Lithium superoxide, \(\mathrm{LiO}_{2}(\mathrm{s}),\) has never been isolated.
Use ideas from Chapter \(12,\) together with data from this chapter and Appendix
\(D\), to estimate \(\Delta H_{f}\) for \(\mathrm{LiO}_{2}(\mathrm{s})\) and assess
whether \(\mathrm{LiO}_{2}(\mathrm{s})\) is thermodynamically stable with
respect to \(\mathrm{Li}_{2} \mathrm{O}(\mathrm{s})\) and
\(\mathrm{O}_{2}(\mathrm{g}).\)
(a) Use the Kapustinskii equation, along with appropriate data below, to
estimate the lattice energy, \(U,\) for \(\left.\mathrm{LiO}_{2}(\mathrm{s}) .
\text { (See exercise } 126 \text { in Chapter } 12 .\right)\) The ionic radii
for \(L\) i \(^{+}\) and \(O_{2}^{-}\) are \(73 \mathrm{pm}\) and \(144 \mathrm{pm},\)
respectively.
(b) Use your result from part (a) in the BornFajans-Haber cycle to estimate
\(\Delta H_{\mathrm{f}}^{2}\) for \(\mathrm{LiO}_{2}(\mathrm{s})\) [Hint: For the
process \(\mathrm{O}_{2}(\mathrm{g})+\mathrm{e}^{-} \rightarrow
\mathrm{O}_{2}^{-}(\mathrm{g}), \Delta H^{\circ}=.\)
\(-43 \mathrm{kJ} \mathrm{mol}^{-1} .\) See Table 21.2 and Appendix \(\mathrm{D}\)
for the other data that are required.]
(c) Use your result from part (b) to calculate the enthalpy change for the
decomposition of \(\mathrm{LiO}_{2}(\mathrm{s})\) to \(\mathrm{Li}_{2}
\mathrm{O}(\mathrm{s})\) and \(\mathrm{O}_{2}(\mathrm{g}) .\) For
\(\mathrm{Li}_{2} \mathrm{O}(\mathrm{s}), \Delta
H_{\mathrm{f}}^{\circ}=-598.73\) \(\mathrm{kJmol}^{-1}.\)
(d) Use your result from part (c) to decide whether
\(\mathrm{LiO}_{2}(\mathrm{s})\) is thermodynamically stable with respect to
\(\mathrm{Li}_{2} \mathrm{O}(\mathrm{s})\) and \(\mathrm{O}_{2}(\mathrm{g}) .\)
Assume that entropy effects can be neglected.