Chapter 21, Problem 61IAE

Lithium superoxide, ${\text{LiO}}_{\text{2}}\text{(s)}$ , has never been isolated. Use ideas from Chapter 12, together with data from this chapter and Appendix D, to estimate ${\Delta }_{r}H°$ for ${\text{LiO}}_{\text{2}}\text{(s)}$ and assess whether ${\text{LiO}}_{\text{2}}\text{(s)}$ is thermodynamically stable with respect to ${\text{LiO}}_{\text{2}}\text{(s)}$ and ${\text{O}}_{\text{2}}\text{(g)}$ .

1. Use the Kapustinskii equation, along with appropriate data below, to estimate the lattice energy, U, for ${\text{LiO}}_{\text{2}}\text{(s)}$ . (See Exercise 127 in Chapter 12.) The ionic radii for ${\text{Li}}^{\text{+}}$ and ${\text{O}}_{\text{2}}{}^{-}$are 73 pm and 144 pm, respectively.
2. Use your result from part (a) in the Born-Fajans-Haber cycle to estimate ${\Delta }_{r}H°$ for ${\text{LiO}}_{\text{2}}(\text{s})$ . [Hint: For the process ${\text{O}}_{\text{2}}\text{(g)}\text{+}{\text{e}}^{–}\to {\text{O}}_{\text{2}}{}^{–}\text{(g),}{\text{Δ}}_{\text{r}}H\text{°}\text{=}–\text{43}$kJ mol-1. See Table 21.2 and Appendix D for the other data that are required.]
3. Use your result from part (b) to calculate the enthalpy of reaction for the decomposition of ${\text{LiO}}_{\text{2}}\text{(s)}$ to ${\text{Li}}_{\text{2}}\text{O(s)}$ and ${\text{O}}_{\text{2}}\text{(g)}$ . For ${\text{Li}}_{\text{2}}\text{O(s),}{\text{Δ}}_{r}H\text{°}\text{=}–\text{597}\text{.73}$kJ mol-1.
4. Use your result from part (c) to decide whether ${\text{LiO}}_{\text{2}}\text{(s)}$ is thermodynamically stable with respect to ${\text{Li}}_{\text{2}}\text{O(s)}$ and ${\text{O}}_{\text{2}}\text{(g)}$ . Assume that entropy effects can be neglected.