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Question #44582

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The Question

Consider the following three octahedral complexes at 298 K: $P = \ce{[Cr(H2O)6]^{3+}}$ $Q = \ce{[Fe(CN)6]^{3-}}$ $R = \ce{[Ni(en)3]^{2+}}$ (where $\ce{en} = \text{ethylenediamine}$ )

A common, yet flawed, heuristic derived from a simplified Valence Bond Theory (VBT) states: 'Strong-field ligands always force spin-pairing to form inner-orbital ( $d^2sp^3$ ) complexes, while weak-field ligands always result in outer-orbital ( $sp^3d^2$ ) complexes.'

Which of the following correctly identifies the actual hybridization and spin-only magnetic moment ( $\mu_{eff}$ ) for $P$ , $Q$ , and $R$ , thereby demonstrating the limitations of this heuristic?

Options

A.
$P$ : $d^2sp^3$ , $3.87\text{ BM} \mid Q$ : $d^2sp^3$ , $1.73\text{ BM} \mid R$ : $sp^3d^2$ , $2.83\text{ BM}$
B.
$P$ : $sp^3d^2$ , $3.87\text{ BM} \mid Q$ : $d^2sp^3$ , $1.73\text{ BM} \mid R$ : $d^2sp^3$ , $0.00\text{ BM}$
C.
$P$ : $sp^3d^2$ , $3.87\text{ BM} \mid Q$ : $sp^3d^2$ , $5.92\text{ BM} \mid R$ : $d^2sp^3$ , $2.83\text{ BM}$
D.
$P$ : $d^2sp^3$ , $3.87\text{ BM} \mid Q$ : $sp^3d^2$ , $5.92\text{ BM} \mid R$ : $sp^3d^2$ , $2.83\text{ BM}$

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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

Valence Bond Theory Hybridization|Spin-Only Magnetic Moment|Crystal Field Splitting (Octahedral)

Why This Question Is Tricky

Common Mistakes

The question tests the fundamental limitation of Valence Bond Theory (VBT) and the common student misconception that 'strong-field ligands always form inner-orbital complexes' and 'weak-field ligands always form outer-orbital complexes.' By selecting $d^3$ ( $\ce{Cr^{3+}}$ ) and $d^8$ ( $\ce{Ni^{2+}}$ ) systems, the problem exposes that for these specific electronic configurations, the availability of inner $d$ -orbitals dictates the hybridization ( $d^2sp^3$ for $d^3$ , $sp^3d^2$ for $d^8$ ), completely independent of the spectrochemical series.

The $d^5$ system ( $\ce{Fe^{3+}}$ ) acts as a control where the heuristic actually works, further trapping students who apply the rule blindly across all options.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Coordination Compounds - Class 12
Concept	Valence Bond Theory Hybridization
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free