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Question #44187

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The Question

According to the Coulson-Moffitt 'bent bond' model of cyclopropane ( $\ce{C3H6}$ ) at $298\text{ K}$ , the $\ce{C-C}$ bonds are formed by orbitals with high $p$ -character to minimize angle strain, forcing the bonding electron density to be highly localized outside the internuclear axis.

If this spatial confinement reduces the transverse positional uncertainty ( $\Delta x$ ) of the $\ce{C-C}$ bonding electrons by a factor of $1/2$ relative to an unstrained $\ce{C-C}$ bond in ethane, by what factor does the minimum zero-point kinetic energy of these electrons increase (based on the Heisenberg Uncertainty Principle), and what is the idealized fractional $s$ -character of the $\ce{C-C}$ bonding orbitals in this model?

Options

A.
$4 \text{ ; } \approx 17\%$
B.
$2 \text{ ; } \approx 33\%$
C.
$4 \text{ ; } \approx 25\%$
D.
$2 \text{ ; } \approx 17\%$

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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

Heisenberg Uncertainty Principle|Hybridization and Geometry|Alkane Conformation Energy Barriers|Cycloalkane Ring Strain

Why This Question Is Tricky

Common Mistakes

This question tests the 'electron density localization fallacy' by bridging Quantum Mechanics and Organic Chemistry.

Students often rigidly apply $sp^3$ hybridization ( $25\%$ $s$ -character) to all saturated alkanes, ignoring that severe ring strain forces rehybridization (Bent/Banana bonds).

Furthermore, they rarely connect steric/angle strain to its quantum mechanical root: spatial confinement of electrons ( $\Delta x$ ) leading to a quadratic spike in zero-point kinetic energy via the Heisenberg Uncertainty Principle.

Option B traps students who assume a linear relationship for kinetic energy and mistakenly assign the $sp^2$ hybridization of the $\ce{C-H}$ bonds to the $\ce{C-C}$ bonds.

Option C traps those who correctly calculate the energy factor but default to standard $sp^3$ hybridization.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Structure of Atom - Class 11 Part 1
Concept	Heisenberg Uncertainty Principle
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free