Problem 77 - Chemistry and Chemical Reactivity

Question

A What arguments would you use to convince another student in general chemistry that \(\mathrm{MgO}\) consists of the ions \(\mathrm{Mg}^{2+}\) and \(\mathrm{O}^{2-}\) and not the ions \(\mathrm{Mg}^{+}\) and \(\mathrm{O}^{-2}\). What experiments could be done to provide some evidence that the correct formulation of magnesium oxide is \(\mathrm{Mg}^{2+} \mathrm{O}^{2-} ?\)

Step-by-Step Solution

Answer

MgO consists of \(\mathrm{Mg}^{2+}\) and \(\mathrm{O}^{2-}\) ions due to stable electronic configurations; experiments like lattice energy and electron transfer verify this.

Step 1: Understandion of Magnesium's Electronic Configuration

The electronic configuration of magnesium (Mg) is \([Ne] 3s^2\). Magnesium is in group 2 of the periodic table, which means it readily loses its two valence electrons to achieve a full orbital, resulting in a \(\mathrm{Mg}^{2+}\) ion. This is because losing two electrons offers a stable noble gas configuration of \(\mathrm{Ne}\).

Step 2: Identify Oxygen's Tendency to Gain Electrons

Oxygen has the electronic configuration of \([He] 2s^2 2p^4\). Being in group 16, oxygen needs 2 more electrons to achieve a filled p orbital, resulting in a stable \(\mathrm{O}^{2-}\) ion. This allows oxygen to achieve the stable electronic configuration of \(\mathrm{Ne}\).

Step 3: Explain Why Other Ionic Forms Are Unlikely

\(\mathrm{Mg}^{+}\) and \(\mathrm{O}^{-}\) are unlikely forms because the energy costs associated with having an unpaired electron configuration are high and do not favor stability. Such a formation lacks the stability gained by both elements achieving a noble gas configuration (\(\mathrm{Ne}\)).

Step 4: Experiment Evidence through Lattice Energy Measurement

Measuring the lattice energy of \(\mathrm{MgO}\) can provide experimental evidence. Lattice energy is highest when both ions achieve the most stable configurations (\(\mathrm{Mg}^{2+}\) and \(\mathrm{O}^{2-}\)). Additionally, corroborating with standard formation enthalpies from tables can support this ionic configuration.

Step 5: Conduct an Electron Transfer Experiment

Using electrochemical methods, observe the electron exchange in \(\mathrm{Mg}\) and \(\mathrm{O}\). An experiment that allows Mg to oxidize fully to \(\mathrm{Mg}^{2+}\) and O to reduce to \(\mathrm{O}^{2-}\) confirms the full electron transfer corroborating the ionic structure \(\mathrm{Mg}^{2+} \mathrm{O}^{2-}\).

Key Concepts

Ionic Compounds

Ionic compounds like magnesium oxide (\(\text{MgO}\)) are formed by the transfer of electrons between atoms, creating ions. In ionic substances, metals like magnesium (Mg) lose electrons, while nonmetals like oxygen (O) gain them. This exchange leads to the formation of positive ions (cations) and negative ions (anions).
This electron transfer generates a strong electrostatic force that holds the ions together in a crystal lattice, giving ionic compounds their characteristic high melting and boiling points.
In the case of \(\text{MgO}\), magnesium donates two electrons to oxygen, forming \(\text{Mg}^{2+}\) and \(\text{O}^{2-}\) ions. This exchange results in both ions achieving a full octet, or noble gas electron configuration, which is extremely stable.

• This explains the preference for \(\text{Mg}^{2+}\) and \(\text{O}^{2-}\) rather than other charges.
• The resulting compound is typically hard, brittle, and conducts electricity well when melted or dissolved in water.

Electron Configuration

Electron configuration is crucial for understanding the reactivity and stability of elements in ionic compounds. This configuration represents the distribution of electrons in an atom's orbitals and helps predict how the element will interact with others.
Magnesium has an electron configuration of \([Ne] 3s^2\), indicating it has two valence electrons in the 3s orbital. Upon losing these electrons, magnesium achieves the stable electron configuration of neon (Ne).
Oxygen, with a configuration of \([He] 2s^2 2p^4\), needs two more electrons to fill its 2p orbital, achieving the stable configuration of neon. When oxygen gains two electrons, it becomes \(\text{O}^{2-}\), a stable ion.

• Achieving a noble gas configuration (complete outer shell) greatly lowers an atom's energy, leading to higher stability.
• Stable configurations like these explain why \(\text{Mg}^{2+}\) and \(\text{O}^{2-}\) are energetically favored.

Lattice Energy

Lattice energy is the energy released when one mole of an ionic crystalline solid forms from its gaseous ions. It serves as a quantitative measure of the strength of the bonds in an ionic compound. Higher lattice energies indicate stronger ionic bonds and greater stability of the compound.
For \(\text{MgO}\), the lattice energy is quite high due to the formation of \(\text{Mg}^{2+}\) and \(\text{O}^{2-}\) ions, which have higher charges. This results in a stronger electrostatic attraction between the ions.

• The magnitude of lattice energy depends on the charge and size of the ions. Larger charges and smaller radii result in larger lattice energies.
• Experimentally, lattice energy can be determined via the Born-Haber cycle or estimated using Coulomb's law.

Measuring \(\text{MgO}\)'s lattice energy and comparing it with theoretical values can indirectly confirm the formation of \(\text{Mg}^{2+}\) and \(\text{O}^{2-}\) ions as it aligns with predicted high lattice energy values.

Electrochemistry

Electrochemistry involves the study of chemical processes that cause electrons to move, a direct link to the reactions in forming ionic compounds. It's key in understanding how electrons are transferred between magnesium and oxygen.
In the context of \(\text{MgO}\), electrochemical experiments can show electron transfer, confirming the presence of \(\text{Mg}^{2+}\) and \(\text{O}^{2-}\). By observing a redox reaction where magnesium is oxidized (loses electrons) and oxygen is reduced (gains electrons), the process of forming \(\text{MgO}\) is exemplified.
An experiment might involve submerging these elements in an electrochemical cell and measuring the flow of electrons. This setup validates the full electron transfer consistent with the oxidation states of \(\text{Mg}^{2+}\) and \(\text{O}^{2-}\).

• Applying electrochemistry provides practical evidence for ion formation, supporting theoretical assumptions.
• Through these experiments, the principles of ionic bonding and lattice energy are also demonstrated.