Write the Born-Haber cycle for the formation of crystalline sodium fluoride
\(\left(\mathrm{Na}^{+} \mathrm{F}^{-}\right)\), starting with solid
\(\mathrm{Na}\) and gaseous
F. Then, using the thermochemical data supplied below, determine its heat of
formation:
(1) \(\mathrm{Na}(\mathrm{s}) \quad \rightarrow \mathrm{Na}(\mathrm{g}) \quad
\Delta \mathrm{H}=+26.0 \mathrm{Kcal}:\) sublimation
(2) \(\mathrm{F}_{2}(\mathrm{~g}) \quad \rightarrow 2 \mathrm{~F}(\mathrm{~g})\)
\(\Delta \mathrm{H}=+36.6 \mathrm{~K}\) cal : dissociation
(3) \(\mathrm{Na}(\mathrm{g}) \rightarrow
\mathrm{Na}^{+}(\mathrm{g})+\mathrm{e}^{-} \quad \Delta \mathrm{H}=+120.0
\mathrm{~K}\) cal : ionization
(4) \(\mathrm{F}(\mathrm{g})+\mathrm{e}^{-} \rightarrow
\mathrm{F}^{-}(\mathrm{g})\)
\(\Delta \mathrm{H}=-83.5 \mathrm{Kcal}:\) electron
addition
(5) \(\mathrm{Na}^{+}(\mathrm{g})+\mathrm{F}^{-}(\mathrm{g}) \rightarrow
\mathrm{Na}^{+}, \mathrm{F}^{-}(\mathrm{s}) \Delta \mathrm{H}=-216.7
\mathrm{Kcal}\) : lattice
formation.