Construct a Born-Haber cycle for the formation of the hypothetical compound NaCl2, where the sodium ion has a charge (the second ionization energy for sodium is given in Table 7.2).
(a) How large would the lattice energy need to be for the formation of NaCl2 to be exothermic?
(b) If we were to estimate the lattice energy of NaCl2 to be roughly equal to that of MgCl2 (2326 kJ / mol from Table 8.2), what value would you obtain for the standard enthalpy of formation, ΔHof, of NaCl2?

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TABLE 8.2Lattice Energies for Some lonic Compounds Lattice Energy Lattice Energy Compound (kJ/mol) LiF LiCl Lil NaF NaCl NaBr Nal KF KCI KBr CsCl CsI Compound (kJ/mol) MgCl2 SrCl2 2326 2127 1030 834 730 910 788 732 682 808 701 671 657 600 MgO CaO SrO 3795 3414 3217 ScN 7547 TABLE 7.2。Successive Values of Ionization Energies, l, for the Elements Sodium through Argon (kJ/mol) Element (inner-shell electrons) 496 738 578 786 101 1000 1251 1521 4562 1451 1817 1577 1907 2252 2298 2666 Mg Al Si 7733 2745 3232 2914 3357 3822 3931 11,577 4356 4964 4556 5159 5771 16,091 6274 7004 6542 7238 21,267 8496 9362 8781 27,107 11,018 11,995 Cl