Question

When \(25.0 \mathrm{~mL}\) of a solution containing both \(\mathrm{Fe}^{2+}\) and \(\mathrm{Fe}^{3+}\) ions is titrated with \(23.0 \mathrm{~mL}\) of \(0.0200 \mathrm{M} \mathrm{KMnO}_{4}\) (in dilute sulfuric acid), all the \(\mathrm{Fe}^{2+}\) ions are oxidized to \(\mathrm{Fe}^{3+}\) ions. Next, the solution is treated with Zn metal to convert all the \(\mathrm{Fe}^{3+}\) ions to \(\mathrm{Fe}^{2+}\) ions. Finally, \(40.0 \mathrm{~mL}\) of the same \(\mathrm{KMnO}_{4}\) solution is added to the solution to oxidize the \(\mathrm{Fe}^{2+}\) ions to \(\mathrm{Fe}^{3+}\). Calculate the molar concentrations of \(\mathrm{Fe}^{2+}\) and \(\mathrm{Fe}^{3+}\) in the original solution.

Short answer

\( \mathrm{Fe}^{2+} = 0.092 \text{ M}; \mathrm{Fe}^{3+} = 0.068 \text{ M} \).

Step-by-step solution

Write the Balanced Chemical Equation

First, write the balanced equation for the reaction between \( \mathrm{Fe}^{2+} \) and \( \mathrm{KMnO}_4 \). In acidic solution, the reaction is: \( 5 \mathrm{Fe}^{2+} + \mathrm{MnO}_4^- + 8 \mathrm{H}^+ \rightarrow 5 \mathrm{Fe}^{3+} + \mathrm{Mn}^{2+} + 4 \mathrm{H}_2\mathrm{O} \). This tells us that one mole of \( \mathrm{MnO}_4^- \) oxidizes 5 moles of \( \mathrm{Fe}^{2+} \).

Calculate Moles of \( \mathrm{KMnO}_4 \) Used

Calculate the moles of \( \mathrm{KMnO}_4 \) used in both titrations. For the first titration: \( 23.0 \text{ mL} \times 0.0200 \text{ mol/L} = 0.00046 \text{ mol} \) of \( \mathrm{KMnO}_4 \). For the second titration: \( 40.0 \text{ mL} \times 0.0200 \text{ mol/L} = 0.00080 \text{ mol} \) of \( \mathrm{KMnO}_4 \).

Calculate Moles of \( \mathrm{Fe}^{2+} \) Initially Present

From the first titration, since 1 mol of \( \mathrm{KMnO}_4 \) reacts with 5 mol of \( \mathrm{Fe}^{2+} \), the moles of \( \mathrm{Fe}^{2+} \) oxidized are \( 0.00046 \times 5 = 0.0023 \text{ moles} \).

Calculate Moles of \( \mathrm{Fe}^{3+} \) from Initial and Reduction Reaction

The Zn reduction converts all the \( \mathrm{Fe}^{3+} \) back to \( \mathrm{Fe}^{2+} \). Then, during the second titration, all \( \mathrm{Fe}^{2+} \) is titrated to \( \mathrm{Fe}^{3+} \), using \( 0.00080 \times 5 = 0.0040 \text{ moles} \) of \( \mathrm{Fe}^{2+} \).

Determine Moles of \( \mathrm{Fe}^{3+} \) Originally Present

The extra moles reacted, \( 0.0040 - 0.0023 = 0.0017 \text{ moles} \), are attributed to the original \( \mathrm{Fe}^{3+} \) ions present.

Calculate Concentrations in the Original Solution

The original concentration of \( \mathrm{Fe}^{2+} \) is \( \frac{0.0023}{0.025} = 0.092 \text{ mol/L} \) and \( \mathrm{Fe}^{3+} \) is \( \frac{0.0017}{0.025} = 0.068 \text{ mol/L} \).

Conclusion

After calculating, the concentrations in the original solution are: \( 0.092 \text{ M} \) of \( \mathrm{Fe}^{2+} \) and \( 0.068 \text{ M} \) of \( \mathrm{Fe}^{3+} \).

Key concepts

Oxidation-Reduction Reactions

An lbr oxidation-reduction reaction, commonly known as a redox reaction, is a type of chemical reaction where electrons are transferred between two substances. In these reactions, one substance is oxidized by losing electrons, while another is reduced by gaining electrons. Understanding redox reactions is crucial in various chemical processes, such as ubattery operations, biological systems, and industrial applications. In the given exercise, the redox reaction involves the oxidation of Fe^{2+} ions to Fe^{3+} ions using KMnO_{4} as the oxidizing agent. During this process, MnO_{4}^{-} is reduced to Mn^{2+} ions, illustrating how electron transfer allows the transformation of reactants into different products. This reaction utilizes the inherent ability of permanganate ions (MnO_{4}^{-}) to change oxidation states, thereby facilitating the oxidation of other ions. To fully grasp redox reactions, focus on tracking the flow of electrons and identifying the oxidation states of participating elements. This understanding aids in balancing redox equations and predicting the outcomes of chemical interactions.

Chemical Equations

Chemical equations are essential for representing chemical reactions in a concise manner. They show reactants transforming into products, often with coefficients representing the number of moles involved in the reaction. Writing balanced chemical equations ensures that the law of conservation of mass is upheld, facilitating accurate stoichiometric calculations.In the provided exercise, the balanced equation for the oxidation of Fe^{2+} by KMnO_{4} is:\[ 5 ext{Fe}^{2+} + ext{MnO}_4^- + 8 ext{H}^+ \rightarrow 5 ext{Fe}^{3+} + ext{Mn}^{2+} + 4 ext{H}_2 ext{O} \] This equation illustrates the stoichiometry between Fe^{2+} ions and MnO_{4}^{-} ions, with one mole of permanganate oxidizing five moles of iron (II) ions. Understanding this relationship is crucial for calculating reactant and product quantities and for performing titrations, like those in the exercise.Balancing chemical equations involves adjusting coefficients to have the same number of atoms of each element on both sides of the equation. Mastery of this skill is vital in applying principles of stoichiometry and conducting accurate chemical analyses.

Molar Concentration

Molar concentration or molarity is a measure of the concentration of a solute in a solution. It is expressed in moles of solute per liter of solution (mol/L). Molarity provides a way to quantify the amount of substance in a given volume, which is crucial in chemical analysis and reaction stoichiometry. In the exercise, calculating the molar concentrations of Fe^{2+} and Fe^{3+} ions involves determining the number of moles of each ion present in the original solution. This is achieved through the use of titrations. From the data given: - Moles of Fe^{2+} initially present: 0.0023 mol - Moles of Fe^{3+} originally present: 0.0017 mol The original volume of the solution containing both ions is 0.025 L (25.0 mL). The molar concentrations are then calculated as: - For Fe^{2+}: 0.092 mol/L - For Fe^{3+}: 0.068 mol/L Understanding molar concentration helps in analyzing solutions and predicting the extent of reactions, ensuring precise adjustments can be made during chemical processes.

Analytical Chemistry

Analytical chemistry involves the study of techniques and methods used to determine the composition of substances. It plays a crucial role in identifying and quantifying chemical species, making it essential in research and industry. Titrations are a core method in analytical chemistry. Redox titrations, like the ones performed in the exercise, are used to determine the concentrations of oxidizing and reducing agents. These involve carefully measured reactions between a titrant (a solution of known concentration) and an analyte (unknown concentration). Understanding the process involves:

• Setting up an experiment where the titrant (here KMnO_{4}) reacts with the analyte (Fe^{2+} ions).
• Monitoring the reaction endpoint where all analyte has reacted.
• Calculating the analyte concentration based on the known volume and concentration of the titrant used.

Analytical chemistry, through techniques like titration, allows chemists to extract accurate data about a material's composition. This data is essential for quality control, research development, and environmental analysis, providing insights into chemical properties and behaviors.