Write balanced equations that describe the following reactions. a. the dissociation of perchloric acid in water b. the dissociation of propanoic acid \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CO}_{2} \mathrm{H}\right)\) in water c. the dissociation of ammonium ion in water

Understanding the balance in chemical equations is crucial for studying reactions such as the dissociation of acids and bases in water. Chemical equations must be balanced to obey the Law of Conservation of Mass, which states that matter cannot be created or destroyed in a chemical reaction. To balance a chemical equation, one must ensure that the number of atoms of each element on the reactant side is equal to the number on the product side.

For instance, when writing the balanced equation for perchloric acid dissociating in water, the equation HClO4(aq) + H2O(l) -> H3O+(aq) + ClO4-(aq) already adheres to the balance requirement since there is one chlorine atom, four oxygen atoms, and two hydrogen atoms on both sides of the equation. Similarly, for propanoic acid and ammonium ion, the equations must also reflect a balance of atoms. This practice ensures the chemical reaction is represented accurately and forms the basis for quantitative analysis in chemistry.

When it comes to the dissociation of weak acids in water, like propanoic acid (CH3CH2CO2H), understanding weak acid behavior is key. Unlike strong acids which dissociate completely in solution, weak acids only partially dissociate into their ions. As a result, an equilibrium is established between the undissociated acid and the ions produced.

The general dissociation of propanoic acid in water is represented as:CH3CH2CO2H(aq) + H2O(l) -> H3O+(aq) + CH3CH2CO2-(aq)This equation highlights the formation of hydronium ions (H3O+) and propanoate ions (CH3CH2CO2-). Since propanoic acid is a weak acid, not all molecules will donate a hydrogen ion to the water, which is why the reaction is set up as a reversible process in equilibrium calculations, typically represented with a double arrow rather than a single arrow used in the exercise.

The behavior of the ammonium ion (NH4+) in water is another important topic in the study of acid-base reactions. When ammonium ions are dissolved in water, they react with water to form ammonia (NH3) and hydronium ions (H3O+). The equation:NH4+(aq) + H2O(l) -> NH3(aq) + H3O+(aq)expresses this reaction. Unlike the dissociation of a weak acid, this reaction involves the ammonium ion which acts as an acid, donating a hydrogen ion to the water molecule.

This process is part of the Bronsted-Lowry acid-base theory, where an acid is defined as a substance that donates a proton (hydrogen ion) and a base is a substance that accepts a proton. The reaction of the ammonium ion with water is a classic example of an acid reacting with a base to create the conjugate base (NH3) and the conjugate acid (H3O+).