Question

The concentration of a solution of potassium permanganate, \(\mathrm{KMnO}_{4}\), can be determined by titration against a known amount of oxalic acid, \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\), according to the following equation: \(5 \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(a q)+2 \mathrm{KMnO}_{4}(a q)+3 \mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow\) \(10 \mathrm{CO}_{2}(g)+2 \mathrm{MnSO}_{4}(a q)+\mathrm{K}_{2} \mathrm{SO}_{4}(a q)+8 \mathrm{H}_{2} \mathrm{O}(l)\) What is the concentration of a \(\mathrm{KMnO}_{4}\) solution if \(22.35 \mathrm{~mL}\) reacts with \(0.5170 \mathrm{~g}\) of oxalic acid?

Short answer

The concentration of KMnO4 solution is 0.1028 M.

Step-by-step solution

Calculate moles of oxalic acid

First, calculate the number of moles of oxalic acid \(\mathrm{H}_{2}\mathrm{C}_{2}\mathrm{O}_{4}\) using its given mass and molar mass.The molar mass of \(\mathrm{H}_{2}\mathrm{C}_{2}\mathrm{O}_{4}\) is calculated as follows:- \(\text{H}: 2 \times 1.01 \, \text{g/mol} = 2.02 \, \text{g/mol}\)- \(\text{C}: 2 \times 12.01 \, \text{g/mol} = 24.02 \, \text{g/mol}\)- \(\text{O}: 4 \times 16.00 \, \text{g/mol} = 64.00 \, \text{g/mol}\)Adding these gives \(90.04 \, \text{g/mol}\).Moles of \(\mathrm{H}_{2}\mathrm{C}_{2}\mathrm{O}_{4}\) = \(\frac{0.5170 \, \text{g}}{90.04 \, \text{g/mol}} = 0.00574 \, \text{mol}\).

Use stoichiometry to find moles of KMnO4

From the balanced equation, \(5 \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) react with \(2 \mathrm{KMnO}_{4}\).Using the stoichiometric coefficients: \[\text{Moles of } \mathrm{KMnO}_{4} = \left( \frac{2}{5} \right) \times 0.00574 \, \text{mol} = 0.002296 \, \text{mol}\]

Calculate the concentration of KMnO4

Convert the volume of \(\mathrm{KMnO}_{4}\) to liters: \[22.35 \, \text{mL} = 0.02235 \, \text{L}\]Concentration of \(\mathrm{KMnO}_{4}\) is given by the formula:\[\text{Concentration} = \frac{\text{Moles}}{\text{Volume in L}} = \frac{0.002296 \, \text{mol}}{0.02235 \, \text{L}} = 0.1028 \, \text{M}\]

Key concepts

Stoichiometry

Stoichiometry is the backbone of chemical calculations, providing a way to understand the quantitative relationships in chemical reactions. In titration, it helps us determine how much of one substance reacts with a certain amount of another. For the titration involving potassium permanganate and oxalic acid, stoichiometry reveals that for every 5 moles of oxalic acid, 2 moles of potassium permanganate are required. This ratio comes from the balanced chemical equation and helps us predict how much reactant is needed or how much product is formed. Knowing this allows chemists to calculate the exact concentrations and amounts of substances in a reaction.

Molar Concentration

Molar concentration, or molarity, indicates the number of moles of a solute in one liter of solution. It's a key measure in chemistry because it allows for easy determination of how much of a substance is present. In the case of determining the concentration of KMnO₄, molarity is calculated by dividing the number of moles of KMnO₄ by the volume of the solution in liters. This concept is crucial when performing titrations, as precise concentrations are necessary to accurately quantify reactions.

Potassium Permanganate

Potassium permanganate ( KMnO₄ ) is a strong oxidizing agent used frequently in titrations. In our reaction, it plays the role of the titrant, reacting with oxalic acid to transfer electrons and complete the chemical reaction. The striking purple color of potassium permanganate solutions also makes it a useful indicator during titrations since color change marks the endpoint of the reaction. Understanding its chemical nature and role in titrations is essential for accurate analyses and interpretations.

Oxalic Acid

Oxalic acid ( H₂C₂O₄ ) is an organic compound acting as a reducing agent in the titration with potassium permanganate. Known for its ability to donate electrons, it helps potassium permanganate change oxidation states during the reaction. Its use in this titration is based on its well-defined role in the balanced chemical equation, which ensures accurate, reproducible results. Recognizing its chemical characteristics, such as solubility and reactivity, underpins successful titration processes.

Balanced Chemical Equation

A balanced chemical equation is essential for reaction understanding and calculations. It shows the precise ratio of reactants and products involved. In the titration of potassium permanganate with oxalic acid, the balanced equation provides critical stoichiometric relationships. For example, it illustrates that 5 moles of oxalic acid react with 2 moles of potassium permanganate. This balance ensures that matter is conserved during the reaction and forms the basis for calculating moles and concentrations of the substances involved. Recognizing the importance of balanced equations is integral to executing accurate titration procedures.