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Question #44602

Difficulty: 8/10 | 🟢 Free

The Question

Consider the diamagnetic polynuclear metal carbonyl $\ce{Fe2(CO)9}$ at $298\text{ K}$ . Let $x$ be the number of metal-metal bonds, $y$ be the number of bridging carbonyl ligands, and $z$ be the Effective Atomic Number (EAN) of each iron center. If $\nu_t$ and $\nu_b$ represent the infrared C-O stretching frequencies of the terminal and bridging carbonyl ligands respectively, which of the following options correctly identifies $(x, y, z)$ and the relationship between the stretching frequencies?

Options

A.
$x = 1$ , $y = 3$ , $z = 36$ , $\nu_t > \nu_b$
B.
$x = 1$ , $y = 3$ , $z = 35$ , $\nu_t > \nu_b$
C.
$x = 1$ , $y = 3$ , $z = 36$ , $\nu_b > \nu_t$
D.
$x = 0$ , $y = 3$ , $z = 35$ , $\nu_t > \nu_b$

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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

Synergic Bonding in Carbonyls|EAN Rule (Sidgwick's Rule)

Why This Question Is Tricky

Common Mistakes

This question tests the validity of the EAN rule in polynuclear metal carbonyls and the nuances of synergic bonding.

The primary trap is the 'Hidden Electron Count' where students calculate the EAN by treating the metal atoms as isolated centers, forgetting that the Fe-Fe metal-metal bond contributes 1 electron to each metal's count.

This leads to an incorrect EAN of 35 (Option B or D).

Additionally, it tests the stereochemical and electronic consequence of bridging ligands: students often mistakenly assume bridging carbonyls have stronger C-O bonds due to being 'anchored' by two metals, failing to realize that dual back-bonding populates the $\pi^*$ antibonding orbital more heavily, thereby reducing the bond order and stretching frequency (Option C trap).

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Coordination Compounds - Class 12
Concept	Synergic Bonding in Carbonyls
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free