Lattice energy is obtained by summing atomization, ionization, electron affinity and formation steps.
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A Born-Haber cycle is a Hess's law construction that breaks the formation of an ionic solid into a sequence of measurable steps. The steps typically include atomization of the metal, ionization of the metal atom, dissociation of the nonmetal molecule, electron gain by the nonmetal atoms, and finally formation of the solid lattice from gaseous ions. Summing all these steps gives the standard enthalpy of formation, which is known, so the unknown lattice enthalpy can be solved for. This analysis explains why ionic compounds can be stable despite the high energy cost of ionization. It is an advanced application that connects atomic properties to the energetics of crystals.
Key ideas: Build the cycle in steps: atomize the metal, ionize it, atomize the nonmetal, add electrons, then form the lattice, and equate the sum to the enthalpy of formation. Solve for lattice enthalpy. Use the correct number of ionization steps and half of the dissociation energy of a diatomic.
Common mistakes and connections: Common slips include forgetting the factor of one half for halogens, mixing the sign of the lattice enthalpy with the lattice dissociation enthalpy, and missing a second ionization for ions such as Mg2+. Comparing theory with the cycle result reveals covalent character in the bonding.
Born-Haber cycle for NaCl: sublimation, ionization, dissociation of Cl2, electron affinity, then the lattice energy drops the system to -411 kJ/mol. The interactive lesson shows this as a live animation or chart.
For NaCl the lattice enthalpy is about -787 kJ per mole, obtained by summing the sublimation, ionization, dissociation, electron affinity and formation steps.
Lattice energy is obtained by summing atomization, ionization, electron affinity and formation steps.
Born-Haber Energetics is a advanced topic in Thermodynamics & Energetics. It builds on beginner and intermediate topics, so review those first if needed.
Study these earlier topics in Thermodynamics & Energetics first: Reaction Enthalpy from Formation Data, Bond Enthalpy Calculations, Enthalpy of Atomization.
The next topics in Thermodynamics & Energetics are Spontaneous Process and Entropy.
Yes. The interactive lesson includes a self-check question on Born-Haber Energetics, and the Thermodynamics & Energetics quiz draws on every topic in this area.
Born-Haber Energetics is topic 28 of 91 in Thermodynamics & Energetics.