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A chemical reaction is a process in which substances, known as reactants, are transformed into other substances, called products. In the given exercise, the reaction involves iron(III) nitrate \((\mathrm{Fe(NO}_3)_3)\) and sodium hydroxide \((\mathrm{NaOH})\) reacting to form iron(III) hydroxide \((\mathrm{Fe(OH)}_3)\) as a precipitate and sodium nitrate \((\mathrm{NaNO}_3)\). This transformation is described by a balanced chemical equation:\[ \mathrm{Fe(NO_3)_3 + 3NaOH \rightarrow Fe(OH)_3 + 3NaNO_3} \]Balancing chemical equations is crucial because it ensures that the same number of each type of atom is present on both sides of the equation. It reflects the Law of Conservation of Mass, stating that matter cannot be created or destroyed during a chemical reaction. This principle helps accurately determine the amounts of reactants and products involved, enabling further calculations in stoichiometry.

Molar mass is an essential concept in stoichiometry that relates the mass of a substance to the number of moles. It allows us to convert between grams and moles, facilitating the calculation of reactants and products in a chemical reaction. For instance, the molar mass of iron(III) hydroxide \((\mathrm{Fe(OH)}_3)\) is 106.87 g/mol. To find it, sum up the atomic masses of each element in its chemical formula:- Fe = 55.85 g/mol- O = 16.00 g/mol (for 3 oxygen atoms, multiply by 3)- H = 1.01 g/mol (for 3 hydrogen atoms, multiply by 3)By adding these values, the molar mass of \(\mathrm{Fe(OH)}_3\) becomes:\[ \text{Molar Mass of } \mathrm{Fe(OH)}_3 = 55.85 + (3 \times 16.00) + (3 \times 1.01) = 106.87 \text{ g/mol} \]Molar mass aids in calculating the amount of substance, or moles, using the formula:\[ \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} \]This calculation is crucial for interpreting chemical reactions quantitatively.

Precipitation reactions are a type of chemical reaction where an insoluble solid, called a precipitate, forms when two solutions are mixed. In the exercise example, iron(III) nitrate \((\mathrm{Fe(NO}_3)_3)\) reacts with sodium hydroxide \((\mathrm{NaOH})\), resulting in the formation of a precipitate, iron(III) hydroxide \((\mathrm{Fe(OH)}_3)\). The reaction can be represented by the following equation:\[ \mathrm{Fe(NO_3)_3 + 3NaOH \rightarrow Fe(OH)_3 + 3NaNO_3} \]Here, \(\mathrm{Fe(OH)}_3\) is the precipitate, which can be observed as a solid that separates from the solution. This type of reaction is used to isolate specific compounds from mixtures, as the precipitate can be filtered and weighed. It plays a vital role in various applications, including chemical analysis and environmental science, where unwanted contaminants are removed as solids.

Mass percent is a measure of the concentration of a component in a mixture and is expressed as a percentage. It is calculated by dividing the mass of the component by the total mass of the sample and then multiplying by 100%.To find the mass percent of \(\mathrm{Fe(NO}_3)_3\) in the sample, follow these steps:1. Calculate the mass of \(\mathrm{Fe(NO}_3)_3\), which from the solution is 0.2428 g.2. Divide this value by the total mass of the sample, which is 0.456 g.3. Multiply the result by 100 to convert it to a percentage.Mathematically, this is shown as:\[ \text{Mass percent of } \mathrm{Fe(NO}_3)_3 = \left( \frac{0.2428 \text{ g}}{0.456 \text{ g}} \right) \times 100\% = 53.25\% \]Understanding mass percent is crucial for determining the composition of a mixture and is widely used in fields like chemistry, pharmacy, and metallurgy. This calculation helps in analyzing the purity of substances and the formulation of chemical solutions.