The Born-Haber Cycle

Ionic bond formation involves electron transfer, which is endothermic. However, the resulting cations and anions attract each other through strong electrostatic forces, forming a stable lattice structure. This lattice formation releases significant energy as heat, making the overall process highly exothermic. The energy released from lattice stabilization exceeds the energy required for electron transfer.

Lattice energy is the total energy required to separate one mole of solid ionic compound into gaseous ions, or equivalently, the energy released when gaseous ions combine to form a solid lattice. A larger magnitude of lattice energy indicates stronger electrostatic attractions between ions and greater stability of the ionic compound. For sodium chloride, the lattice energy is 769 kJ/mol.

The Born-Haber cycle applies Hess's law by breaking ionic compound formation into five hypothetical steps: sublimation of the metal, dissociation of nonmetal molecules, ionization of metal atoms, electron affinity of nonmetal atoms, and lattice formation. Since enthalpy is a state function, the sum of enthalpy changes for these steps equals the standard enthalpy of formation. Solving for lattice energy yields a large negative value, confirming the exothermic lattice formation.

Lattice energy increases rapidly as ion charges increase and ion sizes decrease. Doubling the charges of both cation and anion quadruples the lattice energy. For example, MgO has a much higher lattice energy (3900 kJ/mol) than LiF (1023 kJ/mol) due to higher ion charges. Smaller ions like F– produce higher lattice energies than larger ions like I– when bonded to the same cation, demonstrating the effect of trends in lattice energy ion size and charge.

Lattice energies typically range from 600–4000 kJ/mol, while covalent bond dissociation energies are typically 150–400 kJ/mol for single bonds. This difference exists because lattice energy involves many simultaneous electrostatic interactions between numerous cations and anions in an extended crystal structure, whereas bond dissociation energy measures the interaction between just two atoms in a covalent bond.

Yes, the Born-Haber cycle can calculate any one quantity in the lattice energy equation if all other values are known. If the enthalpy of sublimation, ionization energy, bond dissociation enthalpy, lattice energy, and standard enthalpy of formation are available, the cycle can be rearranged to determine the electron affinity of an atom. This demonstrates the versatility of Hess's law in thermochemical calculations.

The five steps are: (1) sublimation of solid sodium to gaseous sodium, (2) dissociation of diatomic chlorine into gaseous chlorine atoms, (3) ionization of gaseous sodium to form Na+ cations, (4) electron affinity of gaseous chlorine to form Cl– anions, and (5) electrostatic attraction between gaseous ions forming the solid lattice. These steps represent an indirect route equivalent to the direct formation of NaCl from its elements.