Explain the term lattice energy as applied to an ionic solid. Calculate the lattice energy of caesium chloride using the following data.

$\mathrm{Cs} \left(\mathrm{s}\right)\to \mathrm{Cs} \left(\mathrm{g}\right)$  $\mathrm{\Delta H}=+79.2 \mathrm{kJ} {\mathrm{mol}}^{-1}$

$\mathrm{Cs} \left(\mathrm{g}\right)\to {\mathrm{Cs}}^{+} \left(\mathrm{g}\right)$  $\mathrm{\Delta H}=+374.05 \mathrm{kJ} {\mathrm{mol}}^{-1}$

${\mathrm{Cl}}_2 \left(\mathrm{g}\right)\to 2\mathrm{Cl} \left(\mathrm{g}\right)$ $\mathrm{\Delta H}=+241.84 \mathrm{kJ} {\mathrm{mol}}^{-1}$

$\mathrm{Cl} \left(\mathrm{g}\right)+\mathrm{e}\to {\mathrm{Cl}}^{-} \left(\mathrm{g}\right)$  $\mathrm{\Delta H}=-397.90 \mathrm{kJ} {\mathrm{mol}}^{-1}$

$\mathrm{Cs} \left(\mathrm{s}\right)+\frac{1}{2}{\mathrm{Cl}}_2\to \mathrm{CsCl} \left(\mathrm{s}\right)$  $\mathrm{\Delta H}=-623.00 \mathrm{kJ} {\mathrm{mol}}^{-1}$

Draw the structures of $\mathrm{CsCl}$ and ${\mathrm{TiO}}_2$, showing clearly the coordination of the cations and anions. Show how the Born-Haber cycle may be used to estimate the enthalpy of the hypothetical reaction:

$\mathrm{Ca} \left(\mathrm{s}\right)+\frac{1}{2}{\mathrm{Cl}}_2 \left(\mathrm{g}\right)\to \mathrm{CaCl} \left(\mathrm{s}\right)$

Explain why $\mathrm{CaCl} \left(\mathrm{s}\right)$ has never been made even though the enthalpy for this reaction is negative.

The standard enthalpy changes $\mathrm{\Delta H}°$at $298 \mathrm{K}$ for the reaction: $\mathrm{M}\left(\mathrm{s}\right)+\frac{3}{2}{\mathrm{Cl}}_2 \left(\mathrm{g}\right)\to {\mathrm{MCl}}_3 \left(\mathrm{s}\right)$ are given for the first row transition metals: 

$\begin{array}{cccccccccc}& \mathrm{Sc}& \mathrm{Ti}& \mathrm{V}& \mathrm{Cr}& \mathrm{Mn}& \mathrm{Fe}& \mathrm{Co}& \mathrm{Ni}& \mathrm{Cu}\\ \mathrm{\Delta H}°/\mathrm{kJ} {\mathrm{mol}}^{-1}& -339& -209& -138& -160& +22& -59& -131& -280& +357\end{array}$

Use a Born-Haber cycle to account for the change in $\mathrm{\Delta H}°$ as the atomic number of the metal increases. Comment on the relative stabilities of the $+\mathrm{II}$ and $+\mathrm{III}$ oxidation states of the $3\mathrm{d}$ metals.