Exercises: Ionic bonding and Born–Haber cycles

Sodium chloride, $\mathrm{NaCl}$, crystallizes forming a three-dimensional rock salt structure (two interpenetrating ionic sublattices), whereas hydrogen chloride, $\mathrm{HCl}$, forms discrete diatomic molecules in the gas phase at room temperature. Justify, on the basis of the type of bonding and structure, why it makes no physical sense to speak of a "$\mathrm{NaCl}$ molecule" in the solid state, stating how the empirical formula of this ionic compound is defined.

Consider the lithium halides $\mathrm{LiF}$ and $\mathrm{LiI}$. Both compounds crystallize with the same ionic lattice geometry ($\mathrm{NaCl}$ type). Given that the ionic radii are $r(\mathrm{F^-}) = 133\,\mathrm{pm}$ and $r(\mathrm{I^-}) = 220\,\mathrm{pm}$, and considering the Born–Landé equation or Coulomb's law for the lattice energy (taken here as the exothermic process of formation of the lattice from gaseous ions, $\Delta H_{\mathrm{ret}} < 0$): a) Deduce, with justification, which of the two solids has the lattice enthalpy of greater magnitude $(|\Delta H_{\mathrm{ret}}|)$. b) Justify which of the two compounds will have the higher melting point.

Potassium bromide, $\mathrm{KBr(s)}$, dissociates completely into its gaseous ions according to the endothermic process: $\mathrm{KBr(s)} \to \mathrm{K^+(g)} + \mathrm{Br^-(g)}$. For this process, the lattice dissociation enthalpy is $\Delta H_{\mathrm{ret,dis}} = +689\,\mathrm{kJ\times mol^{-1}}$. Determine the standard lattice enthalpy of formation of the lattice, $\Delta H_{\mathrm{ret}}$, corresponding to the reaction $\mathrm{K^+(g)} + \mathrm{Br^-(g)} \to \mathrm{KBr(s)}$, and briefly explain the meaning of the thermodynamic sign obtained.

The ionic compounds magnesium fluoride, $\mathrm{MgF_2}$, and calcium fluoride, $\mathrm{CaF_2}$, are compared. Both have an identical cation/anion charge ratio (+2/−1). Ionic radii data: $r(\mathrm{Mg^{2+}}) = 72\,\mathrm{pm}$, $r(\mathrm{Ca^{2+}}) = 100\,\mathrm{pm}$, and $r(\mathrm{F^-}) = 133\,\mathrm{pm}$. Experimentally, the magnitudes of the lattice enthalpies of formation $(\Delta H_{\mathrm{ret}} < 0)$ for both solids are $\approx 2957\,\mathrm{kJ\times mol^{-1}}$ and $\approx 2630\,\mathrm{kJ\times mol^{-1}}$. a) Assign, with justification, each lattice enthalpy value to its corresponding compound using arguments of electrostatic attraction. b) If $\mathrm{MgF_2}$ is now compared with magnesium oxide, $\mathrm{MgO}$ (where $r(\mathrm{O^{2-}}) = 140\,\mathrm{pm}$ and its $|\Delta H_{\mathrm{ret}}|$ is approximately $3791\,\mathrm{kJ\times mol^{-1}}$), explain the role of the greater charge of the oxide anion in the electrostatic attraction. State why a rigorous quantitative comparison also requires considering the stoichiometry and the structure of the lattices.