Balance the following equations. (a) \(\mathrm{CaO}+\mathrm{HNO}_{3} \longrightarrow \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}+\mathrm{H}_{2} \mathrm{O}\) (b) \(\mathrm{Na}_{2} \mathrm{CO}_{3}+\mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2} \longrightarrow \mathrm{MgCO}_{3}+\mathrm{NaNO}_{3}\) (c) \(\left(\mathrm{NH}_{4}\right)_{3} \mathrm{PO}_{4}+\mathrm{NaOH} \longrightarrow\) \(\mathrm{Na}_{3} \mathrm{PO}_{4}+\mathrm{NH}_{3}+\mathrm{H}_{2} \mathrm{O}\) (d) \(\mathrm{LiHCO}_{3}+\mathrm{H}_{2} \mathrm{SO}_{4} \longrightarrow \mathrm{Li}_{2} \mathrm{SO}_{4}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2}\) (e) \(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}\)

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It is based on the law of conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction. Therefore, a balanced chemical equation is quintessential to stoichiometry as it provides the exact proportions of reactants needed to form a specific quantity of product.

Understanding stoichiometry involves being able to calculate the moles, masses, volumes, and concentrations of substances within a chemical reaction. An example can be drawn from the step-by-step solution provided in the exercise, where coefficients are used to balance the number of atoms of each element on both sides of the equations. These coefficients directly reflect the stoichiometry of the reaction, as they indicate the relative amounts of each substance involved.
For instance, in the balanced equation \[\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}+6\mathrm{O}_{2} \longrightarrow 4\mathrm{CO}_{2}+5\mathrm{H}_{2} \mathrm{O}\], the stoichiometry tells us that one mole of butanol reacts with six moles of oxygen to produce four moles of carbon dioxide and five moles of water.

A chemical reaction is a process where substances, the reactants, undergo a chemical change to form new substances, called the products. During a chemical reaction, bonds between atoms in the reactants are broken and new bonds are formed to create the products. These reactions are represented through chemical equations that show the reactants on the left side of an arrow and the products on the right side.

For a chemical reaction to be accurately represented, the equation must be balanced, meaning the same number of each type of atom must exist on both sides of the equation. Balancing chemical equations is not only crucial for stoichiometry calculations but also for understanding the nature of the reaction. The aforementioned equations from the exercise demonstrate various types of chemical reactions: combination, decomposition, single replacement, and combustion.

Chemical equations provide valuable insights into the chemical reaction, such as the state of reactants and products, whether they are solid (s), liquid (l), gas (g), or aqueous (aq), and the reaction conditions like heat or catalysts that may be necessary.

A chemical formula is a symbolic representation of a substance that displays the elements present and the relative number of atoms of each. In simple terms, it provides the recipe for a molecule, much like a cooking recipe lists ingredients and their amounts. Chemical formulas are crucial in chemical equations as they identify the specific substances involved in the reaction.

For example, take the compound \(\mathrm{NaNO}_{3}\), or sodium nitrate; the chemical formula tells you that each molecule contains one sodium atom (Na), one nitrogen atom (N), and three oxygen atoms (O). In the context of balancing chemical equations, the formulas must be used correctly, respecting the law of conservation of mass and ensuring that the elements' subscripts and the compounds' coefficients are used to balance the reaction correctly.

Chemical formulas can also signify the arrangement of atoms within the molecules, known as structural formulas, giving deeper insight into the molecular geometry and potential chemical properties, although the exercise focuses on the more basic empirical and molecular formulas.