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Question #44204

Difficulty: 8/10 | 🟢 Free

The Question

An advanced organic chemistry student investigates the thermodynamics of reversible carbonyl addition reactions. They measure the equilibrium constants ( $K_1$ , $K_2$ , and $K_3$ ) for the acid-catalyzed formation of diethyl ketals from cyclobutanone (I), cyclopentanone (II), and cyclohexanone (III), respectively, using absolute ethanol at 298 K in a closed system. Given that the standard free energy of reaction ( $\Delta G^\circ$ ) is dictated by the Internal Strain (I-strain) theory during the sp $^2 \rightleftharpoons$ sp $^3$ transition, determine the correct mathematical inequality relating these equilibrium constants.

Options

A.
$K_1 > K_3 > K_2$
B.
$K_1 > K_2 > K_3$
C.
$K_3 > K_1 > K_2$
D.
$K_2 > K_3 > K_1$

Check Your Answer

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

Bond Angle Variations|Hydrate Stability vs. Carbonyl|Esterification Reversibility

Why This Question Is Tricky

Common Mistakes

The question tests the student's understanding of Internal Strain (I-strain) theory in cyclic systems, specifically the thermodynamic driving forces behind the sp2 to sp3 transition.

A common trap is assuming that the 5-membered ring (cyclopentanone), having an internal angle of 108° (closest to the sp3 ideal of 109.5°), would most readily undergo addition.

However, this ignores the hidden variable of torsional (eclipsing) strain.

The sp2 hybridized state in cyclopentanone is thermodynamically favored because it relieves the severe eclipsing interactions present in the fully sp3 hybridized cyclopentane ring.

Conversely, cyclohexanone favors the sp3 state because it achieves a perfectly staggered chair conformation, relieving the partial eclipsing strain of the sp2 state.

This exception to simple angle-based inductive reasoning is a hallmark of advanced organic thermodynamics.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Chemical Bonding and Molecular Structure - Class 11 Part 1
Concept	Bond Angle Variations
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free