Question

100 mL of 0.1 M \( Fe^{2+} \) solution was titrated with \( \frac{1}{60} \) M \( Cr_2O_7^{2-} \) solution in acid medium. What is the volume (in L) of \( Cr_2O_7^{2-} \) solution consumed?

• A. \( 100 \)
• B. \( 10 \)
• C. \( 1 \)
• D. \( 0.1 \)

Hint:

In redox titrations, use the balanced reaction to determine mole ratios. Apply the molarity equation \( M_1V_1 = M_2V_2 \) for volume calculations.

Answer 1

The Correct Option is D

Step 1: Understanding the Redox Reaction
The balanced redox reaction in acidic medium: \[ Cr_2O_7^{2-} + 6Fe^{2+} + 14H^+ \rightarrow 2Cr^{3+} + 6Fe^{3+} + 7H_2O \] From the balanced equation:
- 1 mole of \( Cr_2O_7^{2-} \) reacts with 6 moles of \( Fe^{2+} \).
Step 2: Finding Moles of \( Fe^{2+} \) Given: \[ \text{Molarity} (M) = 0.1, \quad \text{Volume} (V) = 100 \text{ mL} = 0.1 \text{ L} \] Moles of \( Fe^{2+} \): \[ \text{Moles of } Fe^{2+} = M \times V = 0.1 \times 0.1 = 0.01 \text{ moles} \] Step 3: Finding Moles of \( Cr_2O_7^{2-} \)
From the reaction: \[ \text{Moles of } Cr_2O_7^{2-} = \frac{\text{Moles of } Fe^{2+}}{6} = \frac{0.01}{6} = 1.67 \times 10^{-3} \text{ moles} \] Step 4: Finding Volume of \( Cr_2O_7^{2-} \) Solution
Given that the molarity of \( Cr_2O_7^{2-} \) solution is: \[ M = \frac{1}{60} = 0.0167 \text{ M} \] Using the molarity formula: \[ V = \frac{\text{Moles of } Cr_2O_7^{2-}}{\text{Molarity}} \] \[ V = \frac{1.67 \times 10^{-3}}{0.0167} = 0.1 \text{ L} \] Final Answer: The correct volume is \( 0.1 \) L, which matches Option (4).