Before You Begin

Question #44684

Difficulty: 8/10 | 🟢 Free

The Question

Group 4 transition metals $M$ ( $M = \ce{Zr}, \ce{Hf}$ ) form stable octahedral complex anions $\ce{[MCl6]^{x-}}$ in their highest common oxidation state. The potassium salt of this complex, $\ce{K_x[MCl6]}$ , crystallizes in a cubic lattice where the complex anions form a face-centered cubic (FCC) array and $\ce{K+}$ ions occupy the tetrahedral voids. At $298\text{ K}$ , the density of the Zirconium salt is $2.80\text{ g cm}^{-3}$ . Given the atomic masses (in $\text{g mol}^{-1}$ ): $\ce{K} = 39.0$ , $\ce{Cl} = 35.5$ , $\ce{Zr} = 91.0$ , $\ce{Hf} = 178.5$ . Assuming ideal behavior and accounting for the post-lanthanoid radii equality, what is the theoretical density of the Hafnium salt?

Options

A.
$3.44\text{ g cm}^{-3}$
B.
$3.38\text{ g cm}^{-3}$
C.
$5.49\text{ g cm}^{-3}$
D.
$2.80\text{ g cm}^{-3}$

Check Your Answer

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

Density-Volume-Mass Relationship|Post-Lanthanoid Radii Equality|Complex Ion Oxidation States

Why This Question Is Tricky

Common Mistakes

This problem tests the synthesis of periodic trends (Lanthanoid Contraction) with solid-state chemistry (Density-Volume-Mass relationship) and coordination chemistry (Oxidation states).

The primary trap is the assumption that the unit cell volume changes with the heavier 5d element.

Students must recognize that the post-lanthanoid radii equality renders the unit cell volume invariant, making the density strictly a function of the molar mass ratio.

Secondary traps include misidentifying the oxidation state of Group 4 metals (leading to $\ce{K3[MCl6]}$ and a density of $3.38\text{ g cm}^{-3}$ ) or scaling density solely by the atomic mass of the central metal ( $5.49\text{ g cm}^{-3}$ ).

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Some Basic Concepts of Chemistry - Class 11 Part 1
Concept	Density-Volume-Mass Relationship
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free