The following equations are incorrect in some way. Identify and correct each error, and then balance each equation. $$\begin{array}{l}{\text { a. } \mathrm{Li}+\mathrm{O}_{2} \rightarrow \mathrm{LiO}_{2}} \\ {\text { b. } \mathrm{MgCO}_{3} \rightarrow \mathrm{Mg}+\mathrm{C}+3 \mathrm{O}_{2}} \\ {\text { c. } \mathrm{NaI}+\mathrm{Cl}_{2} \rightarrow \mathrm{NaCl}+\mathrm{I}} \\ {\text { d. } \mathrm{AgNO}_{3}+\mathrm{CaCl}_{2} \rightarrow \mathrm{Ca}\left(\mathrm{NO}_{3}\right)+\mathrm{AgCl}_{2}} \\ {\text { e. } 3 \mathrm{Mg}+2 \mathrm{FeBr}_{3} \rightarrow \mathrm{Fe}_{2} \mathrm{Mg}_{3}+3 \mathrm{Br}_{2}}\end{array}$$

Understanding stoichiometry is akin to following a recipe for the perfect chemical reaction. Just as you'd need the right number of eggs and flour to bake a cake, you need the correct ratios of reactants to get the desired products in a chemical equation.

At its core, stoichiometry is the study of the quantitative relationships, or ratios, between reactants and products in chemical reactions. Think of it like this: for every one bicycle you want to build, you need two wheels and one frame. In chemical terms, if you react 2 volume units of hydrogen gas (H2) with 1 volume unit of oxygen gas (O2), you'll produce 2 volume units of water (H2O). This simple ratio – 2:1:2 – is the essence of stoichiometry.

When balancing chemical equations, which is essentially an exercise in stoichiometry, you want to verify that the law of conservation of mass is respected. This means the number of atoms of each element must be equal on both the reactant and product sides of the equation. For example, in the textbook problem 'a', we need to adjust the lithium (Li) and oxygen (O2) so that the same number of atoms are on both sides. The corrected balance would therefore be:
\[4Li + O_2 \rightarrow 2Li_2O\].

In summary, mastering stoichiometry is crucial, as it ensures that chemical reactions are understood and performed correctly, avoiding any wastage of materials or unsafe imbalances.

A chemical reaction is an event where substances, the reactants, transform into new substances, the products. Imagine it as a dance where partners (atoms or molecules) exchange places to form new dance pairs (molecular compounds).

There are several types of chemical reactions, and recognizing them is key to correct balancing. For instance, a single replacement reaction occurs when one element switches places with another element in a compound, as seen in the textbook problem 'c':
\[2NaI + Cl_2 \rightarrow 2NaCl + I_2\].
Here, chlorine (Cl2) replaces iodine (I) in sodium iodide (NaI) to create sodium chloride (NaCl) and iodine (I2). Each type of reaction has its own set of rules for balancing.

Additionally, it's important to pay attention to coefficients—the numbers placed before molecules in an equation. They indicate the multiple of that molecule required to balance the equation. In problem 'd', the correct coefficients ensure we have equal numbers of silver (Ag) and chloride (Cl) atoms on both sides of the equation:
\[2AgNO_3 + CaCl_{2} \rightarrow Ca(NO3)_2 + 2AgCl\].
Understanding the science behind why and how these reactions occur enables students to predict the products of reactions and effectively balance chemical equations.

Molecular compounds are substances formed when two or more atoms join together through covalent bonds. They are like building blocks that attach in specific ways to create a variety of structures with unique properties.

In our textbook exercise, problem 'e' provides an instance where molecular compounds must be properly denoted to reflect reality. Initially, the compound was incorrectly written as \(Fe_2 Mg_3\), but we know that iron (Fe) does not form a molecular compound with magnesium (Mg) in this scenario. Instead, each of the reacting magnesium atoms pairs with two bromine (Br) atoms to create magnesium bromide (MgBr2), a new molecular compound that reflects a proper pairing of atoms:
\[3Mg + 2FeBr_3 \rightarrow 3MgBr_2 + 2Fe\].

Understanding the nature and formation of molecular compounds is essential for grasping the intricacies of chemical reactions. By identifying the correct compounds, students can more accurately predict the outcomes of chemical equations and avoid common mistakes in their formation and representation.