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Question #44581

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The Question

The standard Valence Bond Theory (VBT) assigns identical $d^2sp^3$ hybridization to the central metals in the isoelectronic octahedral series: $\ce{[V(CO)6]^-}$ (I), $\ce{Cr(CO)6}$ (II), and $\ce{[Mn(CO)6]^+}$ (III). However, VBT fails to account for the dynamic electron density shifts caused by synergic bonding.

Let $k_{MC}$ and $k_{CO}$ represent the stretching force constants for the Metal-Carbon and Carbon-Oxygen bonds, respectively.

Consider the substitution of one CO ligand in $\ce{Cr(CO)6}$ by trimethylphosphine ( $\ce{PMe3}$ ) to form $\ce{[Cr(CO)5(PMe3)]}$ .

Which of the following statements correctly correlates the force constants across the isoelectronic series and accurately describes the electronic effect of the $\ce{PMe3}$ substitution on the remaining CO ligands?

Options

A.
$k_{MC}(\text{I}) > k_{MC}(\text{II}) > k_{MC}(\text{III})$ and $k_{CO}(\text{I}) < k_{CO}(\text{II}) < k_{CO}(\text{III})$ . In $\ce{[Cr(CO)5(PMe3)]}$ , the $k_{CO}$ of the remaining CO ligands decreases compared to $\ce{Cr(CO)6}$ because $\ce{PMe3}$ is a stronger $\sigma$ -donor and weaker $\pi$ -acceptor than CO.
B.
$k_{MC}(\text{I}) < k_{MC}(\text{II}) < k_{MC}(\text{III})$ and $k_{CO}(\text{I}) > k_{CO}(\text{II}) > k_{CO}(\text{III})$ . In $\ce{[Cr(CO)5(PMe3)]}$ , the $k_{CO}$ of the remaining CO ligands increases compared to $\ce{Cr(CO)6}$ because $\ce{PMe3}$ withdraws electron density via $d\pi-d\pi$ back-bonding.
C.
$k_{MC}(\text{I}) > k_{MC}(\text{II}) > k_{MC}(\text{III})$ and $k_{CO}(\text{I}) < k_{CO}(\text{II}) < k_{CO}(\text{III})$ . In $\ce{[Cr(CO)5(PMe3)]}$ , the $k_{CO}$ of the remaining CO ligands increases because the formal oxidation state of Cr remains zero, but steric hindrance from $\ce{PMe3}$ elongates the M-C bonds.
D.
$k_{MC}(\text{I}) = k_{MC}(\text{II}) = k_{MC}(\text{III})$ as VBT predicts identical $d^2sp^3$ hybridization. In $\ce{[Cr(CO)5(PMe3)]}$ , the $k_{CO}$ remains unchanged as the Effective Atomic Number (EAN) of Cr remains 36.

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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

Valence Bond Theory Hybridization|Synergic Bonding in Carbonyls|Oxidation State Traps

Why This Question Is Tricky

Common Mistakes

The question tests the 'Hidden Variable' of synergic bonding which overrides the static geometric predictions of Valence Bond Theory (VBT).

Students often assume that identical hybridization ( $d^2sp^3$ ) and EAN compliance imply identical bond parameters (Option D trap).

Furthermore, it tests the electronic effects of spectator ligands ( $\ce{PMe3}$ ) on the primary ligands (CO), requiring students to differentiate between $\sigma$ -donor and $\pi$ -acceptor abilities and their impact on the metal's electron density and subsequent back-bonding.

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