(a) Use orbital diagrams to illustrate what happens when an oxygen atom gains two electrons. (b) Why does \(\mathrm{O}^{3-}\) not exist?

Understanding the electronic configuration of an atom is critical for grasping many fundamental concepts in chemistry. Simply put, the electronic configuration is the arrangement of electrons around the nucleus of an atom in its atomic orbitals. For oxygen, with an atomic number of 8, the configuration is noted as 1s² 2s² 2p⁴. This indicates that the first energy level, or shell, contains two electrons in the 1s orbital, and the second shell has two electrons in the 2s orbital and four electrons in the 2p orbitals.

When we represent this using orbital diagrams, we show the orbitals as boxes or lines and the electrons as arrows, indicating the spin of each electron. The principle of minimizing electron repulsion ensures that electrons will fill an empty or half-filled orbital before pairing up. In oxygen's case, the 2p orbital will have unpaired electrons indicated as: ↑ | ↑ | ↑ in the orbital diagram for the atom.

A solid understanding of electronic configuration lays the groundwork for studying chemical reactions, bonding, and more, as the way electrons are arranged determines how atoms interact with one another.

The formation of ions is a common and important process in chemistry. An ion is an atom or molecule that has gained or lost one or more electrons, thereby acquiring a net electric charge. In the case of oxygen, an oxygen ion commonly forms when the atom gains two electrons, resulting in a negative two charge, written as O²⁻. This process can be visualized in an orbital diagram where the extra electrons fill the empty spaces in the oxygen's 2p orbitals, aligning with the goals of achieving lower energy and greater stability.

The orbital diagram after oxygen gains two electrons will show all the 2p orbitals filled: 2p: ↑↓ | ↑↓ | ↑↓. This fuller electronic configuration illustrates how the oxygen atom has achieved a stable, more energetically favorable state. It's essential to appreciate this transition from oxygen atom to oxygen ion as it underlines the atom's drive towards stability through electron gain or loss.

The octet rule is a chemical principle that reflects the tendency of atoms to prefer to have eight electrons in their valence shell, the outermost electron shell in an atom. This rule is based on the observation that atoms with eight electrons in their valence shell tend to be more stable, resembling the electronic structure of noble gases.

For oxygen, which has six valence electrons, following the octet rule means that gaining two additional electrons to fill its 2p orbitals results in the desirable, stable arrangement of eight valence electrons. This is the driving force behind the oxygen atom's tendency to form the O²⁻ ion. The completion of the octet through the gain of electrons is a recurrent theme in chemical bonding and is at the heart of many ionic and covalent bonding interactions.

Electron repulsion is a principle coming from Coulomb's law, stating that like charges repel each other. In the context of an atom's orbitals, this translates to the behavior that electrons, all negatively charged, will repel one another and seek to minimize this repulsion by occupying different spaces if available.

In oxygen's 2p orbitals, each electron will initially occupy an empty orbital to minimize repulsion: the first three electrons fill as ↑ in each 2p orbital. When oxygen becomes an ion by gaining two additional electrons, to minimize repulsion, these electrons pair up with the existing unpaired electrons, resulting in a fully occupied 2p sublevel with paired spins: ↑↓ | ↑↓ | ↑↓.

Conversely, an oxygen ion with a -3 charge, purportedly O³⁻, would violate the minimized repulsion principle. The extra third electron would have to unnecessarily pair up in a higher energy 3s orbital or contribute to increased repulsion in the filled 2p orbitals, making the O³⁻ ion highly unstable and energetically unfavorable, hence it does not commonly exist.