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Why does magnesium oxide melt at about 2,850 °C while sodium chloride melts at 801 °C? Why is lithium fluoride only slightly soluble in water while caesium iodide dissolves easily? And why does sodium form NaCl rather than NaCl₂? The key quantity behind all of these is the lattice energy — a measure of how strongly the ions in an ionic solid hold together. This article defines it carefully, explains what controls its size, and shows how it connects to real properties.
Definition and sign convention
There are two ways to define lattice energy, and data books use both, so it’s important to check.
Lattice formation enthalpy (ΔH_latt, formation): the enthalpy change when one mole of an ionic solid is formed from its gaseous ions under standard conditions:
Na⁺(g) + Cl⁻(g) → NaCl(s) ΔH = −787 kJ mol⁻¹
This is exothermic (negative): energy is released as oppositely charged ions come together.
Lattice dissociation enthalpy: the reverse — breaking one mole of solid into gaseous ions:
NaCl(s) → Na⁺(g) + Cl⁻(g) ΔH = +787 kJ mol⁻¹
This is endothermic (positive).
The magnitude is the same; only the sign differs. Throughout this article, “a larger lattice energy” means a larger magnitude — stronger ionic bonding. Always state which definition you’re using in an exam answer.
What controls lattice energy?
The attraction between two ions follows Coulomb’s law: the force is proportional to the product of the charges and inversely proportional to the square of the distance between them; the potential energy is proportional to the product of the charges divided by the distance:
Lattice energy ∝ (q₊ × q₋) / (r₊ + r₋)
where q₊ and q₋ are the ion charges and r₊ + r₋ is the distance between ion centres (the sum of the ionic radii). Two factors follow.
Factor 1: ionic charge — the dominant effect
Doubling the charge on both ions multiplies the numerator by four. That’s why compounds with 2+ and 2− ions have lattice energies roughly four times those of similar 1+/1− compounds:
| Compound | Ion charges | Lattice energy (magnitude, kJ mol⁻¹) |
|---|---|---|
| NaF | +1, −1 | 923 |
| MgO | +2, −2 | 3,791 |
| NaCl | +1, −1 | 787 |
| CaO | +2, −2 | 3,401 |
NaF and MgO have similar ion sizes, but MgO’s lattice energy is about four times larger.
Factor 2: ionic size — smaller ions, stronger lattice
Smaller ions can get closer together, so the attraction is stronger. Going down a group, ions get larger and lattice energies fall (see ionic radius):
Varying the anion (sodium halides):
| Compound | Lattice energy (kJ mol⁻¹) |
|---|---|
| NaF | 923 |
| NaCl | 787 |
| NaBr | 747 |
| NaI | 704 |
Varying the cation (fluorides):
| Compound | Lattice energy (kJ mol⁻¹) |
|---|---|
| LiF | 1,037 |
| NaF | 923 |
| KF | 821 |
The effect of size is real but much smaller than the effect of charge.
A third, smaller factor: the lattice arrangement
The exact geometry of the lattice — how many neighbours each ion has and how far away the next shells of ions are — also matters. This is captured in a number called the Madelung constant, which differs slightly between the rock-salt, caesium chloride and fluorite structures (see ionic lattices).
How lattice energy is found
Lattice energy can’t be measured directly: you can’t easily make a mole of gaseous ions and let them condense into a crystal. There are two approaches.
1. Experimental: the Born–Haber cycle
Chemists use Hess’s law to combine measurable quantities — enthalpy of formation, atomisation enthalpies, ionisation energies, electron affinities — into an energy cycle that gives the lattice energy indirectly. This is the Born–Haber cycle (see Born–Haber cycles with worked examples).
2. Theoretical: calculation from a model
Assuming the solid is made of perfectly spherical ions with charges exactly +1, −1 and so on, physicists Max Born, Alfred Landé and others developed equations to calculate lattice energies from the charges, radii and lattice structure.
Theoretical vs experimental: detecting covalent character
Comparing the two tells us how “purely ionic” a compound is:
| Compound | Experimental (Born–Haber) | Theoretical (ionic model) | Difference |
|---|---|---|---|
| NaCl | 787 | 770 | small (about 2 %) |
| KBr | 689 | 671 | small |
| AgCl | 915 | 834 | large (about 10 %) |
| AgI | 889 | 778 | large (about 14 %) |
| ZnS | 3,615 | 3,427 | large |
(Values vary somewhat between data sources; the pattern is what matters.)
- For compounds like NaCl, the values agree closely: the ionic model works well.
- For silver halides and zinc sulfide, the experimental value is noticeably larger than the ionic model predicts. The extra stability comes from covalent character: the small, highly charged or highly polarising cation distorts (polarises) the electron cloud of the large, easily distorted anion, pulling electron density into the space between the ions — partial sharing.
This fits Fajans’ rules: covalent character increases when the cation is small and highly charged and the anion is large and highly charged (see ionic vs covalent bonds).
What lattice energy explains
Melting points and hardness
Larger lattice energies generally mean higher melting points and harder solids:
| Compound | Lattice energy (kJ mol⁻¹) | Melting point |
|---|---|---|
| NaCl | 787 | 801 °C |
| NaF | 923 | 993 °C |
| CaO | 3,401 | about 2,600 °C |
| MgO | 3,791 | about 2,850 °C |
(See properties of ionic compounds.)
Solubility
Dissolving an ionic solid in water involves two energy terms:
- Breaking the lattice (endothermic — the lattice dissociation enthalpy).
- Hydrating the ions (exothermic — water molecules surround and stabilise each ion).
ΔH(solution) ≈ lattice dissociation enthalpy + sum of hydration enthalpies
Solubility depends on the balance of these (and on entropy). Compounds with very large lattice energies — such as MgO, CaF₂ and many compounds of 2+ and 3+ ions with 2− and 3− ions — are often poorly soluble, because the lattice is too strong to break up. For example, many metal carbonates, phosphates and oxides are insoluble, while the corresponding nitrates, which have singly charged anions, are soluble (see solubility rules).
Why sodium forms Na⁺, not Na²⁺
Removing a second electron from sodium would mean breaking into its full inner shell, costing a huge 4,562 kJ mol⁻¹ (sodium’s second ionisation energy). The extra lattice energy that a hypothetical “NaCl₂” would release isn’t nearly enough to pay for this. For magnesium, the second ionisation energy is much smaller (1,451 kJ mol⁻¹), because the second electron still comes from the outer shell; the much larger lattice energy of Mg²⁺ compounds easily repays it. So magnesium forms Mg²⁺ and MgCl₂, not Mg⁺ and MgCl. Lattice energy explains the charges we see.
Common misconceptions
- “Lattice energy is always positive (or always negative).” It depends on whether it’s defined for formation or dissociation.
- “Size matters more than charge.” Charge usually has the far larger effect.
- “Lattice energy can be measured directly.” It’s found indirectly (Born–Haber) or calculated.
- “A higher lattice energy always means lower solubility.” Hydration enthalpies and entropy also matter.
Key takeaways
- Lattice energy is the enthalpy change for forming (exothermic) or breaking (endothermic) one mole of an ionic solid from/into gaseous ions.
- It depends on (q₊ × q₋) / (r₊ + r₋): higher charges (dominant) and smaller ions give larger lattice energies.
- It’s found from Born–Haber cycles or calculated from an ionic model; differences reveal covalent character.
- It helps explain melting points, hardness, solubility and which ion charges form.
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