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Question #45059

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The Question

Consider the conformational analysis of \ce{1,2-difluoroethane} and \ce{1,2-dichloroethane} in the gas phase at $298\text{ K}$ .

Let $W$ be the number of antiperiplanar $\sigma_{C-H} \rightarrow \sigma^*_{C-X}$ hyperconjugative interactions in the most stable conformer of \ce{1,2-difluoroethane}. Let $X$ be the number of antiperiplanar $\sigma_{C-H} \rightarrow \sigma^*_{C-X}$ hyperconjugative interactions in the most stable conformer of \ce{1,2-dichloroethane}. Let $Y$ be the number of gauche $X \cdots X$ interactions in the most stable conformer of \ce{1,2-difluoroethane}. Let $Z$ be the number of gauche $X \cdots X$ interactions in the most stable conformer of \ce{1,2-dichloroethane}.

(where $X$ represents the respective halogen atom in each molecule).

Determine the value of $2W + 3X + Y + Z$ .

Options

A.
3
B.
5
C.
7
D.
12

Check Your Answer

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

Hyperconjugation Logic|Alkane Conformation Energy Barriers

Why This Question Is Tricky

Common Mistakes

Tests the 'Gauche Effect' exception to standard steric hindrance rules.

Students often assume the anti-conformation is universally the most stable for 1,2-disubstituted alkanes due to minimized steric and dipole repulsion.

However, for highly electronegative substituents like fluorine, the gauche conformation is thermodynamically preferred in the gas phase due to stabilizing stereoelectronic hyperconjugation ( $\sigma_{C-H} \rightarrow \sigma^*_{C-F}$ ).

The trap is failing to differentiate the conformational preference of 1,2-difluoroethane (gauche) from 1,2-dichloroethane (anti) and incorrectly counting the orbital overlaps.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Organic Chemistry – Some Basic Principles and Techniques - Class 11 Part 2
Concept	Hyperconjugation Logic
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free