Chemical Bonding and Electronegativity: From Shared Pairs to Ionic Lattices

Why a bond forms: energy against distance

Two hydrogen atoms far apart do not interact. As they approach, each electron is attracted to both nuclei, and the energy falls. Closer still, the two nuclei repel each other strongly and the energy rises. The bond length is the distance at the bottom of this energy well, 74 pm for H₂, and the depth of the well is the bond energy, 436 kJ/mol for H–H in OpenStax Chemistry 2e Table 7.2.

Every bond is a balance of attraction and repulsion, so breaking a bond always costs energy and forming one always releases it. A reaction is exothermic when the bonds formed are stronger overall than the bonds broken.

Electronegativity and the covalent-to-ionic scale

Electronegativity measures how strongly an atom attracts the shared electrons in a bond. Pauling's scale is the most common. It is a dimensionless, calculated number, not a measured property. In OpenStax Figure 7.6, fluorine is highest at 4.0, followed by oxygen at 3.5 and nitrogen and chlorine at 3.0, and the group 1 metals are lowest, such as sodium at 0.9. Values rise across a period and fall down a group.

The difference ΔEN between two bonded atoms gives a rough bond type. OpenStax uses these guideline cut-offs: below 0.4, nonpolar covalent; 0.4 to 1.8, polar covalent; above 1.8, ionic. The more electronegative atom carries the partial negative charge, δ−.

The cut-offs are guidelines with real exceptions. HF has ΔEN = 1.9 but is a covalent molecule, and SiF₄, with ΔEN = 2.2 for each Si–F bond, is a molecular gas. Use ΔEN to compare bonds, not to classify a compound with certainty.

Worked example: ranking six bonds by polarity

Rank B–H, C–Br, N–O, P–Cl, Al–Cl and K–Br from least to most polar, using the older Pauling values in OpenStax Figure 7.6: H 2.1, B 2.0, C 2.5, N 3.0, O 3.5, Al 1.5, P 2.1, Cl 3.0, Br 2.8 and K 0.8.

The differences are B–H 0.1, C–Br 0.3, N–O 0.5, P–Cl 0.9, Al–Cl 1.5 and K–Br 2.0, which is the ranking. Two results surprise many students. In B–H, hydrogen is the negative end, because boron is less electronegative than hydrogen. And K–Br falls in the ionic range, consistent with potassium bromide being an ionic solid, while Al–Cl sits near the top of the polar covalent range; aluminum chloride is described as ionic in some phases and molecular in others.

Dipole moments and percent ionic character

A polar bond has a dipole moment μ = Qr, the size of the separated charge times the distance between the charges. Dipole moments are usually given in debyes: 1 D = 3.336 × 10⁻³⁰ C·m. If an electron's full charge, 1.602 × 10⁻¹⁹ C, were moved across 1 Å, the dipole moment would be 4.803 D. Comparing the measured μ with this fully ionic value gives an approximate percent ionic character, (μ measured / μ fully ionic) × 100.

Worked example 1. The NIST Chemistry WebBook lists, for gas-phase H³⁵Cl, μ = 1.1085 D and an equilibrium bond length of 1.27455 Å. A fully ionic H⁺Cl⁻ at that distance would have μ = 4.803 D/Å × 1.27455 Å = 6.122 D. The percent ionic character is 1.1085/6.122 × 100 = 18.1%. For HF, with WebBook values μ = 1.82618 D and r = 0.91680 Å, the fully ionic value is 4.404 D and the ionic character is 41.5%.

The ranking agrees with ΔEN (0.9 for HCl, 1.9 for HF), but the numbers show how far even a large ΔEN is from a complete transfer of charge. HF is closer to the covalent end than its ΔEN alone suggests.

Lattice energy and Coulomb's law

An ionic solid is held together by the attraction between every cation and every anion in the crystal. Its lattice energy is the energy needed to separate one mole of the solid into gaseous ions. OpenStax defines it as positive, but some textbooks use the reverse process and give negative values, so check the sign convention first.

By Coulomb's law, the attraction grows with the product of the ion charges and falls as the distance between ions grows. Charge usually dominates. OpenStax Section 7.5 lists LiF at 1023 kJ/mol and MgO, whose ions carry charges of 2+ and 2−, at 3900 kJ/mol, almost four times larger. Size matters next: MgF₂ is 2957 kJ/mol and MgI₂ is 2327 kJ/mol, because the larger iodide ion keeps the charges farther apart.

Worked example: a Born–Haber cycle for sodium chloride

Lattice energies cannot be measured directly, so they are found with a Hess's law cycle. Build NaCl(s) from its elements by an indirect route whose steps are all measurable, then require that route to give the same total as the direct formation reaction.

Worked example 2. Use these steps. Sublime sodium, Na(s) → Na(g): +107.5 kJ/mol, the ΔH°f of Na(g) from OpenStax Appendix G. Make chlorine atoms, ½ Cl₂(g) → Cl(g): +121.3 kJ/mol, the ΔH°f of Cl(g). Ionize sodium, Na(g) → Na⁺(g) + e⁻: +495.8 kJ/mol, from the NIST value of 5.1391 eV. Add an electron to chlorine, Cl(g) + e⁻ → Cl⁻(g): −348.6 kJ/mol, from the electron affinity of 3.6131 eV in the NIST Chemistry WebBook. Finally, Na⁺(g) + Cl⁻(g) → NaCl(s) releases the lattice energy, U.

The overall reaction is Na(s) + ½ Cl₂(g) → NaCl(s), with ΔH°f = −411.2 kJ/mol. So 107.5 + 121.3 + 495.8 − 348.6 − U = −411.2, which gives U = 787.2 kJ/mol. Notice that ionization costs more energy than the electron affinity returns. Without the large lattice energy, forming NaCl from its elements would not be exothermic. Published lattice energies for NaCl differ by a few percent with the data and method used (OpenStax quotes 769 kJ), so compare trends rather than last digits.

Estimating reaction enthalpy from bond energies

For gas-phase reactions, you can estimate ΔH by counting bonds: ΔH ≈ Σ(energies of bonds broken) − Σ(energies of bonds formed). Tabulated bond energies are averages over many molecules, so the result is only an estimate and can miss the value from formation enthalpies by tens of kilojoules.

Worked example 3. Estimate ΔH for C₂H₄(g) + H₂(g) → C₂H₆(g). Ethylene's four C–H bonds survive, so ignore them. Broken: one C=C (611 kJ/mol) and one H–H (436 kJ/mol), 1047 kJ in total. Formed: one C–C (345 kJ/mol) and two new C–H (2 × 415 kJ/mol), 1175 kJ in total. ΔH ≈ 1047 − 1175 = −128 kJ. The formation-enthalpy value, from Appendix G, is −84.0 − 52.4 = −136.4 kJ. The estimate has the right sign and is within about 6%.

Bonding misconceptions to avoid

Most errors come from treating rough guidelines as exact rules or from mixing sign conventions. These are the most common.

• Treating ΔEN = 1.8 as a sharp line between covalent and ionic. The scale is continuous, and compounds such as HF and SiF₄ break the rule.
• Confusing electronegativity with electron affinity. Electron affinity is a measured energy for a gaseous atom; electronegativity describes an atom in a bond.
• Assuming the more electronegative atom is always the nonmetal you would expect. Check the table: in B–H and Si–H bonds, hydrogen is the negative end.
• Reversing the bond-energy formula. It is bonds broken minus bonds formed, the opposite order to the formation-enthalpy formula.
• Mixing lattice-energy sign conventions inside one Born–Haber cycle.
• Counting a double bond as two single bonds. A C=C bond (611 kJ/mol) is weaker than two C–C bonds (690 kJ/mol).