Bond Length, Bond Energy, and Bond Order

Bond length is the distance between the nuclei of two bonded atoms, bond energy is the energy needed to break one mole of a particular bond in the gas phase, and bond order is the number of shared electron pairs between two atoms; a higher bond order gives a shorter, stronger bond. In brief: the N–N, N=N and N≡N bonds have lengths of 145, 125 and 110 pm and energies of about 163, 418 and 945 kJ/mol, and bond energies can be used to estimate the enthalpy change of a reaction: ΔH ≈ Σ(bonds broken) − Σ(bonds formed).

These three properties describe the strength and geometry of chemical bonds. They explain why some molecules are inert and others are reactive, and allow chemists to estimate the energy released by reactions when no other data are available. This article defines the properties, shows how they are related, includes tables of average values, explains how to use bond energies to calculate reaction enthalpies, introduces bond order from molecular orbital theory, works through examples and gives the history.

What is bond length?

Bond length is the equilibrium distance between the nuclei of two bonded atoms, where the attraction and repulsion forces balance. It is measured in picometers (1 pm = 10⁻¹² m) or angstroms (1 Å = 100 pm) by spectroscopy and X-ray or electron diffraction. Bond length depends on the sizes of the atoms: it is longer for larger atoms (H–I 161 pm, H–F 92 pm). It also decreases as the bond order increases.

What is bond energy?

The bond dissociation energy is the enthalpy change needed to break one mole of a specific bond in gaseous molecules, forming gaseous atoms or fragments: for example, H–H(g) → 2H(g), ΔH = +436 kJ/mol. It is always positive, since energy is needed to break a bond. The same energy is released when the bond forms. For molecules with more than one bond of the same type, such as the four C–H bonds in methane, the average bond energy is used, since the energy to break each successive bond is slightly different.

What is bond order?

In Lewis theory, the bond order is the number of shared electron pairs between two atoms: 1 for a single bond, 2 for a double bond and 3 for a triple bond. For species with resonance, it is the average, such as 1.5 in ozone. In molecular orbital theory, bond order = ½ (number of electrons in bonding orbitals − number of electrons in antibonding orbitals). This definition works for molecules that Lewis theory cannot describe easily: O₂ has a bond order of 2, N₂ has 3, and the superoxide ion O₂⁻ has 1.5. A bond order of zero means that no stable bond forms, as in He₂ and Ne₂.

Average bond lengths and energies

How are the three properties related?

• Bond order and length: for the same pair of atoms, a higher bond order means a shorter bond.
• Bond order and energy: a higher bond order means a stronger bond, though a double bond is less than twice as strong as a single one.
• Length and energy: shorter bonds between the same types of atoms are stronger. Among the hydrogen halides, the bond energy decreases from H–F (567) to H–I (299) as the bond length increases from 92 to 161 pm.
• Exception: the F–F bond is longer than expected and weak (159 kJ/mol), since the lone pairs on the small fluorine atoms repel each other. This is why fluorine is so reactive.

How do you estimate reaction enthalpies?

In a reaction, bonds in the reactants are broken (energy is absorbed) and new bonds in the products are formed (energy is released). The enthalpy change is estimated as ΔH ≈ Σ(energies of bonds broken) − Σ(energies of bonds formed). A negative result means that the reaction is exothermic. The method is approximate since average bond energies are used and it is applied to gases.

Worked examples

1. H₂ + Cl₂ → 2HCl. Bonds broken: 1 H–H (436) + 1 Cl–Cl (243) = 679 kJ. Bonds formed: 2 H–Cl (2 × 431) = 862 kJ. ΔH = 679 − 862 = −183 kJ. The measured value is −184.6 kJ.

2. Combustion of methane. CH₄ + 2O₂ → CO₂ + 2H₂O (gas). Bonds broken: 4 C–H (4 × 413 = 1,652) + 2 O=O (2 × 498 = 996) = 2,648 kJ. Bonds formed: 2 C=O (2 × 799 = 1,598) + 4 O–H (4 × 463 = 1,852) = 3,450 kJ. ΔH = 2,648 − 3,450 = −802 kJ per mole of methane, which agrees with the experimental value of −802 kJ/mol.

3. Ammonia synthesis. N₂ + 3H₂ → 2NH₃. Bonds broken: 1 N≡N (945) + 3 H–H (3 × 436 = 1,308) = 2,253 kJ. Bonds formed: 6 N–H (6 × 391 = 2,346). ΔH = 2,253 − 2,346 = −93 kJ, close to the experimental value of −92 kJ.
4. Wavelength to break H–H. The energy per molecule is 436 × 10³ ÷ 6.022 × 10²³ = 7.24 × 10⁻¹⁹ J. The wavelength of a photon with this energy is λ = hc ÷ E = (6.626 × 10⁻³⁴ × 2.998 × 10⁸) ÷ 7.24 × 10⁻¹⁹ = 2.74 × 10⁻⁷ m = 274 nm, which is in the ultraviolet.
5. Bond order from molecular orbital counts. N₂: 8 bonding and 2 antibonding electrons, so the bond order is (8 − 2) ÷ 2 = 3. O₂: 8 bonding and 4 antibonding, so (8 − 4) ÷ 2 = 2. O₂⁺: 8 bonding and 3 antibonding, so 2.5, which makes the bond shorter (112 pm) than in O₂ (121 pm).
6. Compare reactivity. The N≡N bond (945 kJ/mol) is much stronger than the F–F bond (159 kJ/mol), so nitrogen gas is unreactive and fluorine gas is very reactive.

How were these quantities measured?

Bond lengths were first measured by X-ray crystallography in the 1910s, and later by electron diffraction and microwave spectroscopy. Bond energies come from thermochemical measurements, spectroscopy and calculations. Linus Pauling used bond energy data to develop his electronegativity scale in 1932. Robert Mulliken’s molecular orbital theory, developed from 1927 onward, gave the definition of bond order that applies to all molecules. Modern computational methods now calculate bond lengths with an accuracy of about 1 pm.

Which mistakes are common?

Mistake 1: Reversing the signs in the enthalpy calculation

ΔH = bonds broken − bonds formed. Breaking bonds costs energy, and forming bonds releases it.

Mistake 2: Assuming that a double bond is twice as strong as a single bond

The C=C bond energy is 614 kJ/mol, not 2 × 346 = 692 kJ/mol.

Mistake 3: Using average bond energies for exact predictions

The results are estimates, usually within about 10%, and they apply to gases.

Mistake 4: Forgetting to count all the bonds

Methane has four C–H bonds, and water has two O–H bonds. Multiply by the number of molecules in the equation.