91影视

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 of the \(\mathrm{Fe}^{2+}\) ions are oxidized to \(\mathrm{Fe}^{3+}\) ions. Next, the solution is treated with \(Z n\) metal to convert all of the \(\mathrm{Fe}^{3+}\) ions to \(\mathrm{Fe}^{2+}\) ions. Finally, \(40.0 \mathrm{~mL}\) of the same \(\mathrm{KMnO}_{4}\) solution are added to the solution in order 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.

Step by step solution

01

Balance the Reaction Equations

First, understand the redox reactions involved. During the titration with KMnO鈧�, \[\text{MnO}_{4}^{-} + 8\text{H}^{+} + 5\text{Fe}^{2+} \rightarrow \text{Mn}^{2+} + 4\text{H}_{2}\text{O} + 5\text{Fe}^{3+}\] Each mole of KMnO鈧� reacts with 5 moles of Fe虏鈦�.

02

Calculate Moles of MnO鈧勨伝 Used

Use the concentration and volume of KMnO鈧� to find the moles used in the first and second titrations. For the first titration: Volume = 23.0 mL = 0.0230 L, Concentration = 0.0200 M, \( \text{moles of MnO}_{4}^{-} = 0.0230 \times 0.0200 = 0.00046 \) moles.

03

Determine Moles of Fe虏鈦� in First Titration

Each mole of KMnO鈧� oxidizes 5 moles of Fe虏鈦�. Therefore, \( \text{moles of Fe}^{2+} = 5 \times 0.00046 = 0.00230 \) moles.

04

Calculate Moles of Fe Ions after Zn Reduction

The zinc reduces all \(\text{Fe}^{3+}\) to \(\text{Fe}^{2+}\) completely. This means the total number of Fe ions (Fe虏鈦� + Fe鲁鈦� initially) is found in the second titration with more KMnO鈧�.

05

Second Titration Calculations

For the second titration: Volume = 40.0 mL = 0.0400 L, \( \text{moles of MnO}_{4}^{-} = 0.0400 \times 0.0200 = 0.00080 \) moles. This accounts for all Fe虏鈦� ions in the solution after Zn reduction.

06

Calculate Total Moles of Fe Ions

The 0.00080 moles of KMnO鈧� oxidizes the total moles of all Fe虏鈦� ions present after Zn reduction: \( \text{total moles of Fe (as Fe}^{2+}) = 5 \times 0.00080 = 0.00400 \) moles.

07

Determine Moles of Fe鲁鈦�

Since total Fe ions initially include both \( \text{Fe}^{2+} + \text{Fe}^{3+} = 0.00400 \) moles And the moles of Fe虏鈦� from the first titration is 0.00230 moles, \( \text{moles of Fe}^{3+} = 0.00400 - 0.00230 = 0.00170 \) moles.

08

Calculate Initial Concentrations

Convert moles to concentrations over the original 25.0 mL solution: For Fe虏鈦�: \( \text{Concentration of Fe}^{2+} = \frac{0.00230}{0.0250} = 0.0920 \: M \) For Fe鲁鈦�: \( \text{Concentration of Fe}^{3+} = \frac{0.00170}{0.0250} = 0.0680 \: M \)

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

KMnO鈧� titration

The titration process involving potassium permanganate (KMnO鈧�) is a fundamental redox process used widely in analytical chemistry. KMnO鈧� acts as a strong oxidizing agent, especially in acidic solutions, whereby it gets reduced while oxidizing other species. In the reaction provided, KMnO鈧� oxidizes Fe虏鈦� ions to Fe鲁鈦� ions. The balanced reaction equation for this process is crucial as it demonstrates the stoichiometry:

• The reaction: \[\text{MnO}_{4}^{-} + 8\text{H}^{+} + 5\text{Fe}^{2+} \rightarrow \text{Mn}^{2+} + 4\text{H}_{2}\text{O} + 5\text{Fe}^{3+}\]
• Each mole of KMnO鈧� reacts with 5 moles of Fe虏鈦�, indicating that for every mole of KMnO鈧� used, 5 moles of Fe虏鈦� ions are oxidized.

Understanding this reaction helps in determining the amount of Fe虏鈦� originally present in the solution by knowing the moles of KMnO鈧� used during titration.

Fe虏鈦� and Fe鲁鈦� ions

The presence of both Fe虏鈦� and Fe鲁鈦� ions in a solution introduces complexity when attempting to determine their individual concentrations. Iron ions switch between Fe虏鈦� (ferrous) and Fe鲁鈦� (ferric) during redox reactions. In this exercise:

• Fe虏鈦� ions are initially present and oxidized by KMnO鈧� to become Fe鲁鈦�.
• Zinc is then used to reduce Fe鲁鈦� back to Fe虏鈦�.

This cyclical oxidation and reduction is vital in distinguishing and calculating the amounts of these ions in the original solution. The insight gained from titrating the reduced solution again with KMnO鈧� allows us to back-calculate the quantity of each type of iron ion initially present.

Zinc reduction

Zinc reduction involves using elemental zinc to reduce Fe鲁鈦� ions back to Fe虏鈦� ions, effectively resetting the oxidation state of iron ions in the solution. This serves as an essential step in differentiating the amounts of Fe虏鈦� and Fe鲁鈦� initially present. Zinc acts as a reducing agent:

• Converts all Fe鲁鈦� ions present into Fe虏鈦�.
• Facilitates the subsequent titration step where KMnO鈧� can again be used to titrate the newly formed Fe虏鈦� ions.

By understanding this reduction process, it becomes possible to accurately assess the total concentration of Fe metal ions before and after initial treatments, aiding in the overall calculations needed to find the concentrations of each individual ion in the original solution.

Molar concentration calculation

Molar concentration reflects the number of moles of a solute present in one liter of solvent. In any redox titration problem, such as the one given, calculating molar concentration is the ultimate goal. Here, after determining the moles of iron ions involved through the titration steps, the concentration of each iron ion type in the original solution can be computed.

• For Fe虏鈦�: Calculated moles (after the first titration) divided by the original volume given in liters yields the molar concentration: \[\text{Concentration of Fe}^{2+} = \frac{0.00230}{0.0250} = 0.0920 \, M\]
• For Fe鲁鈦�: Determine moles by subtracting moles of Fe虏鈦� from total moles and divide by the volume:\[\text{Concentration of Fe}^{3+} = \frac{0.00170}{0.0250} = 0.0680 \, M\]

This calculation confirms that despite the complex series of reactions, the concentration of ions in a solution can be precisely determined, ensuring accurate measurement in experimental chemistry.