Both \(\mathrm{HCO}_{3}^{-}\) and \(\mathrm{HS}^{-}\) are amphoteric. Write an equation to show how each substance can act as an acid, and another equation to show how each can act as a base.

Understanding acid-base reactions is crucial for mastering chemistry. Simply put, these reactions involve the transfer of protons (H+) between substances. When a substance acts as an acid, it donates a proton to another substance, transforming into its conjugate base. Conversely, when the substance behaves as a base, it accepts a proton, resulting in its conjugate acid.

Let's consider \(\text{HCO}_3^-\) (bicarbonate) and \(\text{HS}^-\) (hydrogen sulfide ion) as examples of amphoteric substances. The bicarbonate ion can donate a proton to become carbonate (\(\text{CO}_3^{2-}\)), representing its acid behaviour. Similarly, hydrogen sulfide ion can donate a proton and transform into sulfide (\(\text{S}^{2-}\)). When these substances accept a proton, bicarbonate turns into carbonic acid (\(\text{H}_2\text{CO}_3\)), and hydrogen sulfide ion becomes hydrogen sulfide (\(\text{H}_2\text{S}\)), showcasing their basic properties.

Equations illustrating such transformations help in understanding how substances can interchangeably act as acids or bases, depending on the reaction context. This dynamic ability is a key concept in acid-base chemistry and is critical when analyzing chemical reactions in biological, environmental, and industrial processes.

The concept of proton transfer is at the heart of understanding amphoteric substances and their roles in acid-base reactions. Proton transfer is the process by which a proton, the nucleus of a hydrogen atom (which is simply a hydrogen ion, \(\text{H}^+\)), is passed from one species to another.

In the equations previously mentioned, the amphoteric substances \(\text{HCO}_3^-\) and \(\text{HS}^-\) either release or gain a proton. For instance, in the reaction \(\text{HCO}_3^-\) plus \(\text{H}^+\) forming \(\text{H}_2\text{CO}_3\), bicarbonate \(\text{HCO}_3^-\) accepts a proton and is thus acting as a base. Proton transfer is a symmetric process, meaning that for every proton donor (acid), there must be a proton acceptor (base), and this balance is what drives acid-base reactions forward.

Delving deeper, the strength of an acid or base is determined by its propensity to lose or gain a proton. Strong acids readily donate protons, while strong bases are eager to accept them. Amphoteric substances like \(\text{HCO}_3^-\) and \(\text{HS}^-\) demonstrate that some chemicals can fluctuate between these tendencies, adeptly fitting into the role the reaction conditions require.

Chemical equilibrium is a state in acid-base reactions where the rates of the forward reaction (acid donating a proton) and the reverse reaction (base accepting a proton) are equal, resulting in no net change in the concentration of reactants and products over time. It is a dynamic balance, not a static one, as molecules continue to react, but their overall quantities remain constant.

In the context of amphoteric substances like \(\text{HCO}_3^-\) and \(\text{HS}^-\), equilibrium plays a vital role. When \(\text{HCO}_3^-\) acts as a base by accepting a proton to form \(\text{H}_2\text{CO}_3\), this reaction is reversible, as is its acid reaction forming \(\text{CO}_3^{2-}\). The same applies to \(\text{HS}^-\) when it acts as an acid or a base. The balance between these reversible reactions determines the pH of the solution and influences various biological and chemical processes.

Understanding how to manipulate conditions to favor the formation of products or reactants is essential in controlling chemical reactions. This knowledge is pivotal in industries such as pharmaceuticals and agriculture, where specific reaction outcomes are desired. The study of equilibrium teaches us how changes in concentration, temperature, and pressure can shift the balance, providing an invaluable tool for chemists and engineers.