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Question #99864

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The Question

A neutral, homoleptic carbonyl complex of a first-row transition metal $M$ (Atomic mass $\approx 51 \text{ u}$ ) contains $32.90\%$ carbon by mass. A solution prepared by dissolving $2.19 \text{ g}$ of this complex in $100 \text{ g}$ of benzene freezes at $5.018^\circ\text{C}$ . The freezing point of pure benzene is $5.530^\circ\text{C}$ and its cryoscopic constant is $K_f = 5.12 \text{ K kg mol}^{-1}$ .

Assuming ideal behavior in solution, determine the molecular formula of the complex and the Effective Atomic Number (EAN) of the metal center.

Options

A.
$\ce{M(CO)6}$ , 35
B.
$\ce{M2(CO)12}$ , 36
C.
$\ce{M(CO)5}$ , 33
D.
$\ce{M2(CO)10}$ , 34

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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

Empirical vs Molecular Formula|EAN Rule (Sidgwick's Rule)|d-orbital contraction

Why This Question Is Tricky

Examiner Levers

Assumed Constant Trap

Requires a constant not explicitly given (e.g., specific heat of water).

Difficulty Boost : +3

Common Mistakes

The problem tests the hierarchy of chemical principles: empirical analytical data always supersedes theoretical heuristics like the 18-electron (EAN) rule.

Students often blindly force complexes to obey the EAN rule by dimerizing them (e.g., assuming $\ce{M2(CO)12}$ to reach EAN = 36).

Here, the cryoscopic data explicitly proves the complex is mononuclear ( $\ce{V(CO)6}$ ).

The 'hidden variable' is the d-orbital contraction and steric crowding in Vanadium, which prevents dimerization, leaving it as a rare, stable 17-electron complex.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Some Basic Concepts of Chemistry - Class 11 Part 1
Concept	Empirical vs Molecular Formula
Difficulty	5
Cognitive Load	6
Target Solve Time	150 sec
Access	Free