A solution of potassium permanganate reacts with oxalic acid, \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) to form carbon dioxide and solid manganese(IV) oxide \(\left(\mathrm{MnO}_{2}\right)\). (a) Write a balanced net ionic equation for the reaction. (b) If \(20.0 \mathrm{~mL}\) of \(0.300 M\) potassium permanganate is required to react with \(13.7 \mathrm{~mL}\) of oxalic acid, what is the molarity of the oxalic acid? (c) What is the mass of manganese(IV) oxide formed?

Understanding the balanced net ionic equation is essential for comprehending various chemical reactions, including the one between potassium permanganate and oxalic acid. To arrive at a net ionic equation, we begin by writing a complete balanced chemical equation. This equation represents all reactants and products in their molecular forms. For instance, the reaction involving potassium permanganate (KMnO₄) and oxalic acid (H₂C₂O₄) produces manganese(IV) oxide (MnO₂), carbon dioxide (CO₂), and water (H₂O), as seen in the provided exercise.

From this full equation, we must identify the species that actually participate in the reaction, known as spectator ions, which remain unchanged throughout the process and are omitted from the net ionic equation. Once these spectator ions are removed, the net ionic equation presents only the ions and molecules that undergo a chemical change. In the example given, the sulfate ions (from H₂SO₄) and potassium ions (from KMnO₄) are spectator ions, leading to their exclusion in the net ionic equation.

Writing a balanced net ionic equation includes ensuring that the number of atoms and the charge are balanced on both sides of the reaction. This reflects the conservation of mass and charge. This balanced net ionic equation provides a clear and simplified representation of the chemical reaction, which is crucial for understanding the stoichiometry of the reaction and performing calculations such as molarity.

Molarity is a fundamental concept in chemistry, representing the concentration of a solution. It is defined as the number of moles of solute (the substance being dissolved) per liter of solution. The formula for calculating molarity is: \[ Molarity = \frac{moles \; of \; solute}{volume \; of \; solution \; in \; liters} \]The provided exercise demonstrates a practical application of this formula in determining the molarity of an oxalic acid solution, using the reaction with potassium permanganate. Given the volume and molarity of the potassium permanganate solution, as well as the stoichiometry of the reaction, students can calculate the moles of oxalic acid that reacted.

By applying the stoichiometric relationship between potassium permanganate and oxalic acid from the balanced net ionic equation, we can determine the number of moles of oxalic acid and subsequently its molarity. As seen in the problem, the molarity of oxalic acid is found using the volume of the oxalic acid solution and the moles of oxalic acid, which are obtained through stoichiometric calculations. This illustrates the practicality of molarity calculations in various chemical analyses, allowing students to understand how to relate the quantities of reactants and products in a chemical reaction.

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It is the cornerstone of many calculations in chemistry, allowing for the prediction of amounts of substances consumed and produced. In stoichiometry, the coefficients in a balanced chemical equation provide the ratio of moles of reactants needed and products formed, known as the molar ratio. This ratio is essential for solving problems related to chemical reactions, such as those in the exercise.

In the problem involving the reaction between potassium permanganate and oxalic acid, stoichiometry is used to find the molarity of oxalic acid and the mass of manganese(IV) oxide formed. Following the balanced net ionic equation, the molar ratios between reactants allow us to convert moles of one substance to moles of another. For example, the molar ratio from the balanced equation \[ \frac{5 \; mol \; H_{2}C_{2}O_{4}}{2 \; mol \; KMnO_{4}} \]indicates that 5 moles of oxalic acid will react with 2 moles of potassium permanganate. By knowing the moles of one reactant, the stoichiometry can be applied, as demonstrated in the exercise, to calculate the corresponding moles and, therefore, the mass of manganese(IV) oxide produced.

Grasping the concept of stoichiometry is crucial for students to engage in the balanced, methodical approach to solving chemical problems and understand the proportional relationships in reactions.