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Question #44761

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The Question

A researcher investigates the limiting molar conductivities ( $\Lambda^\circ_m$ ) of the hypothetical unhydrolyzed strong electrolytes $Ti(NO_3)_4\text{(aq)}$ , $Zr(NO_3)_4\text{(aq)}$ , and $Hf(NO_3)_4\text{(aq)}$ at $298\text{ K}$ . The measured $\Lambda^\circ_m$ for $Zr(NO_3)_4\text{(aq)}$ is $486\text{ S cm}^2\text{ mol}^{-1}$ . Given that the limiting ionic conductivity of the nitrate ion, $\lambda^\circ_m(NO_3^-)$ , is $71.5\text{ S cm}^2\text{ mol}^{-1}$ , and considering the effects of the Lanthanoid contraction on hydration enthalpies, which of the following sets most accurately represents the theoretical limiting ionic conductivities ( $\lambda^\circ_m$ ) of the aqueous cations $Ti^{4+}$ , $Zr^{4+}$ , and $Hf^{4+}$ respectively?

Options

A.
$160,\ 200,\ 200\text{ S cm}^2\text{ mol}^{-1}$
B.
$240,\ 200,\ 200\text{ S cm}^2\text{ mol}^{-1}$
C.
$160,\ 200,\ 240\text{ S cm}^2\text{ mol}^{-1}$
D.
$240,\ 200,\ 160\text{ S cm}^2\text{ mol}^{-1}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Exception_Exposure

Learn to identify edge cases and boundary exceptions that JEE examiners hide in math problems.

Concepts Behind This Question

Molar Conductivity Trend|Post-Lanthanoid Radii Equality|Kohlrausch Law Infinite Dilution

Why This Question Is Tricky

Common Mistakes

The question tests the intersection of Kohlrausch's Law and periodic trends, specifically targeting the 'Lanthanoid Contraction' trap.

Students typically assume that ionic mobility increases linearly down a group as bare ionic radius increases (which decreases the hydrated radius).

However, the post-lanthanoid elements Zirconium and Hafnium possess nearly identical bare ionic radii due to poor shielding by 4f electrons.

This 'Hidden Variable' results in nearly identical charge densities, hydrated radii, and limiting molar conductivities for $Zr^{4+}$ and $Hf^{4+}$ .

Furthermore, it tests the counter-intuitive concept that a smaller bare ion ( $Ti^{4+}$ ) has a larger hydrated radius, resulting in lower ionic mobility.

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