Ionic Bonding and Crystal Lattice Structures

Ionic bonding is the electrostatic attraction between positive and negative ions, and an ionic compound forms a crystal lattice, a regular three-dimensional arrangement in which each ion is surrounded by ions of opposite charge. In brief: in sodium chloride, each Na⁺ ion is surrounded by six Cl⁻ ions and each Cl⁻ by six Na⁺, and the energy released when the lattice forms from gaseous ions, the lattice energy, is 787 kJ/mol; the higher the ionic charges and the smaller the ions, the stronger the lattice.

Ionic compounds such as table salt, limestone and many minerals share a set of properties that follow from their lattice structure: they are hard, brittle, have high melting points and conduct electricity only when molten or dissolved. This article explains how ionic bonds form, describes the common lattice structures, introduces lattice energy and Coulomb’s law, compares compounds in a table, works through calculations and explains the properties of ionic compounds.

How does an ionic bond form?

Ionic bonds form between atoms with a low ionization energy (metals) and atoms with a high electron affinity (nonmetals). Sodium gives one electron to chlorine: Na → Na⁺ + e⁻ (this needs 496 kJ/mol) and Cl + e⁻ → Cl⁻ (this releases 349 kJ/mol). The transfer of the electron by itself needs a net input of energy, 147 kJ/mol. The reason why NaCl forms is the strong attraction between the ions as they pack into a lattice, which releases 787 kJ/mol. The overall change is exothermic.

What is a crystal lattice?

In a crystal, the ions are arranged in a repeating pattern. Positive ions attract negative ions from all sides, so there are no separate molecules. The formula of an ionic compound, such as NaCl, shows only the ratio of the ions in the lattice. The number of oppositely charged ions that touch a given ion is called its coordination number.

The structure of the lattice is determined by the ratio of the ion sizes and the ratio of charges. The anions are usually larger than the cations, and the lattice can be pictured as a packing of large anions with the smaller cations in the holes between them.

What is lattice energy?

The lattice energy is the energy released when one mole of an ionic solid forms from its gaseous ions: Na⁺(g) + Cl⁻(g) → NaCl(s). A larger value means a more stable lattice. The size of the lattice energy depends on the ionic charges and sizes through Coulomb’s law. The electrostatic energy is proportional to (q₁ × q₂) ÷ r, where q₁ and q₂ are the charges and r is the distance between the centers of the ions, which is the sum of the ionic radii.

• Doubling the charge of both ions increases the energy by a factor of about four.
• Smaller ions get closer together, so the energy is larger.

Lattice energies and melting points

The distances r are sums of the ionic radii for six-coordinate ions. Lattice energies are values from the Born-Haber cycle, and they differ slightly between sources. Melting points do not follow the lattice energy exactly, since other factors such as the lattice type also influence them (LiF is an example).

What are the properties of ionic compounds?

• High melting and boiling points: a lot of energy is needed to separate the ions from the strong electrostatic attractions.
• Hard but brittle: a blow can shift a layer of ions by one position, so ions of like charge face each other, repel strongly and the crystal splits along a plane.
• Electrical conductivity: solid ionic compounds do not conduct, since the ions are fixed in place. Molten salts and aqueous solutions conduct, because the ions are free to move.
• Solubility: many ionic compounds dissolve in water, which stabilizes the separated ions, but those with very high lattice energy, such as MgO, are insoluble.

Worked examples

1. Compare MgO and NaCl with Coulomb’s law. For MgO, q₁q₂ = (2)(2) = 4 and r = 72 + 140 = 212 pm, so (q₁q₂) ÷ r = 4 ÷ 212 = 0.01887. For NaCl, (1)(1) ÷ (102 + 181) = 1 ÷ 283 = 0.003534. The ratio is 0.01887 ÷ 0.003534 = 5.3. The measured lattice energy ratio is 3,791 ÷ 787 = 4.8, which agrees well with the prediction.
2. Which has the greater lattice energy: NaF or NaCl? The charges are the same. F⁻ is smaller than Cl⁻, so the distance in NaF is smaller and its lattice energy is larger: 923 against 787 kJ/mol.
3. Predict the formula. Aluminum (3+) and oxygen (2−): the smallest numbers that balance charges are 2 and 3, so the formula is Al₂O₃, with 2 × 3 = 6 positive and 3 × 2 = 6 negative charges.
4. Net energy for the transfer in NaCl. Ionization of Na: +496 kJ/mol. Electron gain by Cl: −349 kJ/mol. Net for the ion pair in the gas phase: +147 kJ/mol. Adding the lattice formation (−787 kJ/mol) gives −640 kJ/mol. The sodium must also be vaporized and the Cl₂ molecule split, which require 107 and 122 kJ/mol, so the formation enthalpy of NaCl(s) is 147 + 107 + 122 − 787 = −411 kJ/mol, which agrees with the measured value of −411 kJ/mol.
5. Number of ions in a sample. A 1.00 g crystal of NaCl contains 1.00 ÷ 58.44 = 0.01711 mol of formula units, and 2 × 0.01711 × 6.022 × 10²³ = 2.06 × 10²² ions.
6. Will the compound conduct? Solid CaCl₂: no. Molten CaCl₂: yes. CaCl₂ in water: yes.

What are the common crystal structures?

How was the ionic lattice discovered?

The regular external shape of salt crystals suggested an orderly internal structure. In 1913, William Henry Bragg and William Lawrence Bragg used X-ray diffraction to determine the structure of sodium chloride and showed that there are no NaCl molecules in the crystal, but a lattice of ions. Max Born and Fritz Haber developed the Born-Haber cycle in 1919 to calculate lattice energies from measurable quantities. Alfred Landé and Born earlier proposed formulas for the electrostatic energy of crystals.

Which mistakes are common?

Mistake 1: Drawing a molecule of NaCl

Ionic compounds consist of a lattice. NaCl is a formula unit, not a molecule.

Mistake 2: Saying that electrons are shared in an ionic bond

The bond is mostly electrostatic attraction between ions, although no bond is 100% ionic.

Mistake 3: Thinking that ionic solids conduct electricity

Ions cannot move in the solid, and so the conductivity is negligible.

Mistake 4: Mixing up lattice energy and ionization energy

Lattice energy refers to the formation of the solid from gaseous ions. Ionization energy refers to the removal of an electron from an atom.