Consider the following energy changes: $$\begin{array}{ll} \text {} & \quad { \Delta H} \\ \text {} & {(k J / m o l)} \\ \hline \\ {\mathrm{Mg}(g) \rightarrow \mathrm{Mg}^{+}(g)+\mathrm{e}^{-}} & {735} \\ {\mathrm{Mg}^{+}(g) \rightarrow \mathrm{Mg}^{2+}(g)+\mathrm{e}^{-}} & {1445} \\ {\mathrm{O}(g)+\mathrm{e}^{-} \rightarrow \mathrm{O}^{-}(g)} & {-141} \\ {\mathrm{O}^{-}(g)+\mathrm{e}^{-} \rightarrow 0^{2-}(g)} & {878}\end{array}$$ Magnesium oxide exists as \(\mathrm{Mg}^{2+} \mathrm{O}^{2-}\) and not as \(\mathrm{Mg}^{+} \mathrm{O}^{-}\) Explain.

First, analyze the two given energy changes required to create \(\mathrm{Mg}^{2+}\) and \(\mathrm{O}^{2-}\) ions. For \(\mathrm{Mg}^{2+}\) 1. \(\mathrm{Mg}(g) \rightarrow \mathrm{Mg}^{+}(g) + \mathrm{e}^-\) , \(\Delta H = 735 kJ/mol\) 2. \(\mathrm{Mg}^{+}(g) \rightarrow \mathrm{Mg}^{2+}(g) + \mathrm{e}^-\) , \(\Delta H = 1445 kJ/mol\) For \(\mathrm{O}^{2-}\) 3. \(\mathrm{O}(g) + \mathrm{e}^- \rightarrow \mathrm{O}^{-}(g)\) , \(\Delta H = -141 kJ/mol\) 4. \(\mathrm{O}^{-}(g) + \mathrm{e}^- \rightarrow \mathrm{O}^{2-}(g)\) , \(\Delta H = 878 kJ/mol\)

Now, calculate the total energy changes required to create the \(\mathrm{Mg}^{2+} \mathrm{O}^{2-}\) ion pair from the gaseous elements: $$\Delta H_{\mathrm{Mg}^{2+} \mathrm{O}^{2-}} = \Delta H_1 + \Delta H_2 + \Delta H_3 + \Delta H_4 = 735 + 1445 - 141 + 878 = 2917 kJ/mol$$

Analyze the energy changes required to create \(\mathrm{Mg}^{+}\) and \(\mathrm{O}^{-}\) ions. For \(\mathrm{Mg}^{+}\) 1. \(\mathrm{Mg}(g) \rightarrow \mathrm{Mg}^{+}(g) + \mathrm{e}^-\) , \(\Delta H = 735 kJ/mol\) For \(\mathrm{O}^{-}\) 3. \(\mathrm{O}(g) + \mathrm{e}^- \rightarrow \mathrm{O}^{-}(g)\) , \(\Delta H = -141 kJ/mol\)

Now, calculate the total energy changes required to create the \(\mathrm{Mg}^{+} \mathrm{O}^{-}\) ion pair from the gaseous elements: $$\Delta H_{\mathrm{Mg}^{+} \mathrm{O}^{-}} = \Delta H_1 + \Delta H_3 = 735 - 141 = 594 kJ/mol$$

Magnesium oxide in the form of \(\mathrm{Mg}^{2+} \mathrm{O}^{2-}\) has a total energy change of \(2917 kJ/mol\), while the formation of \(\mathrm{Mg}^{+} \mathrm{O}^{-}\) has a total energy change of \(594 kJ/mol\). Since both cases involve positive energy changes, neither species is energetically preferred over the constituent atoms. However, as ΔH(Mg2+O2-) > ΔH(Mg+O-), the formation of the latter species requires less energy and is somewhat more energetically favored compared to the former. Keep in mind that these results are based solely on the given energy changes and do not account for any other factors that may influence the overall stability of these species in real systems. In conclusion, although \(\mathrm{Mg}^{2+} \mathrm{O}^{2-}\) is not energetically preferred over the constituent atoms, its formation is more energetically favorable compared to \(\mathrm{Mg}^{+} \mathrm{O}^{-}\). Therefore, magnesium oxide exists as \(\mathrm{Mg}^{2+} \mathrm{O}^{2-}\) rather than \(\mathrm{Mg}^{+} \mathrm{O}^{-}\) based on the given energy changes.