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Question #44467

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The Question

The electrophilic addition of \ce{Br2} to 4-\textit{tert}-butylcyclohexene in \ce{CCl4} at 300 K300\text{ K} yields two possible \textit{trans}-dibromide stereoisomers: the diaxial product (A) and the diequatorial product (B). The thermodynamic parameters for the respective reaction pathways are given below:

\textbf{Pathway A (Diaxial):} ΔH‡=35.0 kJ/mol\Delta H^\ddagger = 35.0\text{ kJ/mol}, ΔS‡=−20.0 J K−1mol−1\Delta S^\ddagger = -20.0\text{ J K}^{-1}\text{mol}^{-1} ΔH∘=−110.0 kJ/mol\Delta H^\circ = -110.0\text{ kJ/mol}, ΔS∘=−100.0 J K−1mol−1\Delta S^\circ = -100.0\text{ J K}^{-1}\text{mol}^{-1}

\textbf{Pathway B (Diequatorial):} ΔH‡=55.0 kJ/mol\Delta H^\ddagger = 55.0\text{ kJ/mol}, ΔS‡=−15.0 J K−1mol−1\Delta S^\ddagger = -15.0\text{ J K}^{-1}\text{mol}^{-1} ΔH∘=−130.0 kJ/mol\Delta H^\circ = -130.0\text{ kJ/mol}, ΔS∘=−100.0 J K−1mol−1\Delta S^\circ = -100.0\text{ J K}^{-1}\text{mol}^{-1}

Determine the standard Gibbs free energy of reaction (ΔG∘\Delta G^\circ) for the formation of the major product at 300 K300\text{ K}.

Options

  • A.

    -80.0 kJ/mol

  • B.

    -100.0 kJ/mol

  • C.

    41.0 kJ/mol

  • D.

    59.5 kJ/mol

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Step-by-Step Solution

Explanation

How the Examiner Thinks

Numerical_Precision

Improve calculation stamina and avoid rounding errors in high-stakes competitive examinations.

Concepts Behind This Question

Stereochemical Outcome of Halogenation|Gibbs Energy and Spontaneity|State vs Path Functions

Why This Question Is Tricky

Common Mistakes

The question tests the student's ability to distinguish between kinetic and thermodynamic control in the context of stereochemical halogenation.

The 'hidden variable' is the irreversibility of bromination at room temperature, which dictates kinetic control.

Students often calculate the overall reaction spontaneity (ΔG∘\Delta G^\circ) and incorrectly assume that the most thermodynamically stable product (diequatorial, ΔG∘=−100.0 kJ/mol\Delta G^\circ = -100.0\text{ kJ/mol}) will be the major product.

However, the rigid conformation of 4-tert-butylcyclohexene forces the bromonium ion opening to proceed via a lower-energy chair-like transition state (Fuerst-Plattner rule), leading to the less stable diaxial product.

By calculating ΔG‡\Delta G^\ddagger, students must identify the kinetically favored pathway and then report its corresponding ΔG∘\Delta G^\circ.

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Question Information

SubjectChemistry
ChapterHydrocarbons - Class 11 Part 2
ConceptStereochemical Outcome of Halogenation
Difficulty8
Cognitive Load7
Target Solve Time160 sec
AccessFree