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Question #44313

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The Question

Lithium and magnesium exhibit a diagonal relationship, characterized by the high polarizing power of their cations, which leads to significant covalent character and ion-pairing of their salts in non-ideal solvents. In a mixed aqueous-dioxane solvent ( $K_f = 4.0 \text{ K kg mol}^{-1}$ , $T_f^\circ = 273.15 \text{ K}$ ), a $0.15 \text{ molal}$ solution of \ce{LiCl} exhibits a freezing point of $272.25 \text{ K}$ . In the same solvent, \ce{MgCl2} undergoes complete primary dissociation into \ce{[MgCl]+} and \ce{Cl-}. The secondary dissociation of \ce{[MgCl]+} into \ce{Mg^{2+}} and \ce{Cl-} has a degree of dissociation ( $\alpha_2$ ) exactly equal to the degree of dissociation ( $\alpha$ ) of \ce{LiCl} in its $0.15 \text{ molal}$ solution. Assuming no other complexation occurs, what is the freezing point depression ( $\Delta T_f$ ) of a $0.10 \text{ molal}$ solution of \ce{MgCl2} in this solvent?

Options

A.
$1.00 \text{ K}$
B.
$0.80 \text{ K}$
C.
$1.20 \text{ K}$
D.
$0.60 \text{ K}$

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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

Diagonal Relationship|Van’t Hoff Factor (i) Application|Freezing Point Depression (Pure Solvent)

Why This Question Is Tricky

Common Mistakes

This question tests the intersection of Inorganic periodic trends (Diagonal Relationship, Fajans' Rules) and Physical Chemistry (Colligative Properties).

The 'Hidden Variable' is the solvent-dependent ion-pairing caused by the high charge density of \ce{Li+} and \ce{Mg^{2+}}.

Students often fall into the trap of assuming strong electrolytes always have $i=2$ or $i=3$ .

Furthermore, the problem tests the stepwise dissociation mechanism of \ce{MgCl2}.

A common error is applying the degree of dissociation ( $\alpha=0.5$ ) to the overall reaction \ce{MgCl2 \rightleftharpoons Mg^{2+} + 2Cl-}, which incorrectly yields $i = 1 + 2(0.5) = 2.0$ and a $\Delta T_f$ of $0.80 \text{ K}$ .

Quick Facts About This Question

Question Information

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