# Lattice energy

File:Diamant27.png
Diamond Crystal Lattice

The lattice energy of an ionic solid is a measure of the strength of bonds in that ionic compound. It is given the symbol U and is equivalent to the amount of energy required to separate a solid ionic compound into gaseous ions. Lattice energy can also be considered as the energy given off when gaseous ions form an ionic solid. It is dependent on ionic charge and the ionic radius: as the charge of the ions increases the lattice energy increases (becomes more negative), and as the radius decreases (the ions in the ionic solid are closer together) the lattice energy increases.

Lattice energy deals primarily with metals. It cannot be determined directly but can be by using experimental data in the Born Haber cycle and from theoretical calculations.

## Calculation

Lattice energy is the energy change when an ionic compound is separated into tangents. It is given in units of kilojoules per mole. For example, when solid sodium chloride is separated into gaseous sodium and chlorine ions

$\text{NaCl (s)} \to \text{Na}^+ \text{(g)} + \text{Cl}^- \text{(g)}$

the lattice energy is 786 kJ/mol.

Lattice energy is usually calculated by using the Born-Haber cycle. The Kapustinskii equation can also be used.

Lattice energy, the potential energy of two interacting ions (taken as two point charges), can also be calculated by using a modified version of Coulomb's law: $E = k\cdot \frac{q_1q_2}{r}$, where $k=8.99 \cdot 10^9 \text{J-m}/\text{C}^2$, ${r}$ is the distance between the centers of the ions, and $q_1,q_2$ are the charges on the ions.[1]

## Lattice enthalpy

The lattice enthalpy is the enthalpy change involved in formation of the ionic compound from gaseous ions. Some chemists define it as the energy to break the ionic compound into gaseous ions. The former definition is invariably exothermic and the latter is endothermic.

## Relative Strengths of Lattice Energy

Lattice energy is inversely related to the distances of ionic bonds. Barium Oxide (BaO), for instance, has a bond radius of 275 picometers and a lattice energy of 3054 kJ/mol while Sodium Chloride (NaCl) has a bond radius of 283 picometers and a lattice energy of 786 kJ/mol.

## References

1. Brown, Theodore L, H Eugene Lemay, and Bruce E. Bursten. Chemistry: The Central Science. pp265. New Jersey: Prentice Hall, 2000.