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Question #44517

Difficulty: 8/10 | 🟢 Free

The Question

An aqueous system is prepared at $298 \text{ K}$ by mixing exactly $50.0 \text{ moles}$ of $\ce{H2O(l)}$ , $0.40 \text{ moles}$ of a completely soluble 1:1 strong electrolyte $\ce{NX}$ , and $0.50 \text{ moles}$ of a sparingly soluble 1:1 salt $\ce{MX}$ . The final volume of the aqueous solution is exactly $1.0 \text{ L}$ . Given that the solubility product of $\ce{MX}$ at $298 \text{ K}$ is $K_{sp} = 5.0 \times 10^{-2}$ , what is the exact relative lowering of vapor pressure ( $\frac{\Delta P}{P^\circ}$ ) of the solution? Assume ideal behavior for all dissolved species.

Options

A.
$\frac{1}{51}$
B.
$\frac{9}{259}$
C.
$\frac{1}{101}$
D.
$\frac{9}{509}$

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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

Raoult’s Law Ideal vs Non-Ideal|Common Ion Effect on Solubility|Vapor Pressure Lowering (Mole Fraction)

Why This Question Is Tricky

Common Mistakes

The problem tests the intersection of Colligative Properties (Raoult's Law) and Ionic Equilibrium (Common Ion Effect).

A common student error is to assume that all added solute dissolves, thereby calculating the mole fraction using the total moles of salt added ( $0.50 \text{ mol}$ of $\ce{MX}$ + $0.40 \text{ mol}$ of $\ce{NX}$ ).

This ignores the thermodynamic solubility limit imposed by the $K_{sp}$ and the common ion effect, which forces $0.40 \text{ moles}$ of $\ce{MX}$ to remain as a non-volatile, undissolved solid that does not contribute to vapor pressure lowering.

By requiring the calculation of the true equilibrium concentration of dissolved particles, the question bypasses rote formulaic application and tests deep conceptual understanding of phase equilibria.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Solutions - Class 12
Concept	Raoult’s Law Ideal vs Non-Ideal
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free