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.

Step by step solution

01

Calculate the lattice energy using the Kapustinskii equation

The Kapustinskii equation is given by \(U=-1923Z^+Z^-n(r^++r^-)^{-\frac{9}{10}}\), where \(Z^+\) and \(Z^-\) are the charges on the cation and anion, n is the number of ions in the formula unit, and \(r^+\) and \(r^-\) are the ionic radii of the cation and anion in picometers. For \(\mathrm{LiO_2}\), \(Z^+=\ +1\), \(Z^-=\ -1\), n = 3, \(r^+=73\ \mathrm{pm}\), and \(r^-=144\ \mathrm{pm}\). Substituting these values in the equation gives \(U=-1923(1)(1)(3)(73+144)^{-\frac{9}{10}}.\)

02

Use the Born-Haber cycle to calculate \(\Delta H_f^2\) for \(\mathrm{LiO_2}\)

The Born-Haber cycle involves summing the enthalpies for various process to obtain the heat of formation. For \(\mathrm{LiO_2}\), this includes the sublimation of Li (159.36 kJ/mol), the ionization of Li (520.22 kJ/mol), the dissociation of O2 (248.68 kJ/mol), and the addition of an electron to O2 to form O2- (-43 kJ/mol). The heat of formation is then \(\Delta H_f^2 = U + 159.36 + 520.22 + 248.68 - 43.\)

03

Calculate the enthalpy change for the decomposition of \(\mathrm{LiO}_2\) to \(\mathrm{Li}_2 \mathrm{O}\) and \(\mathrm{O}_2\)

The enthalpy change for the reaction \(\mathrm{LiO}_2(\mathrm{s}) \rightarrow \mathrm{Li}_2 \mathrm{O}(\mathrm{s}) + \mathrm{O}_2(\mathrm{g})\) is given by \(\Delta H = \Delta H_f^{2, \mathrm{LiO}_2} - \Delta H_f^{\circ, \mathrm{Li}_2\mathrm{O}}\) where \(\Delta H_f^{\circ, \mathrm{Li}_2\mathrm{O}} = -598.73\) kJ/mol.

04

Assess the stability of \(\mathrm{LiO}_2\)

If the enthalpy change calculated in Step 3 is positive, then \(\mathrm{LiO}_2\) is not stable with respect to \(\mathrm{Li}_2 \mathrm{O}\) and \(\mathrm{O}_2\), because it indicates that the decomposition reaction is favored. If the enthalpy change is negative, then \(\mathrm{LiO}_2\) is stable with respect to \(\mathrm{Li}_2 \mathrm{O}\) and \(\mathrm{O}_2\), because it indicates that the reverse reaction (formation of \(\mathrm{LiO}_2\)) is favored.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!