To determine the concentration of the $\text{Fe}^{2+}$ solution, we can use the stoichiometry of the titration reaction and the concept of molarity, which is defined as:

$\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}$

Step 1: Determine the moles of $\text{Ce}^{4+}$ added at equivalence point

Given:

• Volume of $\text{Ce}^{4+}$ added = $5.339 \, \text{mL} = 0.005339 \, \text{L}$
• Molarity of $\text{Ce}^{4+}$ solution = $0.655 \, \text{M}$

The number of moles of $\text{Ce}^{4+}$ added can be calculated as:

$\text{moles of } \text{Ce}^{4+} = \text{Molarity of } \text{Ce}^{4+} \times \text{Volume of } \text{Ce}^{4+}$ $= 0.655 \, \text{M} \times 0.005339 \, \text{L} = 0.003497 \, \text{mol}$

Step 2: Stoichiometry of the reaction

In the redox titration between $\text{Fe}^{2+}$ and $\text{Ce}^{4+}$, the balanced chemical equation is:

$\text{Ce}^{4+} + \text{Fe}^{2+} \rightarrow \text{Ce}^{3+} + \text{Fe}^{3+}$

From the equation, we see that 1 mole of $\text{Ce}^{4+}$ reacts with 1 mole of $\text{Fe}^{2+}$. Thus, the moles of $\text{Fe}^{2+}$ in the solution are equal to the moles of $\text{Ce}^{4+}$ at the equivalence point.

$\text{moles of } \text{Fe}^{2+} = 0.003497 \, \text{mol}$

Step 3: Calculate the concentration of $\text{Fe}^{2+}$

Now, we can calculate the concentration of the $\text{Fe}^{2+}$ solution using the formula:

$\text{Concentration of } \text{Fe}^{2+} = \frac{\text{moles of } \text{Fe}^{2+}}{\text{Volume of } \text{Fe}^{2+} \text{ solution in liters}}$ $= \frac{0.003497 \, \text{mol}}{17.607 \, \text{mL} \times \frac{1}{1000} \, \frac{\text{L}}{\text{mL}}} = \frac{0.003497}{0.017607} \, \text{M} = 0.199 \, \text{M}$

Final Answer:

The concentration of the $\text{Fe}^{2+}$ solution is $0.199 \, \text{M}$.

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. What is the significance of the equivalence point in a titration?
2. How does the volume of added water affect the titration result?
3. Can the molarity of $\text{Fe}^{2+}$ be affected by impurities in the solution?
4. How would using a different oxidizing agent instead of $\text{Ce}^{4+}$ affect the titration?
5. What are potential errors in titration experiments and how can they be minimized?

Tip: Always record the exact volume at the equivalence point in a titration to ensure accurate molarity calculations.