Lattice Energy - Practice Questions & MCQ

The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔH_lattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid MX, the lattice energy is the enthalpy change of the process:

$\mathrm{MX}(s) \longrightarrow \mathrm{M}^{n+}(g)+\mathrm{X}^{n-}(g) \quad \Delta H_{\text {lattice }}$

The lattice energy ΔH_lattice of an ionic crystal can be expressed by the following equation:

$\Delta \mathrm{H}_{\text {lattice }}=\frac{\mathrm{C}\left(\mathrm{Z}^{+}\right)\left(\mathrm{Z}^{-}\right)}{\mathrm{R}_0}$

in which C is a constant that depends on the type of crystal structure; Z⁺ and Z^– are the charges on the ions, and Ro is the interionic distance. Thus, the lattice energy of an ionic crystal increases rapidly as the charges of the ions increase and the sizes of the ions decrease. 

The Born-Haber Cycle

It is not possible to measure lattice energies directly. However, the lattice energy can be calculated using the equation given in the previous section or by using a thermochemical cycle. The Born-Haber cycle is an application of Hess’s law that breaks down the formation of an ionic solid into a series of individual steps:

• ΔH_f°, the standard enthalpy of formation of the compound

• IE, the ionization energy of the metal

• EA, the electron affinity of the nonmetal

• ΔH_s°, the enthalpy of sublimation of the metal

• D, the bond dissociation energy of the nonmetal

• ΔH_lattice, the lattice energy of the compound

The figure given below shows the Born-Haber cycle for the formation of solid cesium fluoride.

The Born-Haber cycle shows the relative energies of each step involved in the formation of an ionic solid from the necessary elements in their reference states.

For Caesium fluoride, the lattice energy can be calculated using the given values as follows:

$\Delta H_{\text {lattice }}=(553.5+76.5+79.4+375.7+328.2) \mathrm{kJ} / \mathrm{mol}=1413.3 \mathrm{~kJ} / \mathrm{mol}$