Bond Parameters

Full Notes

4.3.1 Bond Length

Bond length (R) is the equilibrium distance between nuclei of two bonded atoms.

The covalent radius (r_A) is the measure of the distance between an atom’s core and its point of contact with a bonded atom.

Bond lengths are measured in picometres (pm) and determined experimentally by:

• X-ray diffraction
• Electron diffraction
• Spectroscopic methods

Shorter bonds are stronger, and bond length depends on:

• Bond order (more bonds = shorter length)
• Atomic size
• Hybridization (more s-character → shorter bond)

The van der Waals radius applies when atoms are not bonded. It is half the distance between non-bonded atoms in neighbouring molecules and often measured as half of the distance between two similar atoms in separate molecules in a solid.

4.3.2 Bond Angle

A bond angle is the angle between two bonds originating from the same central atom.

Bond angles give useful information about a molecule’s 3D shape and hybridization.

4.3.3 Bond Enthalpy

Also known as bond dissociation enthalpy, this is the amount of energy required to break one mole of bonds in gaseous molecules.

• Expressed in kJ mol⁻¹.
• Higher bond enthalpy = stronger bond.

Example: Breaking and forming H–H bond:

• Breaking: H₂(g) → 2H(g), ΔH = +436 kJ mol⁻¹
• Forming: 2H(g) → H₂(g), ΔH = −436 kJ mol⁻¹

Average bond enthalpy is used when a molecule has more than one identical bond (e.g., O–H in H₂O ≈ 463 kJ mol⁻¹).

4.3.4 Bond Order

Bond order refers to the number of chemical bonds between a pair of atoms:

• Single bond = order 1
• Double bond = order 2
• Triple bond = order 3

Higher bond order means a stronger and shorter bond.

4.3.5 Resonance Structures

Some molecules cannot be represented by a single Lewis structure and show resonance.

The actual structure of the molecule is a hybrid of all valid structures (called a resonance hybrid).

Resonance stabilizes a molecule because electrons are delocalized and bond order becomes fractional (e.g., 1.5 in O₃).

Resonance structures must:

• Differ only in electron positions, not atom positions.
• Have the same number of paired and unpaired electrons.
• The resonance hybrid is more stable than any individual form.

Examples of Resonance Structures

Ozone (O₃)

Ozone has two valid structures. The actual structure is a resonance hybrid where both O–O bonds are intermediate in length and strength with a bond order of 1.5.

Carbonate ion (CO₃²⁻)

Three resonance structures exist, each with one C=O and two C–O⁻ bonds. The hybrid has all C–O bonds equivalent and intermediate in length.

Benzene (C₆H₆)

Benzene has alternating single and double bonds forming a resonance hybrid with delocalized electrons across the ring.

4.3.6 Polarity of Bonds

A polar covalent bond forms when two atoms with different electronegativities bond together, leading to unequal sharing of electrons.

Shared electrons are pulled more toward the more electronegative atom, resulting in partial charges:

• δ⁺ (less electronegative atom)
• δ⁻ (more electronegative atom)

Example: H–Cl → H(δ⁺)–Cl(δ⁻)

Dipole Moment

A dipole moment (μ) measures bond polarity and is defined by:

Units: Debye (D) where 1 D = 3.33564 × 10⁻³⁰ C·m.

Dipole moments are represented as a crossed arrow, pointing toward the negative end of the bond.

What Determines Molecular Polarity?

A molecule’s polarity depends on both bond polarity and molecular symmetry.

Non-polar Molecules

If polar bonds are arranged symmetrically, dipoles cancel out → Non-polar molecule.

Examples:

• CO₂: Each C=O bond is polar, but the molecule is linear, so dipoles cancel (non-polar).
• CCl₄: Each C–Cl bond is polar, but the tetrahedral shape cancels dipoles (non-polar).

Polar Molecules

If dipoles do not cancel due to asymmetry, the molecule is polar.

• H₂O: O–H bonds are polar and form a bent shape (104.5°) → Dipoles do not cancel → Polar molecule.
• CHCl₃: Different bond polarities prevent dipole cancellation → Polar molecule.

Ionic Bonding and Covalent Character

Just as covalent bonds can have partial ionic character, ionic bonds can have partial covalent character.

The partial covalent character of ionic bonds was explained by Fajans’ rules:

• The smaller the cation and the larger the anion, the greater the covalent character.
• The greater the cation charge, the greater the covalent character.
• For cations of the same size and charge, those with (n−1)dⁿns⁰ configuration (transition metals) are more polarising than those with noble gas configurations (ns²np⁶).

Summary

• Bond length, bond angle, and bond enthalpy describe bond geometry and strength.
• Bond order indicates the number of shared electron pairs; higher order means shorter and stronger bonds.
• Resonance leads to delocalisation and fractional bond order, increasing stability.
• Bond polarity arises from electronegativity differences; dipole moment quantifies it.
• Molecular polarity depends on bond polarity and molecular geometry.
• Ionic bonds may show covalent character as predicted by Fajans’ rules.