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Question #99842

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The Question

The C-O stretching frequency ( $\bar{\nu}$ ) is related to the bond force constant ( $k$ ) by the harmonic oscillator model, where $k$ is directly proportional to the Effective Bond Order (EBO). The stretching frequency of free \ce{CO} is $2143 \text{ cm}^{-1}$ , and its EBO is defined as exactly $3.00$ .

Consider the following species: (I) Free \ce{CO} (II) \ce{CO3^{2-}} (III) \ce{[V(CO)6]^-} ( $\bar{\nu}_{\ce{CO}} = 1860 \text{ cm}^{-1}$ ) (IV) \ce{H3B <- CO} ( $\bar{\nu}_{\ce{CO}} = 2165 \text{ cm}^{-1}$ )

Assuming the reduced mass of the C-O oscillator remains constant, calculate the approximate EBO of the C-O bond in species (III) and (IV) respectively. Furthermore, determine the correct increasing order of C-O bond lengths ( $d_{\ce{C-O}}$ ) for the four species.

Options

A.
$\text{EBO(III)} = 2.26$ , $\text{EBO(IV)} = 3.06$ ; $d_{\ce{C-O}}$ order: $\text{IV} < \text{I} < \text{III} < \text{II}$
B.
$\text{EBO(III)} = 2.60$ , $\text{EBO(IV)} = 3.03$ ; $d_{\ce{C-O}}$ order: $\text{IV} < \text{I} < \text{III} < \text{II}$
C.
$\text{EBO(III)} = 2.26$ , $\text{EBO(IV)} = 3.06$ ; $d_{\ce{C-O}}$ order: $\text{I} < \text{IV} < \text{III} < \text{II}$
D.
$\text{EBO(III)} = 2.60$ , $\text{EBO(IV)} = 2.97$ ; $d_{\ce{C-O}}$ order: $\text{I} < \text{III} < \text{IV} < \text{II}$

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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

Precision in Atomic Mass Units|Complex Ion Oxidation States|Valence Bond Theory Hybridization

Why This Question Is Tricky

Examiner Levers

Extraneous Data

Provides unnecessary variables (Red Herrings) to test conceptual focus.

Difficulty Boost : +3

Assumed Constant Trap

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

Difficulty Boost : +3

Common Mistakes

This problem tests the 'Hidden Variable' of the non-linear relationship between stretching frequency and bond order ( $\text{EBO} \propto \bar{\nu}^2$ , not $\bar{\nu}$ ), trapping students who use simple proportionality (yielding 2.60).

Furthermore, it targets a major 'Chemical Exception' in Coordination Chemistry: while metal carbonyls weaken the C-O bond via $\pi$ -backbonding, coordination to a pure Lewis acid like \ce{BH3} actually strengthens the C-O bond.

This occurs because the lone pair donated by \ce{CO} resides in the $5\sigma$ orbital, which has slight antibonding character.

Depleting it increases the effective bond order above 3.0, defying the standard MO filling assumption that free \ce{N2} or \ce{CO} represents the absolute maximum bond order of 3.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Some Basic Concepts of Chemistry - Class 11 Part 1
Concept	Precision in Atomic Mass Units
Difficulty	8
Cognitive Load	8
Target Solve Time	180 sec
Access	Free