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Question #44763

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The Question

The transport of alkali metal cations ( $M^+$ ) is evaluated in two distinct solvent systems at $298\text{ K}$ :

System $\alpha$ : Pure water (analogous to the hydrophilic environment of Vitamin C). System $\beta$ : A weakly coordinating, sterically bulky semi-polar solvent (analogous to the hydrophobic lipid environment of Vitamin A), where effective solvation shells cannot form around the cations.

Let $\lambda^\circ_\alpha(M^+)$ and $\lambda^\circ_\beta(M^+)$ represent the limiting ionic molar conductivities in systems $\alpha$ and $\beta$ , respectively. Identify the correct relationship for the conductivity trends and the dominant physical parameter governing the mobility in System $\beta$ .

Options

A.
$\lambda^\circ_\alpha$ : $Cs^+ > K^+ > Na^+ > Li^+$ ; $\lambda^\circ_\beta$ : $Li^+ > Na^+ > K^+ > Cs^+$ ; Parameter in $\beta$ : Bare crystallographic radius
B.
$\lambda^\circ_\alpha$ : $Li^+ > Na^+ > K^+ > Cs^+$ ; $\lambda^\circ_\beta$ : $Cs^+ > K^+ > Na^+ > Li^+$ ; Parameter in $\beta$ : Effective solvated radius
C.
$\lambda^\circ_\alpha$ : $Cs^+ > K^+ > Na^+ > Li^+$ ; $\lambda^\circ_\beta$ : $Li^+ > Na^+ > K^+ > Cs^+$ ; Parameter in $\beta$ : Maximum ion-dipole stabilization energy
D.
$\lambda^\circ_\alpha$ : $Cs^+ > K^+ > Na^+ > Li^+$ ; $\lambda^\circ_\beta$ : $Cs^+ > K^+ > Na^+ > Li^+$ ; Parameter in $\beta$ : Solvent viscosity

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Mechanism_Trap

Don't get tricked by the process! Learn the mechanical traps used in competitive exam questions.

Concepts Behind This Question

Molar Conductivity Trend|Vitamin Solubility Logic

Why This Question Is Tricky

Common Mistakes

The trap tests the assumption that $Li^+$ always has the lowest conductivity due to its high charge density.

Students often memorize the aqueous trend ( $Cs^+ > Li^+$ ) without understanding that it is entirely dependent on the formation of a hydration sphere.

By shifting the environment to a weakly coordinating, lipid-like solvent (using the Vitamin A/C analogy to hint at hydrophobic vs hydrophilic domains), the 'hidden variable'—the solvent's ability to form a solvation shell—is removed.

This exposes the bare crystallographic radius as the sole determinant of Stokes' drag, perfectly inverting the standard aqueous trend.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Electrochemistry - Class 12
Concept	Molar Conductivity Trend
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free