Chapter 6, Problem 6.94SP

We saw in Section 6.7 that the reaction of solid sodium with giseous chlorine to yield solid sodium chloride $\left({\text{Na}}^{+}{\text{CI}}^{-}\right)$ is favorable by 411 kJ/mol. Calculate the energy change for the alternative reaction that yields chlorine sodide $\left({\text{Cl}}^{+}{\text{Na}}^{-}\right)$ , and then explain why sodium chloride formation is preferred.
$\text{2Na}\left(s\right)+{\text{Cl}}_{\text{2}}\left(g\right)\to {\text{2Cl}}^{+}{\text{Na}}^{-}\left(s\right)$
Assume that the lattice energy for ${\text{Cl}}^{+}{\text{Na}}^{-}$ is the same as that for ${\text{Na}}^{+}{\text{Cl}}^{-}$ . The following data are needed in addition to that found in Section 6.7:
$\begin{array}{l}{E}_{\text{ea}}\text{for Na}\left(g\right)=-\text{52}\text{.9 kJ/mol}\\ E_{\text{i1}}\text{for Cl}\left(g\right)=+1251\text{ kJ/mol}\end{array}$