Question

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

Short answer

Magnesium oxide forms as ${\mathrm{Mg}}^{2+}{\mathrm{O}}^{2-}$ rather than ${\mathrm{Mg}}^{+}{\mathrm{O}}^{-}$ because both ions achieve greater stability by adopting noble gas configurations as required by the octet rule. In doing so, Magnesium loses two electrons to form ${\mathrm{Mg}}^{2+}$, and Oxygen gains two electrons to form ${\mathrm{O}}^{2-}$.

Step-by-step solution

Recall the electron configurations of Magnesium and Oxygen atoms

Start by recalling the electron configurations of Magnesium (Mg) and Oxygen (O). Magnesium has an atomic number of 12 and an electron configuration of $$1s^{2}2s^{2}2p^{6}3s^2.$$ Oxygen has an atomic number of 8 and an electron configuration of $$1s^{2}2s^{2}2p^4.$$

Consider the ionization energies of Magnesium and Oxygen atoms

Ionization energy is the energy required to remove an electron from an atom or ion. Magnesium has two ionization energies, as it can lose one or two electrons from its outermost shell. - The first ionization energy of Magnesium corresponds to the energy required to remove the first 3s electron, forming ${\mathrm{Mg}}^{+}$. - The second ionization energy of Magnesium corresponds to the energy required to remove the second 3s electron, forming ${\mathrm{Mg}}^{2+}$. Since Oxygen needs to gain electrons to attain a stable configuration, it has electron affinity. - Oxygen can gain one electron to form ${\mathrm{O}}^{-}$ or two electrons to form ${\mathrm{O}}^{2-}$.

Recall the octet rule

The octet rule states that atoms tend to gain, lose, or share electrons to have a full outer shell containing eight electrons. - When Magnesium loses two electrons to form ${\mathrm{Mg}}^{2+}$, it attains a stable noble gas configuration: $1s^{2}2s^{2}2p^6$ - When Oxygen gains two electrons to form ${\mathrm{O}}^{2-}$, it also attains a stable noble gas configuration: $1s^{2}2s^{2}2p^6$

Analyze the stability of ions

Comparing the stability of ions formed in the different cases: - Forming ${\mathrm{Mg}}^{2+}$ and ${\mathrm{O}}^{2-}$ leads both ions to have a stable noble gas configuration, which is highly stable and tends to occur in nature. - Forming ${\mathrm{Mg}}^{+}$ and ${\mathrm{O}}^{-}$, on the other hand, would result in incomplete electron configurations and would make both ions less stable.

Conclude

As a result of this analysis, we can conclude that Magnesium oxide forms as ${\mathrm{Mg}}^{2+}{\mathrm{O}}^{2-}$ rather than ${\mathrm{Mg}}^{+}{\mathrm{O}}^{-}$ due to the greater stability achieved by both ions when they adopt noble gas configurations by losing or gaining electrons as required by the octet rule.

Key concepts

Electron Configuration

Electron configuration represents how electrons are arranged within an atom. Each element has a unique electron configuration which determines its chemical properties. For magnesium, with an atomic number of 12, the electron configuration is $1s^{2}2s^{2}2p^{6}3s^2$. This tells us that magnesium has two electrons in its outermost shell. Oxygen, with an atomic number of 8, has the electron configuration $1s^{2}2s^{2}2p^4$. Oxygen is two electrons short of completing its outer shell.

• Electrons fill the lowest energy levels first, from the 1s orbital outwards.
• Atoms seek to stabilize by having a full outer shell, often resembling the nearest noble gas.

Knowing the electron configuration helps predict how elements will interact. Magnesium, with two 3s electrons, is ready to lose them for stability. Oxygen, needing electrons, readily accepts to complete its outer shell.

Ionization Energy

Ionization energy is critical in understanding how and why elements form ions. This is the energy required to remove an electron from an atom. For magnesium to become ${\mathrm{Mg}}^{2+}$, two electrons are removed, each requiring specific ionization energy. The first ionization removes the first 3s electron, while the second ionization removes the second 3s electron.

• The first ionization energy is usually less than the second, as removing the first electron increases the effective nuclear charge.
• Higher energy is generally required for each successive electron removal because the remaining electrons are held more tightly by the positive nucleus.

Oxygen, however, doesn't lose electrons. Instead, it gains electrons, described by electron affinity—the energy change when an atom gains an electron. Thus, fewer ionizations mean lower energy requirements for magnesium losing two electrons than if oxygen were to increase its negative charge beyond its stable form as ${\mathrm{O}}^{2-}$.

Octet Rule

The octet rule is a guiding principle for understanding chemical bonding and reactions. It states that atoms are usually more stable when their outer shell contains eight electrons, similar to a noble gas configuration. Magnesium, when forming ${\mathrm{Mg}}^{2+}$, loses its two outermost electrons to achieve $1s^{2}2s^{2}2p^6$, matching the electron configuration of neon. Oxygen gains electrons to form ${\mathrm{O}}^{2-}$, achieving $1s^{2}2s^{2}2p^6$ as well.

• The octet rule explains why ${\mathrm{Mg}}^{2+}$ and ${\mathrm{O}}^{2-}$ ions are stable.
• Noble gases naturally have full outer shells, contributing to their lack of reactivity.

This tendency of atoms to reach a stable, full electron shell configuration drives the formation of stable ionic compounds. By following the octet rule, elements achieve lower energy states, resulting in more stable compounds such as magnesium oxide, ${\mathrm{Mg}}^{2+}{\mathrm{O}}^{2-}$, instead of a less stable ${\mathrm{Mg}}^{+}$ with ${\mathrm{O}}^{-}$.