Write the chemical equation for the ionization of each of the following weak acids in water. (For polyprotic acids, write only the equation for the first step in the ionization.) (a) \(\mathrm{HNO}_{2}\) (c) \(\mathrm{HAsO}_{4}^{2-}\) (b) \(\mathrm{H}_{3} \mathrm{PO}_{4}\) (d) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{NH}^{+}\)

Chemical equations are symbolic representations of chemical reactions. They depict the substances involved in a reaction, known as reactants and products, and show how they transform from one to another. Key features of chemical equations include the reactant(s) on the left side, the product(s) on the right side, and an arrow indicating the direction of the reaction. In the case of ionization of weak acids in water, such as HNO_2 or H_3PO_4, the chemical equation demonstrates the process by which these acids donate a proton (hydrogen ion, H^+) to water, resulting in the formation of a conjugate base and the hydronium ion (H_3O^+). The process is reversible, as indicated by the double-headed arrow, emphasizing the dynamic equilibrium between the weak acid and its conjugate base in solution.

For students, it's essential to balance the chemical equation, ensuring the conservation of mass and charge. Each element must have the same number of atoms on both sides of the equation, and the total charge should also be equal. This helps in understanding the stoichiometry of reactions, which is fundamental for all chemical processes.

Polyprotic acids are acids that can donate more than one proton per molecule. Common examples include H_3PO_4 (phosphoric acid), which can donate three protons. However, in many cases, especially in introductory chemistry, we often focus on the initial step of ionization, which involves the release of the first proton. This is because the first dissociation usually occurs at a significantly higher rate than subsequent ones.

When tackling exercises involving polyprotic acids, it's vital to remember that each step of ionization has its own equilibrium constant, and the strength of the acid decreases with each successive proton donation. As such, the initial ionization step is the most significant and is usually the only one considered in introductory problems. Understanding the sequential nature of ionization in polyprotic acids helps students comprehend the complexity of acid-base chemistry and calculate pH values more accurately in a step-wise fashion.

A conjugate base is formed when an acid loses a proton, revealing an important aspect of the acid-base relationship—the stronger the acid, the weaker its conjugate base. When a weak acid like HNO_2 ionizes in water, the remaining ion, NO_2^−, is the conjugate base. It's worth noting that conjugate bases can often reaccept the proton they lost, especially if they're in the presence of a strong acid. This back-and-forth between acid and base forms the basis of chemical equilibrium in acid-base reactions.

Understanding conjugate bases is crucial for predicting the outcome of reactions, and for understanding buffer systems—solutions that resist changes in pH when acids or bases are added. By recognizing the connection between acids and their conjugate bases, students can better grasp the principles of pH, pKa, and the strength of different acids and bases.

The hydronium ion, H_3O^+, is a water molecule that has accepted an extra proton. This species is much more stable than a bare proton and is the usual form of the positively charged hydrogen ion in aqueous solutions. Whenever acids ionize in water, hydronium ions are formed as one of the products, as seen in the chemical equations for the ionization of weak acids.

The concentration of hydronium ions in a solution is directly related to the solution's acidity and is used to calculate the pH. A higher concentration of hydronium ions corresponds to a lower pH and thus a more acidic solution. Recognizing the role of hydronium ions is essential for students learning about acidity, pH calculations, and the behavior of acids and bases in water.