The Born-Haber Cycle

Formation of ionic bonds requires an electron transfer from a metal to a nonmetal atom - a process that is often endothermic. However, when elemental sodium and chlorine react to form a solid sodium chloride crystal, it's a highly exothermic process. But where is the energy coming from?

According to Coulomb’s law, cations and anions are attracted to each other by strong electrostatic forces into a solid array or lattice. The resulting lattice structure is stabilized by decreasing the potential energy, which is released as heat, an exothermic reaction. 

The total energy associated with the formation or breakdown of a crystalline lattice into its gaseous constituents is called lattice energy. 

In a solid ionic compound, a large number of charged particles interact with each other making it difficult to determine the exact value of the lattice energy experimentally. However, it can be calculated using Hess’s law in a hypothetical series of steps called the Born–Haber cycle, which represents the formation of an ionic compound from its constituent elements.

For example, the Born-Haber cycle for sodium chloride formation considers two alternate routes, one direct and another indirect. The direct route represents the standard enthalpy of formation of NaCl from elemental sodium and chlorine. 

The indirect route has five steps. In the first step, solid-state sodium is converted into its gaseous form. Next, diatomic chlorine molecules dissociate into gaseous chlorine atoms. 

The third and fourth steps account for the electron transfer to form ions. An electron is removed from the gaseous sodium to form a sodium cation. The electron is then taken up by the gaseous chlorine to form a chloride anion. 

In the final step, the electrostatic attraction between the gaseous ions leads to the formation of the lattice structure.

Hess’s law states that the change in the overall enthalpy of a stepwise process is the sum of the enthalpy changes of each step. Meaning the enthalpy value of the direct route equals the sum of enthalpies of the five steps.

By solving the equation for lattice energy, a large negative value is determined, which signifies an exothermic reaction.