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Question #44195

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The Question

An equimolar aqueous mixture of $\ce{La^{3+}}$ and $\ce{Lu^{3+}}$ is subjected to cation-exchange chromatography using a synthetic sulfonic acid resin. An aqueous ammonium citrate buffer is used as the eluent. The metal ion that elutes first is isolated and converted to its anhydrous chloride salt, $\ce{M_ACl3}$ , while the later eluting metal is converted to $\ce{M_BCl3}$ .

Separate aqueous solutions of $\ce{M_ACl3}$ and $\ce{M_BCl3}$ are prepared at an identical nominal molality of $0.5 \text{ mol kg}^{-1}$ . In these non-ideal solutions, the extensive formation of primary hydration spheres significantly reduces the mass of 'free' solvent, causing deviations from ideal colligative behavior. Let $i_A$ and $i_B$ be the apparent van't Hoff factors derived from their respective freezing point depressions.

Which of the following correctly identifies $\ce{M_A}$ and the relationship between $i_A$ and $i_B$ ?

Options

A.
$\ce{M_A} = \ce{Lu}$ ; $i_A > i_B$
B.
$\ce{M_A} = \ce{Lu}$ ; $i_A < i_B$
C.
$\ce{M_A} = \ce{La}$ ; $i_A > i_B$
D.
$\ce{M_A} = \ce{La}$ ; $i_A < i_B$

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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

Periodic Properties of Lanthanides|Molecular Mass Abnormalities|Solutions

Why This Question Is Tricky

Common Mistakes

This question tests a dual-layered 'Chemical Exception' regarding the Lanthanide Contraction.

Students often mistakenly assume that a smaller bare ionic radius (Lu3+) leads to stronger binding in the resin and greater ion-pairing in solution (which would lower the van't Hoff factor).

The trap is failing to account for the 'Hydration Sphere Reversal': the smallest bare ion becomes the largest hydrated ion.

This causes it to elute first in chromatography and, crucially, to tie up more solvent molecules in aqueous solution.

At moderate concentrations, this solvent depletion overrides Debye-Hückel ion-pairing effects, causing an anomalous increase in the effective molality and the apparent van't Hoff factor for the heavier lanthanide.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Classification of Elements and Periodicity in Properties - Class 11 Part 1
Concept	Periodic Properties of Lanthanides
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free