Provide the balanced reaction that occurs when \(\mathrm{HNO}_{3}\) is dissolved in water and provide the \(K_{\mathrm{a}}\) expression for \(\mathrm{HNO}_{3}\).

When discussing chemical reactions, it's essential to grasp the concept of chemical equilibrium. Equilibrium in a chemical process is the state where the rates of the forward and reverse reactions are equal, leading to no net change in the concentration of reactants and products over time.

This dynamism is not indicative of a static system, but rather one where reactions occur continuously, yet balance each other out. The law of mass action governs this equilibrium, dictating that at a constant temperature, a certain ratio of the product of concentrations of reactants and products, each raised to the power of their respective coefficients in the balanced equation, is sustained.

The equilibrium expression is typically represented as a capital K with subscripts to denote different types of equilibria, such as Kc for concentration, Kp for partial pressure, and Ka for the acid ionization constant. In the particular case of Ka, it measures the strength of an acid in a solution, reflecting the level of ionization into its constituent ions.

Strong acids are distinguished by their ability to completely ionize in solution. This full ionization means that when a strong acid like nitric acid (\(HNO_3\)) is dissolved in water, it donates all its available protons (\(H^+\) ions) to the water molecules, thereby forming hydronium ions (\(H_3O^+\) ions) and leaving behind the corresponding anions—in this case, nitrate ions (\(NO_3^-\)).

The property of complete ionization makes strong acids unique, as it renders their dissociation in water a one-way street. Unlike weak acids that establish an equilibrium where both the acid and its ions are present in significant amounts, for strong acids, almost no original acid molecules remain after the reaction with water. This characteristic is evidenced in their very high Ka values, which signifies a heavily favored forward reaction and typically leads to the omission of strong acids in the equilibrium expression, as they are virtually non-existent in their non-ionized form in the solution.

The dissolution of nitric acid (\(HNO_3\)) in water exemplifies the behavior of strong acids. When mixed with water, nitric acid undergoes a single direction reaction where it releases a proton, which is captured by a water molecule to form the hydronium ion (\(H_3O^+\)), simultaneously forming a nitrate ion (\(NO_3^-\)). This reaction can be depicted by the balanced chemical equation: \[HNO_3 + H_2O \rightarrow H_3O^+ + NO_3^-\]

As nitric acid fully ionizes, its dissolution leans entirely towards the production of hydronium and nitrate ions, with no significant reverse reaction to regenerate nitric acid. Due to this complete ionization, the necessity to write a Ka expression for nitric acid doesn't typically arise. While theoretically, one could write out a Ka expression as in the step-by-step solution, the practice is not common because the concentration of the non-ionized form in the solution is negligibly small—approaching zero. As a result, the ratio for the Ka would approach infinity, further underscoring the asset of nitric acid as a strong acid.