Lattice energies can also be calculated for covalent solids using a Born-Haber cycle, and the network solid silicon dioxide has one of the highest ${{\mathbf{\Delta H}}^o}_{\mathrm{Lattice}}$values. Silicon oxide is found in pure crystalline form as transparent rock quartz. Much harder than glass, this material was one prized for making lenses for optical devices and expensive spectacles. Use appendix B and the following data to calculate${{\mathbf{\Delta H}}^o}_{\mathrm{Lattice}}$ of ${\mathbf{SiO}}_2$ :

_{$\begin{array}{l}\mathbf{Si}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\to \mathbf{Si}\mathbf{\left(}\mathbf{g}\mathbf{\right)}{\mathbf{\Delta H}}^o\mathbf{=}\mathbf{454}\mathbf{kJ}\\ \mathbf{Si}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\to {\mathbf{Si}}^{4+}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}\mathbf{4}{\mathbf{e}}^{-}{\mathbf{\Delta H}}^o\mathbf{=}\mathbf{9949}\mathbf{kJ}\\ {\mathbf{O}}_2\mathbf{\left(}\mathbf{g}\mathbf{\right)}\to \mathbf{2}\mathbf{O}\mathbf{\left(}\mathbf{g}\mathbf{\right)}{\mathbf{\Delta H}}^o\mathbf{=}\mathbf{498}\mathbf{kJ}\\ \mathbf{O}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}\mathbf{2}{\mathbf{e}}^{-}\to {\mathbf{O}}^{2-}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}}{\mathbf{\Delta H}}^o\mathbf{=}\mathbf{737}\mathbf{kJ}\end{array}$}

The Born-Haber cycle is a series of enthalpy changes that results in the development of a solid, crystalline ionic compound from elemental atoms in their standard state while lowering the enthalpy of the solid compound's formation to zero.

Hess’s law states that the change in enthalpy for a reaction is the same whether the reaction takes place in one or a series of steps.

From the given cycle it is clear that the enthalpy of formation is -910.9kJ.

So, we can calculate the${{\mathbf{\Delta H}}^o}_{\mathrm{Lattice}}$ of ${\mathbf{SiO}}_2$ by adding all the enthalpies in the multistep process and ${{\mathbf{\Delta H}}^o}_{\mathrm{Lattice}}$ compared with the enthalpy of formation.

Hence

$\begin{array}{l}\mathbf{454}\mathbf{kJ}\mathbf{+}\mathbf{9949}\mathbf{kJ}\mathbf{+}\mathbf{498}\mathbf{kJ}\mathbf{+}\mathbf{737}\mathbf{kJ}\mathbf{+}{{\mathbf{\Delta H}}^o}_{\mathrm{lattice}}\mathbf{=}\mathbf{-}\mathbf{910}\mathbf{.}\mathbf{9}\mathbf{kJ}\mathbf{(}\mathbf{enthalpy}\mathbf{of}\mathbf{formation}\mathbf{)}\\ {{\mathbf{\Delta H}}^o}_{\mathrm{lattice}}\mathbf{=}\mathbf{-}\mathbf{12548}\mathbf{.}\mathbf{9}\mathbf{kJ}\end{array}$

Hence, -12458.9 is the highest lattice energy of silicon oxide.