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Question #44685

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The Question

An experiment is conducted to determine the degree of dissociation ( $\alpha$ ) of an isotopically pure salt, $\ce{^6Li^{35}Cl}$ , in aqueous solution. Exactly $20.492\text{ g}$ of the salt is dissolved in $1000.0\text{ g}$ of pure water at $298\text{ K}$ . The vapor pressure of the resulting solution is measured to be $23.3602\text{ Torr}$ , while the vapor pressure of pure water at this temperature is $23.7600\text{ Torr}$ . Given the exact isotopic masses: $\ce{^6Li} = 6.015\text{ u}$ , $\ce{^{35}Cl} = 34.969\text{ u}$ , $\ce{^1H} = 1.008\text{ u}$ , $\ce{^{16}O} = 15.999\text{ u}$ . Calculate the degree of dissociation ( $\alpha$ ) of $\ce{^6Li^{35}Cl}$ .

Options

A.
90.0%
B.
96.5%
C.
86.8%
D.
93.2%

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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

Precision in Atomic Mass Units|Molecular Mass Abnormalities|Vapor Pressure Lowering (Mole Fraction)

Why This Question Is Tricky

Common Mistakes

This problem tests the 'Precision in Atomic Mass Units' exception within Colligative Properties.

Students habitually use memorized standard atomic weights (Li $\approx$ 6.94, Cl $\approx$ 35.45), which represent isotopic averages.

For an isotopically pure sample, this introduces a massive $>3\%$ error in the molar mass ( $42.39$ vs $40.984$ g/mol), leading to the $96.5\%$ trap.

Furthermore, it tests the 'Van t Hoff Factor Integration' by requiring the exact RLVP formula ( $\Delta P / P_s$ ) rather than the dilute approximation ( $\Delta P / P^0$ ), which yields the $86.8\%$ trap.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Some Basic Concepts of Chemistry - Class 11 Part 1
Concept	Precision in Atomic Mass Units
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free