Consider the following energy changes: Magnesium oxide exists as \(\mathrm{Mg}^{2+} \mathrm{O}^{2-}\) and not as \(\mathrm{Mg}^{+} \mathrm{O}^{-}\). Explain.

To understand the ionic states, let's first find the electron configurations of magnesium (Mg) and oxygen (O) in their elemental forms. The atomic number of magnesium is 12, so the electron configuration is \(1s^{2}2s^{2}2p^{6}3s^{2}\). The atomic number of oxygen is 8, so the electron configuration is \(1s^{2}2s^{2}2p^{4}\).

When analyzing the electron configurations, note that atoms tend to reach a stable state by obtaining a full valence shell, which is the same configuration as the nearest noble gas. For magnesium and oxygen, the nearest noble gases are neon (Ne) and argon (Ar). For magnesium: - Losing 2 electrons will give Magnesium the electron configuration of neon: \(1s^{2}2s^{2}2p^{6}\). It will form a stable magnesium ion with a \(+2\) charge: \(\mathrm{Mg}^{2+}\). - Losing 1 electron will not lead to a stable electron configuration similar to that of a noble gas. A \(\mathrm{Mg}^{+}\) ion will still have one unpaired electron in the 3s orbital. For oxygen: - Gaining 2 electrons will give Oxygen the electron configuration of neon: \(1s^{2}2s^{2}2p^{6}\). It will form a stable oxide ion with a \(-2\) charge: \(\mathrm{O}^{2-}\). - Gaining 1 electron will not lead to a stable electron configuration similar to that of a noble gas. An \(\mathrm{O}^{-}\) ion will have one unpaired electron in the 2p orbital.

Since atoms tend to achieve a stable electron configuration similar to that of the nearest noble gas, the most favorable combination for magnesium oxide will be the one with fully filled valence shells. In our case, combining magnesium and oxygen ions with charges \(\mathrm{Mg}^{2+}\) and \(\mathrm{O}^{2-}\) will result in stable ions: \[\mathrm{Mg}^{2+}+\mathrm{O}^{2-} \rightarrow \mathrm{MgO}\] On the other hand, combining \(\mathrm{Mg}^{+}\) and \(\mathrm{O}^{-}\) would not allow magnesium and oxygen to achieve a stable configuration, resulting in an unstable compound. Therefore, magnesium oxide exists as \(\mathrm{Mg}^{2+} \mathrm{O}^{2-}\), which allows the ions to have a complete octet and achieve stability.