Explain the crystal structure of sodium chloride $(NaCl)$.

(N/A) The crystal structure of $NaCl$ consists of a face-centered cubic $(fcc)$ lattice where $Cl^{-}$ ions occupy the corners and face centers,while $Na^{+}$ ions occupy the octahedral voids (edge centers and body center). The formation of $NaCl$ from its gaseous ions is described by the Born-Haber cycle:
$(i)$ Ionization enthalpy $(\Delta_{i} H)$ :
$Na_{(g)} \rightarrow Na_{(g)}^{+} + e^{-} \ldots \Delta_{i} H = 495.8 \ kJ \ mol^{-1}$
$(ii)$ Electron gain enthalpy $(\Delta_{eg} H)$ :
$Cl_{(g)} + e^{-} \rightarrow Cl_{(g)}^{-} \ldots \Delta_{eg} H = -348.7 \ kJ \ mol^{-1}$
Sum of $(i) + (ii) = 147.1 \ kJ \ mol^{-1}$ (Endothermic step).
$(iii)$ Lattice enthalpy $(\Delta_{L} H)$ :
$Na_{(g)}^{+} + Cl_{(g)}^{-} \rightarrow NaCl_{(s)} \ldots \Delta_{L} H = -788 \ kJ \ mol^{-1}$
Total enthalpy change $= (i) + (ii) + (iii) = -640.9 \ kJ \ mol^{-1}$.
Since the total enthalpy change is negative,the formation of $NaCl$ is an exothermic process,and the crystal lattice is stable.