J. D. Lee Solutions for Chapter: The Ionic Bond, Exercise 1: Exercise 1

Show by means of a diagram, and a simple calculation, the minimum value of the radius ratio ${\mathrm{r}}^{+}/{\mathrm{r}}^{-}$, which permits a salt to adopt a cesium chloride type of structure.

Give the co-ordination number of the ions and describe the crystal structures of zinc blende, wurtzite and sodium chloride in terms of close packing and the occupancy of the tetrahedral and the octahedral holes.

$\mathrm{CsCl}, \mathrm{CsI}, \mathrm{TlCl}$ and $\mathrm{TlI}$ all adopt a caesium chloride structure. The inter-ionic distances are: $\mathrm{Cs}-\mathrm{Cl} \Rightarrow 3.06 {\mathrm{A}}^{°}, \mathrm{Cs}-\mathrm{I} \Rightarrow 3.41 {\mathrm{A}}^{°}, \mathrm{Tl}-\mathrm{Cl} \Rightarrow 2.55 {\mathrm{A}}^{°}$ and $\mathrm{Tl}-\mathrm{I}\Rightarrow 2.90 {\mathrm{A}}^{\circ }$. Assuming that the ions behave as hard spheres and that the radius ratio in $\mathrm{TlI}$ has the limiting value, calculate the ionic radii for ${\mathrm{Cs}}^{+}, {\mathrm{Tl}}^{+}, {\mathrm{Cl}}^{-}, {\mathrm{I}}^{-}$ in eight-coordination.

Write down the Born-Lande equation and define the terms in it. Use the equation to show why some crystals, which according to the radius ratio concept should adopt a coordination number of $8$, in fact have a coordination number of $6$.

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.

List the types of defects that occur in the solid-state and give an example of each. Explain in each case if any electrical conduction is possible and by what mechanism.