Write a balanced equation for each of the following: $$\begin{array}{c}{\text { a. copper(II) sulfate }+\text { ammonium sulfide } \rightarrow} \\ {\text { copper(II) sulfide + ammonium sulfate }} \\ {\text { b. nitric acid + barium hydroxide } \rightarrow} \\ {\text { water + barium nitrate }}\end{array}$$ $$ \begin{array}{c}{\text { c. barium chloride + phosphoric acid } \rightarrow} \\\ {\text { barium phosphate + hydrochloric acid }}\end{array} $$

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows us to predict how much of each substance is needed and how much will be produced in a reaction. This is crucial when preparing chemicals in a lab or in industrial processes to ensure that materials are not wasted and that reactions proceed to completion.

When balancing chemical equations, stoichiometry requires that the same number of atoms for each element is present on both sides of the equation. This conservation of mass is a fundamental concept in chemistry. For example, in the provided exercise, the balanced equations ensure that the number of atoms of copper, sulfur, oxygen, nitrogen, hydrogen, barium, chlorine, and phosphorus are equal on both the reactant and product side. By following stoichiometry rules, we ensure that the equations accurately represent the chemical process at hand.

In practical terms, stoichiometry involves calculating moles, which are a measure of the amount of substance. It employs the Avogadro constant, which is approximately equal to \(6.022 \times 10^{23}\) entities per mole, to convert between atoms, molecules, or ions and moles. Thus, understanding stoichiometry is essential for successfully balancing chemical equations and for many aspects of chemical practice.

A chemical reaction is a process where substances, known as reactants, transform into different substances, called products. This transformation happens as a result of breaking and forming chemical bonds, which requires or releases energy. Reactions are represented by chemical equations that symbolically present these physical changes.

For example, in our exercise, the reaction between copper(II) sulfate and ammonium sulfide forming copper(II) sulfide and ammonium sulfate is a type of chemical reaction. It's important to understand that during these reactions, atoms are not created or destroyed; they are simply rearranged, abiding by the Law of Conservation of Mass. Therefore, a balanced chemical equation will have the same number of atoms of each element in the reactants as in the products.

There are many types of chemical reactions, including synthesis, decomposition, single replacement, double replacement, and combustion. Each type has its own pattern of reactants and products, which can be identified through routine practice and understanding the properties of the involved substances.

A chemical formula represents the composition of a substance using the symbols of its constituent elements and numerical subscripts that indicate the number of each type of atom present. Formulas are the shorthand that chemists use to describe the exact composition of molecules and compounds.

For instance, in the balanced chemical equation \( CuSO_4 + 2 (NH_4)_2S \rightarrow CuS + 2 (NH_4)_2SO_4 \), each chemical formula indicates a unique substance. The formula \( CuSO_4 \) specifies one copper atom, one sulfur atom, and four oxygen atoms. When we look at the equation, the subscript numbers are pivotal for balancing, as they tell the exact ratio in which different atoms combine to form compounds.

In the context of balancing chemical equations, not only do the individual formulas need to reflect the real substances, but they also must be balanced as a whole to satisfy the laws of stoichiometry. Understanding chemical formulas is essential for identifying reactants and products and for calculating their moles during stoichiometric computations. The ability to decipher and use these formulas is fundamental for anyone studying chemistry.