Write the Lewis structure of each of the following species and indicate which are radicals: (a) the superoxide ion, \(\mathrm{O}_{2}{ }^{-}\); (b) the methoxy group, \(\mathrm{CH}_{3} \mathrm{O}\); (c) \(\mathrm{XeO}_{4}\); (d) \(\mathrm{HXeO}_{4}^{-}\).

Valence electrons are the electrons in the outermost shell of an atom, and they play a crucial role in chemical bonding and the formation of molecules. These electrons determine the atom's chemical properties and how it will react with other atoms to form compounds. For example, in the exercise provided, valence electrons are counted to predict the bonding and structure of different molecules or ions, such as the superoxide ion \(\mathrm{O}_2^{-}\), methoxy group \(\mathrm{CH}_3\mathrm{O}\), xenon tetroxide \(\mathrm{XeO}_4\), and perxenic acid ion \(\mathrm{HXeO}_4^{-}\).

When drawing the Lewis structure, the first step is always to determine the total number of valence electrons available for bonding. Different elements have varying numbers of valence electrons; for instance, oxygen typically has six while carbon has four. By understanding the count of valence electrons, you can identify how the atoms can share or transfer electrons to achieve a full outer shell, following the octet rule or, in the case of transition metals and beyond, expanded octets.

The octet rule is a chemical rule of thumb that reflects the observation that atoms of main-group elements tend to bond in such a way that each atom has eight electrons in its valence shell, giving it the same electronic configuration as a noble gas. The rule is applicable in most of the p-block elements, excluding hydrogen, helium, lithium, and beryllium. For many compounds, achieving an octet of electrons through sharing, gaining, or losing electrons allows for stability.

The Lewis structures in the provided exercises illustrate the octet rule. For example, in the superoxide ion \(\mathrm{O}_2^{-}\), each oxygen atom strives to complete its octet. Similarly, in xenon tetroxide \(\mathrm{XeO}_4\) and perxenic acid ion \(\mathrm{HXeO}_4^{-}\), the central xenon atom and the oxygen atoms all follow the octet rule. The presence of an extra electron or a positive or negative charge can sometimes affect how the octet rule is satisfied, which is why ions are often formed.

Electron pairing refers to the concept that electrons occupy orbitals in pairs with opposite spins. In Lewis structures, unpaired electrons are represented as dots that do not share space with another dot, while paired electrons are shown as two dots together or a line representing a bond between atoms.

In the context of the exercise, identifying whether species are radicals or not depends on electron pairing. Radicals are species with at least one unpaired electron, and they tend to be highly reactive due to this unpaired electron. For the superoxide ion \(\mathrm{O}_2^{-}\), there's an extra valence electron that cannot be paired, making it a radical. In contrast, the methoxy group \(\mathrm{CH}_3\mathrm{O}\), xenon tetroxide \(\mathrm{XeO}_4\), and perxenic acid ion \(\mathrm{HXeO}_4^{-}\) all have paired electrons, adhering to the rule that stable molecules often have all electrons paired up. Understanding electron pairing is not only essential for determining the stability of molecules but also for predicting reactivity and chemical behavior in various chemical reactions.