Born-Haber closes an energy loop to isolate the one value you can't measure
Lattice energy can't be measured directly, so the Born-Haber cycle gets it indirectly. Every other step from the pure elements to the ionic solid is known, and by Hess's law the whole loop sums to zero. Rearranged, the lattice energy U is whatever is left over. Each step is one physical process: turning the metal to gas, ionizing it, splitting the non-metal's bond, adding electrons, and forming the compound.
The five steps in the cycle
| Step | Process | Energy term |
|---|---|---|
| Sublimation | M(s) → M(g) | ΔHsub |
| Ionization | M(g) → M+(g) + e− | ∑IE |
| Bond dissociation | ½ X2(g) → X(g) | ½ΔHbond |
| Electron affinity | X(g) + e− → X−(g) | EA |
| Formation | M(s) + ½ X2(g) → MX(s) | ΔHf |
Lattice energy itself is the step M+(g) + X−(g) → MX(s). It is the only unknown, so the closed loop pins it down.
Two things set how large it gets
Lattice energy scales with the product of the ion charges and inversely with the distance between ion centers. Bigger charges and smaller ions both make it stronger.
| Compound | Lattice energy (kJ/mol) |
|---|---|
| NaCl | 786 |
| KCl | 717 |
| NaF | 910 |
| CaF2 | 2630 |
| CaO | 3520 |
| MgO | 3850 |
Compare NaCl (both ions 1±) with MgO (both 2±): quadrupling the charge product plus smaller ions pushes the energy roughly fivefold higher.
Two mistakes to avoid
- Lattice energy is not bond dissociation energy. Lattice energy dismantles the whole crystal into gas ions (NaCl: 786 kJ/mol). Bond dissociation breaks a single gas-phase molecule (NaCl(g): 226 kJ/mol). Different quantities.
- Watch the sign convention. Some sources report the released (negative) value, others the required (positive) value. State which you mean before comparing tables.
Common questions
How does the Born-Haber cycle find lattice energy?
It is a Hess's law loop. You add up every energy step from the elements to the solid compound (sublimation, ionization, bond dissociation, electron affinity, and formation), and because the loop closes to zero, lattice energy is the one unknown you solve for.
Why is MgO lattice energy so much higher than NaCl?
MgO is about 3850 kJ/mol versus 786 for NaCl. The Mg2+ and O2- ions each carry a 2+ or 2- charge instead of 1, and both ions are smaller. Lattice energy rises with the product of the charges and falls as the ions get farther apart, so higher charges plus a shorter distance multiply the effect.
Is lattice energy positive or negative?
It depends on the definition. As the energy needed to pull the crystal apart into gaseous ions it is positive (endothermic). The Born-Lande equation returns a negative value because it describes the ions coming together; take the absolute value for the standard positive figure.
Does high lattice energy mean the salt is insoluble?
Not on its own. Solubility depends on lattice energy versus the hydration energy released when water surrounds the ions. NaF has a high lattice energy yet dissolves well because its ions are strongly hydrated.
