Oxalic acid \(\left(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right)\) is present in many plants and vegetables. (a) Balance the following equation in acid solution: $$ \mathrm{MnO}_{4}^{-}+\mathrm{C}_{2} \mathrm{O}_{4}^{2-} \longrightarrow \mathrm{Mn}^{2+}+\mathrm{CO}_{2} $$ (b) If a 1.00 -g sample of \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) requires \(24.0 \mathrm{~mL}\) of \(0.0100 M \mathrm{KMnO}_{4}\) solution to reach the equivalence point, what is the percent by mass of \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) in the sample?

Balancing chemical equations is a foundational skill in chemistry essential for understanding how different substances react. In the context of redox reactions, the process becomes slightly more complex, involving the balancing of both mass and charge.

Redox titrations, such as the one described in the example, require careful attention to the transfer of electrons between the reactants. The half-reaction method is often employed, splitting the overall reaction into two parts: oxidation (loss of electrons) and reduction (gain of electrons). By balancing the number of electrons transferred in each half-reaction, we can ensure that the overall equation is both mass and charge balanced. This method highlights the stoichiometric relationship between reactants and products, an essential concept in quantitative chemistry.

Acid-base titration is a quantitative analytical procedure used to determine the concentration of an unknown solution by reacting it with a standard solution of known concentration. In the provided exercise, a redox titration is performed using KMnO₄ as the titrant to react with oxalic acid (H₂C₂O₄).

The endpoint of the titration is reached when the correct stoichiometric ratio between the titrant and analyte is achieved, which corresponds to the completion of the reaction. The volume of titrant used at the equivalence point provides valuable information that can be used to calculate the amount of substance in the sample, which is a critical aspect of stoichiometry.

Stoichiometry is the branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. It involves calculations that are based on the laws of conservation of mass and charge.

In the given exercise, stoichiometry is applied to determine the quantity of oxalic acid in the sample, using the balanced chemical equation as a roadmap. By calculating the moles of KMnO₄ (the titrant) used, and understanding the molar ratios from the balanced equation, we can derive the amount of oxalic acid that was present in the sample. This type of calculation is essential for various applications in both laboratory and industrial settings where precise chemical formulation is required.

Percent composition is a measure of the relative amounts of each element within a compound, expressed as a percentage of the total mass. In a chemical analysis context, determining the percent composition of a sample can reveal its purity or the presence of specific ingredients.

In the exercise, after calculating the mass of oxalic acid in the sample, the percent by mass is obtained by dividing the mass of the identified substance (oxalic acid) by the total mass of the sample, and then multiplying by 100. This simple calculation gives us insight into the concentration of a particular component in a mixture and is a valuable tool in lab analyses and quality control processes.