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Question #44207

Difficulty: 8/10 | 🟢 Free

The Question

An aqueous solution of D-ribose (\ce{C5H10O5}, molar mass $= 150 \text{ g mol}^{-1}$ ) is prepared at $298 \text{ K}$ . At this temperature, the molarity of the solution is $2.0 \text{ M}$ and its density is $1.20 \text{ g mL}^{-1}$ . The solution is subsequently heated to $353 \text{ K}$ in a sealed vessel (assume negligible solvent vaporization). At $353 \text{ K}$ , the density of the solution decreases to $1.15 \text{ g mL}^{-1}$ due to thermal expansion. Given that the vapor pressure of pure water at $353 \text{ K}$ is $260 \text{ Torr}$ , determine the vapor pressure of the solution at $353 \text{ K}$ . Assume ideal behavior for the vapor phase and that Raoult's Law is applicable.

Options

A.
$250.0 \text{ Torr}$
B.
$251.3 \text{ Torr}$
C.
$252.4 \text{ Torr}$
D.
$195.0 \text{ Torr}$

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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

State vs Path Functions|Concentration Units Dependency|Vapor Pressure Lowering (Mole Fraction)

Why This Question Is Tricky

Common Mistakes

This problem tests the conceptual boundary between path-dependent concentration units (Molarity, which changes with thermal expansion) and state-function-compatible units (Mole Fraction/Molality).

Students often fall into the trap of recalculating the Molarity at the new temperature using the new density ( $1.15 \text{ g mL}^{-1}$ ), yielding $M_{new} = 1.916 \text{ M}$ , and then applying the flawed approximation $x_A \approx \frac{55.55}{55.55 + M_{new}}$ , which incorrectly yields $251.3 \text{ Torr}$ .

By forcing the calculation across a temperature gradient, the problem validates whether the student recognizes that the absolute ratio of moles (Mole Fraction) remains invariant regardless of the volumetric path taken by the solution.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Thermodynamics - Class 11 Part 1
Concept	State vs Path Functions
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free