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Question #44657

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The Question

At $298\text{ K}$ , gaseous Boron trifluoride ( $\ce{BF3}$ ) reacts with Ammonia ( $\ce{NH3}$ ) to form the Lewis acid-base adduct $\ce{F3B\cdot NH3(s)}$ . Infrared spectroscopy reveals that the dominant B-F symmetric stretching frequency shifts from $\sim 1450\text{ cm}^{-1}$ in free $\ce{BF3}$ to $\sim 1100\text{ cm}^{-1}$ in the adduct. Assuming the reduced mass ( $\mu$ ) of the B-F oscillator remains approximately constant, which of the following correctly correlates the dimensional shift in the B-F bond stretching force constant ( $k_{BF}$ ) with the underlying electronic and structural changes?

Options

A.
$k_{BF}$ decreases by a factor of $\sim 1.7$ ; the B-F bond length increases because the $sp^2 \rightarrow sp^3$ rehybridization of Boron eliminates $p\pi-p\pi$ back-bonding, reducing the effective bond order.
B.
$k_{BF}$ decreases by a factor of $\sim 1.3$ ; the B-F bond length increases due to enhanced steric crowding in the tetrahedral geometry, which forces the fluorine atoms apart without altering the bond order.
C.
$k_{BF}$ increases by a factor of $\sim 1.7$ ; the B-F bond length decreases because the dative $\ce{N \rightarrow B}$ bond increases the electron density on Boron, strengthening the B-F $\sigma$ -bonds via increased $s$ -character.
D.
$k_{BF}$ decreases by a factor of $\sim 0.76$ ; the B-F bond length remains constant, but the force constant drops due to the $+I$ effect of the $\ce{NH3}$ group destabilizing the B-F $\sigma$ -bond.

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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

Dimensional Consistency of Constants|Back Bonding Strength|Hybridization and Geometry

Why This Question Is Tricky

Common Mistakes

This question tests the intersection of Chemical Bonding and Physical Spectroscopy.

The 'trap' lies in two areas: mathematically, students often forget that the force constant scales with the square of the frequency (leading to the distractor 1.3 or 0.76); chemically, students often attribute bond length changes purely to VSEPR steric repulsions (Option B) rather than the quantum mechanical loss of $p\pi-p\pi$ back-bonding.

The problem forces the student to reconcile the dimensional shift in the force constant with the exact electronic mechanism (hybridization change quenching the partial pi-character).

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Some Basic Concepts of Chemistry - Class 11 Part 1
Concept	Dimensional Consistency of Constants
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free