Zinc and magnesium metal each react with hydrochloric acid according to the following equations: $$ \begin{aligned} \mathrm{Zn}(s)+2 \mathrm{HCl}(a q) & \longrightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g) \\ \mathrm{Mg}(s)+2 \mathrm{HCl}(a q) & \longrightarrow \mathrm{MgCl}_{2}(a q)+\mathrm{H}_{2}(g) \end{aligned} $$ A \(10.00-\mathrm{g}\) mixture of zinc and magnesium is reacted with the stoichiometric amount of hydrochloric acid. The reaction mixture is then reacted with \(156 \mathrm{~mL}\) of \(3.00 \mathrm{M}\) silver nitrate to produce the maximum possible amount of silver chloride. a. Determine the percent magnesium by mass in the original mixture. b. If \(78.0 \mathrm{~mL}\) of \(\mathrm{HCl}\) was added, what was the concentration of the \(\mathrm{HCl} ?\)

Understanding chemical reaction equations is foundational for studying chemistry and mastering stoichiometry. These equations illustrate how substances, the reactants, undergo a chemical change to form new substances, the products. In the exercise, we encounter two similar equations involving zinc (Zn) and magnesium (Mg) reacting with hydrochloric acid (HCl).

Each equation has a one-to-two molar ratio between the metal and HCl, meaning one mole of metal reacts with two moles of HCl. It's crucial to balance these equations to respect the Law of Conservation of Mass, ensuring that the number of atoms for each element is the same on both sides of the reaction. The balanced equations provide a roadmap to calculate the moles of reactants and products formed during the reaction, which serves as the key step in stoichiometry.

For instance, when working with the given exercise, we determined the moles of chloride ions (Cl⁻) produced in the reaction to further react with silver nitrate (AgNO₃) and form silver chloride (AgCl). By meticulously following each step dictated by the balanced equations, we ensure accurate calculations and a thorough understanding of the chemical processes at play.

Molar mass calculation involves finding the mass of one mole of a substance, typically in grams per mole (g/mol). Essentially, the molar mass acts as a conversion factor between the weight of a substance and the amount in moles. To solve the exercise, we first needed the molar masses of zinc and magnesium. The molar mass is the sum of the masses of all atoms in a molecule and can be found on the periodic table.

For instance, as presented in our exercise, the molar mass of zinc is 65.38 g/mol, and for magnesium, it is 24.305 g/mol. Knowing these values allows us to convert the given mass of the metal mixture into moles, which is pivotal in stoichiometry. This molar mass helps us calculate moles of metal from a known mass, thereby enabling us to delve into subsequent stoichiometric calculations such as determining the mass of zinc in our mixture.

The percent composition by mass is an essential quantity in chemistry that signifies the mass percentage of each element within a compound or a mixture of elements. In the context of the exercise, after calculating the mass of zinc and magnesium in the mixture, the percent composition of magnesium was the target.

The formula used is straightforward: $$Percentage(Element) = \frac{mass(Element)}{total mass of mixture} \times 100$$
Calculating the percent composition by mass provides valuable insights into the mixture's makeup, crucial for characterizing materials and predicting the outcome of chemical reactions. By applying this concept, as shown in the solution, we determined that magnesium comprised approximately 84.50% of the original 10.00 g mixture. This measure is not only fundamental for the given problem but also widely used in various chemical analysis and synthesis planning.