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Question #44662

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The Question

A $100 \text{ mL}$ aqueous solution containing $0.1 \text{ M } \ce{K2Cr2O7}$ and excess $\ce{H2SO4}$ is treated with $V \text{ mL}$ of $0.4 \text{ M } \ce{H2O2}$ at $273 \text{ K}$ in the presence of diethyl ether. The organic layer, containing the blue-colored complex $\ce{CrO5}$ , is completely separated. The extracted $\ce{CrO5}$ is then titrated against a $0.2 \text{ M}$ acidified $\ce{KMnO4}$ solution. It requires exactly $50 \text{ mL}$ of the $\ce{KMnO4}$ solution to completely oxidize the peroxy linkages of $\ce{CrO5}$ to $\ce{O2(g)}$ , leaving chromium in the $+6$ oxidation state as $\ce{Cr2O7^{2-}}$ .

Assuming ideal stoichiometry and $100\%$ extraction efficiency, determine the actual value of $V$ . Furthermore, what would be the calculated value of $V$ if one incorrectly assumes that the average oxidation state of Cr in $\ce{CrO5}$ dictates its $n$ -factor during the titration?

Options

A.
$62.5 \text{ mL}$ and $41.7 \text{ mL}$
B.
$62.5 \text{ mL}$ and $35.7 \text{ mL}$
C.
$31.3 \text{ mL}$ and $41.7 \text{ mL}$
D.
$125.0 \text{ mL}$ and $83.3 \text{ mL}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Mechanism_Trap

Don't get tricked by the process! Learn the mechanical traps used in competitive exam questions.

Concepts Behind This Question

Limiting Reagent Stoichiometry|Average vs. Actual Oxidation State|Peroxy Linkage Identification

Why This Question Is Tricky

Common Mistakes

The core concept tests the limitation of the 'Average Oxidation State' method in redox stoichiometry.

When a molecule contains peroxy linkages (like $\ce{CrO5}$ ), calculating the $n$ -factor using the average oxidation state of the central atom leads to an incorrect value if the peroxy bonds undergo a specific redox transformation while the central atom does not.

Here, the actual $n$ -factor is 4 (derived from the oxidation of 4 peroxy oxygens), but the average oxidation state method yields a mathematically skewed $n$ -factor of 6.

This directly impacts the stoichiometric calculations in titrations, serving as a lethal trap for students who rely on algebraic oxidation state formulas instead of structural redox analysis.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Some Basic Concepts of Chemistry - Class 11 Part 1
Concept	Limiting Reagent Stoichiometry
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free