A thermochemical cycle using Hess's law to calculate lattice energy from measurable enthalpies.
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The Born-Haber cycle applies Hess's law to break the formation of an ionic solid into a series of steps whose enthalpies can be measured or estimated. The steps include sublimation of the metal, its ionization, dissociation of the nonmetal, electron gain by the nonmetal and finally the formation of the lattice. Because the overall enthalpy of formation is measurable, the unknown lattice energy can be calculated as the remaining term. The cycle can also test whether a hypothetical compound would be stable, since if the lattice energy cannot offset the costly ionization steps, the compound will not form. It is a direct application of energy conservation to ionic solids.
Key ideas: Write the steps in order: sublimation of metal, ionization energy, bond dissociation (half for diatomic gas), electron affinity, lattice energy, and the sum equals the enthalpy of formation. Rearrange to solve for the lattice energy. For NaCl: 107 plus 496 plus 122 minus 349 plus U equals -411, giving U about -787 kJ/mol.
Common mistakes and connections: Frequent mistakes are forgetting to use half the bond energy for X2 when forming one mole of MX, getting signs wrong for electron affinity, and missing the second ionization energy for MgCl2 or the second electron affinity for oxides. Remember the sign convention of U. Links to Hess's law, lattice energy and ionization energy trends.
Hess law cycle for NaCl: +107, +496, +122, -349 and the lattice energy -787 add up to a formation enthalpy of -411 kJ/mol. The interactive lesson shows this as a live animation or chart.
Applied to sodium chloride, the cycle gives a lattice energy near 787 kJ/mol, and it shows that NaCl2 would be unstable because the second ionization of sodium costs too much energy.
A thermochemical cycle using Hess's law to calculate lattice energy from measurable enthalpies.
Born-Haber Cycle is a advanced topic in Bonding & Molecular Structure. It builds on beginner and intermediate topics, so review those first if needed.
Study these earlier topics in Bonding & Molecular Structure first: Fajans' Rules, Polarizability, Lattice Energy.
The next topics in Bonding & Molecular Structure are Properties of Ionic Compounds and Properties of Covalent Compounds.
Yes. The interactive lesson includes a self-check question on Born-Haber Cycle, and the Bonding & Molecular Structure quiz draws on every topic in this area.
Born-Haber Cycle is topic 28 of 104 in Bonding & Molecular Structure.