Molecular compounds, lattice energy

The lattice energy of a molecular compound corresponds to the energy of sublimation at 0 K. This energy cannot be measured directly, but it is equal to the enthalpy of sublimation at a temperature T plus the thermal energy needed to warm the sample from 0 K to this temperature, minus RT. RT is the amount of energy required to expand one mole of a gas at a temperature T to an infinitely small pressure. These amounts of energy, in principle, can be measured and therefore the lattice energy can be determined experimentally in this case. However, the measurement is not simple and is subject to various uncertainties. 

Generally, increasing molecular size, heavier atoms and more polar bonds contribute to an increased lattice energy of a molecular crystal. Typical values are argon 7.7 kJ mol-1 krypton 11.1 kJmol-1 organic compounds 50 to 150 kJ mol-1. 

For compounds that are ionic rather than molecular solids, AHf can be calculated by appropriately combining the heats of formation of the gas phase ions (computed or experimental) with the lattice energy (converted to enthalpy [91]). We have developed formulas for lattice energies in terms of properties of the electrostatic potentials on the anions surfaces [92], for any of three possible cations NH4+, Na+ and K+. 

In a more accurate picture of ionic crystals, the ions are held together in a three-dimensional lattice by a combination of electrostatic attraction and covalent bonding. Although there is a small amount of covalent character in even the most ionic compounds, there are no directional bonds, and each Li ion is surrounded by six F ions, each of which in turn is surrounded by six Li ions. The crystal molecular orbitals form energy bands, described in Chapter 7. 

We can also determine lattice energy indirectly, by assuming that the formation of an ionic compound takes place in a series of steps. This procedure, known as the Born-Haber cycle, relates lattice energies of ionic compounds to ionization energies, electron affinities, and other atomic and molecular properties. It is based on Hess s law (see Section 6.5). Developed by Max Bom and Fritz Haber, the Bom-Haber cycle defines the various steps that precede the formation of an ionic solid. We will illustrate its use to find the lattice energy of lithium fluoride. 

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