Identify and correct each error in the following equations, and then balance each equation. a. \(\mathrm{Li}+\mathrm{O}_{2} \longrightarrow \mathrm{LiO}_{2}\) b. \(\mathrm{H}_{2}+\mathrm{Cl}_{2} \longrightarrow \mathrm{H}_{2} \mathrm{Cl}_{2}\) c. \(\mathrm{MgCO}_{3} \longrightarrow \mathrm{MgO}_{2}+\mathrm{CO}_{2}\) d. \(\mathrm{NaI}+\mathrm{Cl}_{2} \longrightarrow \mathrm{NaCl}+\mathrm{I}\)

Chemical reactions involve the transformation of substances through breaking and forming chemical bonds. Starting materials are called reactants, and the substances formed are products. Chemical equations represent these reactions and must follow the established rules of chemistry. For example, in part (a), the reaction involves lithium (\text{Li}) and oxygen (\text{O}\(_2\)). The initial incorrect formula, \text{LiO}\(_2\), was corrected to \text{Li}\(_2\)\text{O}, showing the proper product: lithium oxide.
In part (b), we adjusted the product \text{H}\(_2\)\text{Cl}\(_2\) to \text{HCl}, the correct molecule formed in the reaction between hydrogen and chlorine.

Stoichiometry is the study of the quantitative relationships between the amounts of reactants and products in a chemical reaction. It allows us to balance chemical equations by ensuring the same number of each type of atom on both sides of the equation. For instance, in part (a), we balanced the equation correctly as:
\text{4 Li + O}\(_2\) \text{→ 2 Li}\(_2\)\text{O}.
In part (d), we recognized the need to balance iodine molecules and updated the equation to:
\text{2 NaI + Cl}\(_2\) \text{→ 2 NaCl + I}\(_2\).
This shows that two sodium iodide (\text{NaI}) molecules react with one chlorine molecule (\text{Cl}\(_2\)) to produce two sodium chloride (\text{NaCl}) molecules and one iodine molecule (\text{I}\(_2\)).

The law of conservation of mass states that mass in an isolated system is neither created nor destroyed in a chemical reaction. This means the mass of reactants must equal the mass of the products. For each reaction given in the exercise, we balance the equations to comply with this principle.
For example, in part (c), we changed the incorrect product \text{MgO}\(_2\) to \text{MgO}, giving us:
\text{MgCO}\(_3\) \text{→ MgO + CO}\(_2\).
This adjustment ensures that the number of magnesium (Mg), carbon (C), and oxygen (O) atoms are conserved.

Chemical formulas represent the types and numbers of atoms in a molecule. Correct formulas are crucial to writing and balancing chemical equations. In the given problems, we corrected the formulas to reflect the actual products formed in chemical reactions.
In part (b), the hydrocholoric acid's formula was corrected from \text{H}\(_2\)\text{Cl}\(_2\) to \text{HCl}, acknowledging the correct combination of hydrogen and chlorine atoms to form the compound.
Similarly, in part (d), the product \text{I} was corrected to the diatomic molecule \text{I}\(_2\), respecting iodine's natural state as a diatomic element.