against 0.23 D). In NH₃ the lone-pair dipole on N points the same way as the resultant of the N–H bond dipoles and adds to it; in NF₃ it points opposite to the N–F resultant and largely cancels it.