State which of the following species are amphiprotic and write chemical equations illustrating the amphiprotic character of these species: (a) \(\mathrm{H}_{2} \mathrm{O}\) (b) \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) (c) \(\mathrm{S}^{2-}\) (d) \(\mathrm{CO}_{3}^{2-}\) (e) \(\mathrm{HSO}_{4}^{-}\)

When we talk about proton donors and proton acceptors, we're delving into the behaviors of acids and bases within a chemical setting. A proton donor, simply put, is a substance that releases hydrogen ions (\textbf{H}^+), while a proton acceptor is a substance that receives them. This exchange is fundamental to many chemical reactions, especially those in aqueous solutions.

To classify as an amphiprotic species, a substance must have the ability to play both roles; it must contain at least one hydrogen atom to lose and also the potential to accept a proton. For instance, water (\textbf{H}\(_2\)\textbf{O}) exemplifies an amphiprotic substance perfectly. It can donate a proton to become hydroxide (\textbf{OH}^-), and it can also accept a proton to form hydronium (\textbf{H}\(_3\)\textbf{O}^+).

The language of chemical equations is critical for depicting the transformations occurring in a chemical reaction. Consider them as the mathematical sentences describing the exchange of electrons, protons, and various ions. To properly convey an amphiprotic species' behavior, it's essential to scribe two separate equations; one where it acts as an acid (donor) and another where it operates as a base (acceptor). Taking \textbf{H}\(_2\)\textbf{PO}\(_4\)^- as an example, the equation showing its acidic nature combines it with water to form \textbf{HPO}\(_4\)^{2-} and hydronium, while its basic side illustrates the gain of a proton to become \textbf{H}\(_3\)\textbf{PO}\(_4\). This dual representation captures the amphiprotic essence of a molecule, demonstrating its versatility in chemical reactions.

The concepts of acids and bases are central to understanding amphiprotic substances. In essence, an acid is defined as a compound that can donate a proton, whilst a base is one that can accept a proton. This is based on the Brønsted-Lowry theory of acids and bases, which focuses on the transfer of protons. A good example is the hydrogen sulfate ion (\textbf{HSO}\(_4\)^-), which can give up a hydrogen ion to become sulfate (\textbf{SO}\(_4\)^{2-}), acting as an acid. Conversely, it can also accept a hydrogen ion to form sulfuric acid (\textbf{H}\(_2\)\textbf{SO}\(_4\)), operating as a base. Understanding this bidirectional capability is crucial in grasping the role of amphiprotic substances in balancing chemical reactions and maintaining equilibrium in various systems, from biological to industrial processes.