Home▸Chemistry & Materials▸Born-Haber Cycle — Lattice Energy of Ionic Crystals

💠 Born-Haber Cycle — Lattice Energy of Ionic Crystals

Build the Born-Haber cycle step by step for NaCl, MgO, CaF2 or KBr — sublimation, ionization, dissociation, electron affinity and lattice formation — and watch Hess's Law solve the lattice energy live on an animated energy staircase.

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How the Born-Haber Cycle Works

The Born-Haber cycle breaks the formation of an ionic crystal lattice from its elements in their standard states into five measurable steps: first the metal sublimes from solid to gas (ΔHsub), then the gaseous metal atom is ionized, losing one or more electrons (IE). In parallel, the nonmetal molecule dissociates into separate atoms (D, or ½D for elements that need only one atom per formula unit), and each nonmetal atom picks up an electron to become an anion (EA, electron affinity). Finally the gaseous cations and anions come together to build the solid crystal lattice, releasing the lattice energy ΔHlattice — typically the largest-magnitude and always exothermic step of the whole cycle.

Because Hess's Law requires that the direct formation of the compound from its elements (ΔHf) release or absorb exactly the same total energy as the five-step indirect route, the lattice energy can be solved for by rearranging the closed cycle: ΔHlattice = ΔHf − (ΔHsub + IE + D + EA). On the diagram the path climbs (endothermic steps: sublimation, ionization, dissociation) and then drops sharply (electron affinity and, especially, lattice formation), always finishing at exactly the same energy level as the direct dashed ΔHf arrow on the right — a visual proof of Hess's Law.

Hess's Law closure: ΔHf = ΔHsub + IE + ½D + EA + ΔHlattice
Solve for lattice energy: ΔHlattice = ΔHf − (ΔHsub + IE + ½D + EA)
Sign convention: positive = endothermic (energy absorbed, path climbs) · negative = exothermic (energy released, path drops)
Coulombic trend: ΔHlattice ∝ −(z⁺ × z⁻) / (r⁺ + r⁻)

Frequently Asked Questions

What is the Born-Haber cycle?

The Born-Haber cycle is a thermochemical cycle, based on Hess's Law, that breaks the formation of an ionic solid from its elements into a sequence of measurable steps — sublimation of the metal, ionization of the metal atom, dissociation of the nonmetal molecule, electron affinity of the nonmetal atom, and lattice formation from the gaseous ions — so that the one step that cannot be measured directly, lattice energy, can be calculated from the others.

How does Hess's Law let you solve for lattice energy?

Hess's Law states that the total enthalpy change for a reaction is the same regardless of the path taken, as long as the start and end points match. Because the direct formation enthalpy delta-H-f and the five-step indirect route both start at the elements and end at the ionic solid, their sums must be equal: delta-H-f = delta-H-sub + IE + half-D + EA + delta-H-lattice, which rearranges to give the one unknown, delta-H-lattice.

Why is electron affinity sometimes positive, as with oxygen forming O2-?

Adding a first electron to a neutral atom like oxygen releases energy (EA1 is exothermic), but adding a second electron to the resulting O- ion means forcing a negative charge onto an already negative ion, which requires energy input and makes EA2 endothermic. For MgO, EA1 plus EA2 is net positive (unfavorable) even though the final lattice energy is hugely exothermic once the ions come together.

Why can't lattice energy be measured directly in the lab?

Lattice energy is defined as the enthalpy change when gaseous ions come together to form one mole of solid ionic crystal (or the reverse, for lattice dissociation) — a process that never happens in isolation in a real experiment, since you cannot produce a beaker of free-floating gaseous cations and anions and watch them condense. The Born-Haber cycle sidesteps this by using only steps that are experimentally measurable.

What does a more negative lattice energy mean physically?

A more negative (more exothermic) lattice energy means the ionic bonds in the crystal are stronger, which correlates with a higher melting point, greater hardness, and lower solubility. Lattice energy grows more negative with smaller ionic radii and higher ionic charges, which is why MgO (2+ and 2- ions) has a far larger lattice energy than NaCl (1+ and 1- ions).

About this simulation

This simulator turns the abstract Born-Haber cycle into a live, draggable energy staircase. Choose an ionic compound, then watch five thermochemical steps — sublimation, ionization, dissociation, electron affinity and lattice formation — climb and drop across the diagram, always landing exactly where the directly-measured enthalpy of formation says they should, because Hess's Law leaves no other option.

🔬 What it shows

An animated energy staircase that climbs through sublimation, ionization and bond dissociation, then drops sharply through electron affinity and lattice formation — a glowing marker traces the five-step indirect path while a dashed line on the right shows the single-step direct route (ΔHf), visually proving Hess's Law: both routes must land on exactly the same final energy.

🎮 How to use

Pick NaCl, MgO, CaF₂ or KBr from the compound dropdown to load realistic default values and slider ranges, then drag any of the four step sliders — sublimation, ionization, dissociation or electron affinity — and watch the stats panel and the diagram's final drop instantly recompute the lattice energy that Hess's Law demands.

💡 Did you know?

The cycle is named after Max Born and Fritz Haber, who independently proposed it in 1919 — the same Haber who developed the Haber-Bosch process for ammonia synthesis. Lattice energies calculated this way for simple ionic salts typically agree with purely electrostatic Born-Lande calculations to within a few percent, strong evidence that compounds like NaCl really are almost perfectly ionic.

Frequently asked questions

Why does MgO have such a huge lattice energy compared to NaCl?

Lattice energy scales roughly with the product of the ionic charges divided by the distance between ion centers (from Coulomb's law). MgO's ions carry charges of +2 and -2 — four times the charge product of NaCl's +1 and -1 ions — and Mg2+ and O2- are also smaller than Na+ and Cl-, so MgO's lattice energy (around -3800 kJ/mol) dwarfs NaCl's (around -790 kJ/mol).

Is lattice energy the same thing as lattice enthalpy?

They are used almost interchangeably in most courses, but strictly lattice energy refers to the internal energy change at 0 K for separating a solid into gaseous ions, while lattice enthalpy is the enthalpy change (which includes a small p-delta-V term) usually quoted at 298 K. The numerical difference is small enough that Born-Haber cycles built from ΔHf, ΔHsub, IE, D, and EA — all of which are enthalpies — are conventionally reported as lattice enthalpy.

Why does CaF2 need two electron affinity and two dissociation contributions?

Each formula unit of CaF2 requires two fluoride ions, so the cycle must dissociate one whole F2 molecule into two F atoms (rather than half a molecule, as for the 1:1 salts) and then add an electron to each of the two F atoms, effectively doubling both the dissociation-energy and electron-affinity terms compared with a 1:1 salt like NaCl.

How accurate are Born-Haber lattice energies compared to a theoretical Born-Lande calculation?

For strongly ionic compounds like the alkali halides, Born-Haber (experimental, via Hess's Law) and Born-Lande or Kapustinskii (theoretical, from electrostatics) lattice energies typically agree within a few percent. Larger discrepancies — as seen for some transition-metal or silver halides — signal that the bonding has significant covalent character that the purely ionic electrostatic model does not capture.

What real-world properties does lattice energy predict?

Compounds with large lattice energies tend to have high melting and boiling points, high hardness, low solubility in water, and low volatility, because breaking the ionic lattice apart takes a large energy input. This is why MgO is used as a refractory (furnace-lining) material that survives extremely high temperatures, while more weakly bound salts like KBr are comparatively soft and dissolve readily.

Why is ionization energy always endothermic while electron affinity is often exothermic?

Ionization energy is always endothermic because removing an electron from a neutral atom means pulling it away from the attractive pull of the nucleus, which always costs energy. A first electron affinity is usually exothermic because adding an electron to a neutral atom is attractive right up until the resulting negative charge starts to repel further electrons, which is why second and later electron affinities (as in O2- or S2- formation) become endothermic.

⚙ Under the hood

Climb an animated energy staircase through sublimation, ionization, dissociation and electron affinity to solve for the lattice energy of an ionic solid like NaCl or MgO via Hess's Law.

Born-Haber CycleLattice EnergyIonic CrystalElectron AffinityCanvas 2D

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install