Balance each of the following equations. Classify each reaction as synthesis, decomposition, single-displacement, or doubledisplacement. (a) \(\mathrm{H}_{2}+\mathrm{Br}_{2} \longrightarrow \mathrm{HBr}\) (b) \(\mathrm{BaO}_{2}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{BaSO}_{4}(s)+\mathrm{H}_{2} \mathrm{O}_{2}(a q)\) (c) \(\mathrm{Ba}\left(\mathrm{ClO}_{3}\right)_{2} \stackrel{\Delta}{\longrightarrow} \mathrm{BaCl}_{2}+\mathrm{O}_{2}\) (d) \(\mathrm{CrCl}_{3}+\mathrm{AgNO}_{3} \longrightarrow \mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3}+\mathrm{AgCl}\)

Understanding how to balance chemical equations is essential for studying any chemical reaction. The principle behind it involves ensuring that the same number of each type of atom is present on both sides of the equation, keeping in mind the Law of Conservation of Mass.

To balance a chemical equation, we look at each element that appears in the reactants and products and adjust the coefficients—numbers placed before the compounds—to balance the atoms. For example, in equation (a) \(\text{H}_2 + \text{Br}_2 \to 2\text{HBr}\), we add the coefficient '2' in front of \(\text{HBr}\) to balance the hydrogen and bromine atoms. This methodical process is straightforward for simple reactions but can be challenging for more complex scenarios.

A synthesis reaction is a type of chemical process in which two or more substances combine to form a single more complex product. One hallmark of this reaction is simplicity—starting from basic building blocks and synthesizing a more complex compound.

For instance, reaction (a) \(\text{H}_2 + \text{Br}_2 \to 2\text{HBr}\) is a classic example of a synthesis reaction where hydrogen and bromine gas react to create hydrogen bromide. Synthesis reactions are fundamental processes that are mirrored in countless chemical manufacturing industries and biological systems.

In contrast to synthesis reactions, decomposition reactions involve the breakdown of a compound into two or more simpler substances. These reactions often require an input of energy, such as heat denoted by \(\Delta\), to drive the decomposition.

The equation (c) \(\text{Ba}(\text{ClO}_3)_2 \to \text{BaCl}_2 + 3\text{O}_2\) showcases a decomposition reaction. Here, barium chlorate decomposes into barium chloride and oxygen gas when heated. These types of reactions are crucial for understanding processes like the breakdown of organic matter or the preparation of various chemicals in a lab.

In a single-displacement reaction, also known as a substitution reaction, an element reacts with a compound, displacing another element from it.

While the textbook problem provided doesn't include a specific example for this type, a generalized equation looks like \(\text{A} + \text{BC} \to \text{AC} + \text{B}\) where element \(\text{A}\) replaces \(\text{B}\) in the compound \(\text{BC}\). Such reactions are visible in electrochemical cells or in the reactions involving metals and their salts in aqueous solutions.

Double-displacement reactions, also known as metathesis reactions, occur when components of two compounds switch places to form two new compounds. This type of reaction is seen in both examples (b) and (d) from the exercise.

In example (b) \(\text{BaO}_2(s) + \text{H}_2\text{SO}_4(aq) \to \text{BaSO}_4(s) + \text{H}_2\text{O}_2(aq)\), there is an exchange between \(\text{Ba}^{2+}\) and \(\text{H}^{+}\) ions. In example (d) \(\text{CrCl}_3 + 3\text{AgNO}_3 \to \text{Cr(NO}_3)_3 + 3\text{AgCl}\), \(\text{Ag}^{+}\) and \(\text{Cr}^{3+}\) switch partners. This reaction type is common in ionic compounds and is often used in chemistry to precipitate one of the products or to drive a reaction to completion.