Lattice Energy of Ionic Compounds

The lattice energy U of an ionic compound is defined as the energy required to convert one mole of crystalline solid into its component cations and anions in their thermodynamic standard states (non-interacting gaseous ions at standard temperature and pressure). It can be calculated using either the Born-Land6 equation 

Kapustinskii noted that if the Madelung constant A is divided by the number of ions per formula unit for a number of crystal structures, nearly the same value is obtained. Furthermore, as both A/n and re increase with the coordination number, their ratio A/nre is expected to be approximately the same from one structure to another. Therefore, Kapustinskii proposed that the structure of any ionic solid is energetically equivalent to a hypothetical rock-salt structure and its lattice energy can be calculated using the Madelung constant of NaCl and the appropriate ionic radii for (6,6) coordination. 

Formula Space group Compound name Coordination mode Madelung constant 

The lattice energies calculated using this equation are compared with those obtained from the Born-Haber cycle in Table 4.2.4. 

Ionic Compound Born-Haber Kapustinskii Ionic compound Born-Haber Kapustinskii 

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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. 

The calculation of lattice energies of ionic compounds is very important since, in general, there is no direct way to measure them experimentally, although they can be obtained from certain experimental data using the Born-Haber cycle which is discussed immediately below. For example, the heat of vaporization of NaCl does not give the lattice energy because up to the highest temperatures at which accurate measurements can be made the gas phase consists of NaCl molecules (or ion pairs), and it has so far proved impossible to get an accurate estimate of the heat of dissociation of NaCl(g) into Na+(g) and Cl (g) since NaCl(g) normally dissociates into atoms. 

The first ionization potential of boron, 8.296 eV, is rather high, and the next two are much higher. Thus the total energy required to produce B3 + ions is far more than would be compensated by lattice energies of ionic compounds or by hydration of such ions in solution. Consequently, simple electron loss to form a cation plays no part in boron chemistry. Instead, covalent bond formation is of major importance, and boron compounds usually resemble those of other non-metals, notably silicon, in their properties and reactions. 

Born-Haber cycle. The cycle that relates lattice energies of ionic compounds to ionization energies, electron affinities, heats of sublimation and formation, and bond enthalpies. (9.3)... 

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