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Question #44136

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The Question

Compound $\textbf{X}$ is synthesized by the stoichiometric reaction of $1\text{ equivalent}$ of phthalic anhydride with $1\text{ equivalent}$ of anhydrous $\ce{H2O2}$ in ether. After isolation, $3.64\text{ g}$ of $\textbf{X}$ is dissolved in $100\text{ g}$ of benzene at $298\text{ K}$ . The freezing point of the solution is depressed by $0.6144\text{ K}$ . Assuming $\textbf{X}$ undergoes partial dimerization in benzene via intermolecular hydrogen bonding, determine the van't Hoff factor ( $i$ ) and the dimerization equilibrium constant ( $K_d$ ) of $\textbf{X}$ . \ (Given: $K_f(\text{benzene}) = 5.12\text{ K kg mol}^{-1}$ ; Atomic masses: $\ce{C}=12, \ce{H}=1, \ce{O}=16$ )

Options

A.
$i = 0.60, K_d = 50\text{ kg mol}^{-1}$
B.
$i = 0.55, K_d = 234\text{ kg mol}^{-1}$
C.
$i = 0.60, K_d = 2.78\text{ kg mol}^{-1}$
D.
$i = 0.60, K_d = 2.0\text{ kg mol}^{-1}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Numerical_Precision

Improve calculation stamina and avoid rounding errors in high-stakes competitive examinations.

Concepts Behind This Question

Peroxy Linkage Identification|Molecular Mass Abnormalities|Stoichiometric Coefficient Division

Why This Question Is Tricky

Common Mistakes

The problem tests two critical advanced concepts: 1) Peroxy Linkage Identification: Students often assume the reaction of an anhydride with hydrogen peroxide yields a standard dicarboxylic acid (phthalic acid, M=166) rather than a peroxy acid (monoperoxyphthalic acid, M=182).

This 'Hidden Variable' alters the true molar mass and initial molality (Trap B). 2) Stoichiometric Coefficient Division: When calculating the dimerization constant, students frequently misapply the degree of association ( $\alpha$ ) by using $i = 1 - \alpha$ instead of $i = 1 - \alpha/2$ (Trap C), or they forget to square the monomer concentration in the $K_d$ expression (Trap D).

The distractors are precisely engineered to catch these thermodynamic and structural oversights.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Redox Reactions - Class 11 Part 2
Concept	Peroxy Linkage Identification
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free