Balance each of the following: $$\begin{array}{l}{\text { a. } \mathrm{Zn}+\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2} \rightarrow \mathrm{Pb}+\mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}} \\ {\text { b. } \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}+\mathrm{NaOH} \rightarrow \mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4}+\mathrm{H}_{2} \mathrm{O}} \\\ {\text { c. } \mathrm{Al}+\mathrm{CuSO}_{4} \rightarrow \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}+\mathrm{Cu}}\end{array}$$

Stoichiometry is the calculation of reactants and products in chemical reactions. It's a core concept in chemistry that involves using the coefficients of each substance in a balanced chemical equation to understand the ratio of the number of moles of each substance involved in the reaction.

In the problems provided above, stoichiometry allows us to balance chemical equations by ensuring that the number of atoms for each element is the same on both sides of the equation, thereby adhering to the law of conservation of mass. For instance, in equation b, the stoichiometry was calculated to determine that two moles of sodium hydroxide (NaOH) react with one mole of oxalic acid (H_2C_2O_4) to produce one mole of sodium oxalate (Na_2C_2O_4) and two moles of water (H_2O). Understanding stoichiometry is crucial for students as it aids in predicting the amounts of substances consumed and produced in any given chemical reaction.

Chemical reactions involve the transformation of one or more substances into new substances. The starting materials, known as reactants, undergo chemical changes to form new substances called products. Fundamental types of chemical reactions include synthesis, decomposition, single replacement, and double replacement, among others.

In the exercise example, we have instances of single replacement reactions. In equation a, zinc (Zn) replaces lead (Pb) in lead(II) nitrate [Pb(NO_3)_2] to form zinc nitrate [Zn(NO_3)_2] and solid lead. These reactions can only occur if the reacting species follow certain activity series rules, which imply that certain elements can replace others based on their reactivity level. Being able to correctly identify the type of chemical reaction involved is vital to predicting the products and correctly balancing the chemical equation.

The law of conservation of mass states that in a closed system, the mass of the reactants must equal the mass of the products. In terms of chemical reactions, this means that atoms cannot be created or destroyed; they must be conserved from the reactants to the products.

This law is the reason behind the necessity to balance chemical equations, as seen in the given exercise solutions. When balancing the equations, we are effectively ensuring that the number of atoms of each element is constant, thus preserving the total mass. In equation c, zinc (Zn) reacts with copper(II) sulfate (CuSO4), and through the accurate balancing of the equation, we can account for all of the aluminum (Al), copper (Cu), sulfur (S), and oxygen (O) atoms. While seemingly simple, understanding and applying the law of conservation of mass is essential for chemical equation balancing and is a foundational principle in both chemistry and physics.