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Question #44242

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The Question

Consider the gas-phase Diels-Alder cycloaddition: $\ce{1,3-Butadiene(g) + Ethene(g) -> Cyclohexene(g)}$ at $298\text{ K}$ . The standard thermodynamic parameters for the reaction are $\Delta H^\circ = -167\text{ kJ mol}^{-1}$ and $\Delta S^\circ = -180\text{ J K}^{-1}\text{mol}^{-1}$ . Despite being thermodynamically favorable, the reaction does not proceed at an observable rate at $298\text{ K}$ . Experimental kinetic data reveals an anomalously low Arrhenius pre-exponential factor $A \approx 10^6\text{ M}^{-1}\text{s}^{-1}$ (compared to a typical collision frequency of $\sim 10^{11}\text{ M}^{-1}\text{s}^{-1}$ ). Based on Transition State Theory, which of the following correctly evaluates the standard Gibbs free energy ( $\Delta G^\circ_{298}$ ) and identifies the primary kinetic bottleneck?

Options

A.
$\Delta G^\circ_{298} = -113.36\text{ kJ mol}^{-1}$ ; The kinetic bottleneck is a highly negative entropy of activation ( $\Delta S^\ddagger \ll 0$ ) due to a rigid, highly ordered cyclic transition state, which drastically reduces $A$ and increases $\Delta G^\ddagger$ .
B.
$\Delta G^\circ_{298} = +113.36\text{ kJ mol}^{-1}$ ; The reaction is thermodynamically forbidden at $298\text{ K}$ , and the low pre-exponential factor $A$ is a result of the endergonic nature of the transition state.
C.
$\Delta G^\circ_{298} = -113.36\text{ kJ mol}^{-1}$ ; The kinetic bottleneck is a highly positive entropy of activation ( $\Delta S^\ddagger \gg 0$ ), which exponentially decreases the pre-exponential factor $A$ according to the Eyring equation.
D.
$\Delta G^\circ_{298} = -220.64\text{ kJ mol}^{-1}$ ; The reaction is spontaneous, but the kinetic inertness arises because the activation energy ( $E_a$ ) is equal to the standard enthalpy of reaction ( $\Delta H^\circ$ ), trapping the reactants.

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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

Spontaneity Criteria|Activation Energy Trap|Steady State Approximation

Why This Question Is Tricky

Common Mistakes

This question tests the decoupling of thermodynamic spontaneity ( $\Delta G^\circ$ ) from kinetic feasibility ( $\Delta G^\ddagger$ ).

The primary trap is conflating the reaction entropy ( $\Delta S^\circ$ ) with the entropy of activation ( $\Delta S^\ddagger$ ).

Furthermore, it tests the mathematical relationship in the Eyring equation: students often incorrectly assume that a 'low' pre-exponential factor $A$ is caused by a 'positive' entropy of activation, failing to realize that $A \propto e^{\Delta S^\ddagger / R}$ .

The chemical context (Diels-Alder) perfectly illustrates a scenario where a strong enthalpic driving force is bottlenecked by the severe entropic penalty of forming a highly ordered transition state.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Thermodynamics - Class 11 Part 1
Concept	Spontaneity Criteria
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free