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Question #44666

Difficulty: 8/10 | 🟢 Free

The Question

A $1.2 \text{ M}$ aqueous solution of a highly soluble organic weak monoprotic acid ( $HA$ , molar mass = $150 \text{ g mol}^{-1}$ ) has a density of $1.08 \text{ g mL}^{-1}$ at $298 \text{ K}$ . When this solution is cooled, it begins to freeze at $-2.604^\circ\text{C}$ . Given the cryoscopic constant of water $K_f = 1.86 \text{ K kg mol}^{-1}$ , what is the degree of dissociation ( $\alpha$ ) of the acid at its freezing point?

Options

A.
5.0%
B.
16.7%
C.
26.0%
D.
10.5%

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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

Concentration Unit Interconversion|Molecular Mass Abnormalities

Why This Question Is Tricky

Common Mistakes

This problem tests the critical distinction between molarity and molality in colligative property calculations, specifically when dealing with concentrated non-ideal solutions of weak electrolytes.

The 'Hidden Variable' is the true mass of the solvent, which must be derived by subtracting the solute's mass from the total solution mass.

Students frequently fall into the trap of approximating molality as molarity (yielding 16.7%) or using the solution's mass as the solvent's mass (yielding 26.0%).

It forces the integration of concentration unit interconversion with the temperature-dependent van 't Hoff factor.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Some Basic Concepts of Chemistry - Class 11 Part 1
Concept	Concentration Unit Interconversion
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free