Write a neutralization reaction for each acid and base pair. (a) \(\mathrm{HF}(a q)\) and \(\mathrm{Ba}(\mathrm{OH})_{2}(a q)\) (b) \(\mathrm{HClO}_{4}(a q)\) and \(\mathrm{NaOH}(a q)\) (c) \(\mathrm{HBr}(a q)\) and \(\mathrm{Ca}(\mathrm{OH})_{2}(a q)\) (d) \(\mathrm{HCl}(a q)\) and \(\mathrm{KOH}(a q)\)

A chemical equation represents the overall change that occurs during a chemical reaction. It shows the reactants, substances that start a chemical reaction, and the products, the substances formed as a result of the reaction, using their chemical formulas. In a properly written chemical equation, the number of atoms for each element is the same on both the reactant and product sides, conforming to the law of conservation of mass.

For example, when hydrofluoric acid (\textbf{HF}) reacts with barium hydroxide (\textbf{Ba(OH)2}), they form barium fluoride (\textbf{BaF2}) and water (\textbf{H2O}). The chemical equation for this reaction is:\[2\textbf{HF}(aq) + \textbf{Ba(OH)}_2(aq) \rightarrow \textbf{BaF}_2(s) + 2\textbf{H}_2\textbf{O}(l)\] This conveys not only the substances involved but also their physical states, such as \textbf{(aq)} for aqueous solutions and \textbf{(l)} for liquids.

Acid-base reactions, also known as neutralization reactions, involve an acid and a base reacting to form a salt and water. In aqueous solutions, acids typically donate hydrogen ions (\textbf{H}^+), while bases donate hydroxide ions (\textbf{OH}^-). The hydrogen ions from the acid combine with the hydroxide ions from the base to create water molecules.

For instance, hydrochloric acid (\textbf{HCl}) neutralizes potassium hydroxide (\textbf{KOH}) to form potassium chloride (\textbf{KCl}) and water, as shown in the equation:\[\textbf{HCl}(aq) + \textbf{KOH}(aq) \rightarrow \textbf{KCl}(aq) + \textbf{H}_2\textbf{O}(l)\] It's crucial for the reaction to be balanced in order to reflect the actual stoichiometry, which implies the exact proportions in which chemicals react.

Balancing a chemical equation is the process of ensuring that there are equal numbers of each atom on the reactant and product sides of the equation. This is based on the principle that mass cannot be created or destroyed in a chemical reaction. To balance an equation, one must manipulate the coefficients, the numbers placed before compounds in an equation, without altering the chemical formulas of the reactants and products.

An example is the reaction between hydrobromic acid (\textbf{HBr}) and calcium hydroxide (\textbf{Ca(OH)2}). To balance the reaction, coefficients are adjusted so that there are equal numbers of each type of atom on both sides:\[2\textbf{HBr}(aq) + \textbf{Ca(OH)}_2(aq) \rightarrow \textbf{CaBr}_2(aq) + 2\textbf{H}_2\textbf{O}(l)\] The '2' in front of \textbf{HBr} ensures there are two bromide ions (\textbf{Br}^-) to combine with calcium (\textbf{Ca}^{2+}) and two hydrogen ions (\textbf{H}^+) to form two molecules of water, satisfying the law of conservation of mass.