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Question #44661

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The Question

A $3.0 \text{ M}$ solution of a non-volatile, non-electrolyte solute (molar mass $= 60 \text{ g mol}^{-1}$ ) is prepared in a special isotopic water solvent at $312 \text{ K}$ . The solvent is a mixture of $\ce{H2O}$ and $\ce{D2O}$ such that the overall atomic ratio of $\ce{H:D}$ in the solvent is $1:3$ . The density of the resulting solution is $1.155 \text{ g mL}^{-1}$ . If the vapor pressure of the pure isotopic solvent mixture at $312 \text{ K}$ is $53.00 \text{ torr}$ , what is the vapor pressure of the solution? (Assume ideal behavior and that the isotopic composition of the vapor phase does not significantly alter the bulk solvent composition).

Options

A.
$50.00 \text{ torr}$
B.
$50.22 \text{ torr}$
C.
$49.93 \text{ torr}$
D.
$50.44 \text{ torr}$

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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

Isotopic Average Atomic Mass|Colligative Property Definition|Concentration Units Dependency

Why This Question Is Tricky

Common Mistakes

This problem tests the 'Concentration Units Dependency' trap combined with 'Isotopic Average Atomic Mass'.

Students often mechanically use $18 \text{ g mol}^{-1}$ for the molar mass of aqueous solvents.

Here, the isotopic substitution ( $\ce{H:D} = 1:3$ ) shifts the solvent's molar mass to $19.5 \text{ g mol}^{-1}$ .

Failing to account for this intrinsic mass shift when converting from an extrinsic volumetric property (Molarity) to a mole-fraction-dependent colligative property (Relative Lowering of Vapor Pressure) leads to incorrect solvent moles.

Distractor B assumes pure $\ce{H2O}$ , Distractor C assumes pure $\ce{D2O}$ , and Distractor D forgets to subtract the solute mass from the total solution mass.

Quick Facts About This Question

Question Information

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