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Question #44572

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The Question

A neutral coordination complex $\ce{X}$ with the formula $\ce{[M(NH3)4Cl2]}$ (where $\ce{M}$ is a 3d transition metal) exhibits a spin-only magnetic moment of $4.90 \text{ BM}$ at $298 \text{ K}$ . Spectroscopic analysis reveals that the complex lacks a $C_3$ axis of symmetry but possesses a principal $C_4$ axis. Which of the following statements correctly identifies the number of isolable geometric isomers of $\ce{X}$ at $298 \text{ K}$ and the underlying quantum mechanical rationale?

Options

A.
$2$ isomers (\textit{cis} and \textit{trans}); $\ce{M}$ is in a $d^6$ high-spin state ( $t_{2g}^4 e_g^2$ ), which undergoes only weak dynamic Jahn-Teller distortion, preserving the stability of both isomers under average $O_h$ symmetry.
B.
$1$ isomer (\textit{trans}); $\ce{M}$ is in a $d^4$ high-spin state ( $t_{2g}^3 e_g^1$ ), causing a strong static Jahn-Teller elongation that thermodynamically locks the weaker $\ce{Cl^-}$ ligands in the axial positions.
C.
$1$ isomer (\textit{cis}); $\ce{M}$ is in a $d^4$ low-spin state ( $t_{2g}^4 e_g^0$ ), causing a tetragonal compression that forces the stronger $\ce{NH3}$ ligands into the axial positions to maximize crystal field stabilization.
D.
$2$ isomers (\textit{cis} and \textit{trans}); the magnetic moment indicates a $d^4$ low-spin configuration, which lacks Jahn-Teller distortion in the $e_g$ set, allowing ideal $O_h$ symmetry and stable isomerism.

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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

Geometric Isomerism Requirements|Crystal Field Splitting (Octahedral)|Spin-Only Magnetic Moment

Why This Question Is Tricky

Common Mistakes

This question tests the intersection of Crystal Field Theory, Jahn-Teller distortion, and stereochemistry.

Students typically memorize that $\ce{[MA4B2]}$ complexes have two geometric isomers (cis and trans).

The trap is the magnetic moment ( $4.90 \text{ BM}$ ), which leaves two possibilities ( $d^4$ HS or $d^6$ HS).

The 'hidden variable' is the symmetry data, which proves a static tetragonal distortion ( $D_{4h}$ ).

Students must realize that strong JT distortion (from $d^4$ HS $e_g^1$ ) destroys the equivalence of the coordination sphere, making the cis isomer thermodynamically unstable and leaving only the trans isomer.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Coordination Compounds - Class 12
Concept	Geometric Isomerism Requirements
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free