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Question #44826

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The Question

Kinetic studies of the nucleophilic addition of $\ce{CN^-}$ to propan-2-one ( $P$ ) and 2,2,4,4-tetramethylpentan-3-one ( $Q$ ) in an aqueous buffer at $298\text{ K}$ reveal that the rate constant ratio is $\frac{k_P}{k_Q} = 10^4$ . Computational analysis indicates that the activation energy ( $E_a$ ) for both processes is virtually identical. Calculate the difference in the entropy of activation, $(\Delta S^\ddagger_P - \Delta S^\ddagger_Q)$ , and identify the primary physical rationale for the kinetic inertness of $Q$ . (Given: $R = 8.314\text{ J K}^{-1}\text{ mol}^{-1}$ , $\ln 10 = 2.303$ )

Options

A.
$+76.6\text{ J K}^{-1}\text{ mol}^{-1}$ ; Bulky tert-butyl groups in $Q$ restrict the solid angle of nucleophilic attack, drastically lowering the Arrhenius pre-exponential factor ( $A$ ).
B.
$-76.6\text{ J K}^{-1}\text{ mol}^{-1}$ ; Bulky tert-butyl groups in $Q$ restrict the solid angle of nucleophilic attack, drastically lowering the Arrhenius pre-exponential factor ( $A$ ).
C.
$+76.6\text{ J K}^{-1}\text{ mol}^{-1}$ ; The $sp^2 \rightarrow sp^3$ rehybridization in $Q$ increases the activation energy ( $E_a$ ) due to severe steric crowding in the transition state.
D.
$+18.3\text{ J K}^{-1}\text{ mol}^{-1}$ ; The +I effect of tert-butyl groups reduces the electrophilicity of the carbonyl carbon, lowering the collision frequency ( $Z$ ).

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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

Arrhenius Pre-exponential Factor|Nucleophilic Addition Sterics

Why This Question Is Tricky

Common Mistakes

Students typically assume that a decrease in reaction rate is solely due to an increase in the activation energy ( $E_a$ ) caused by steric repulsion in the transition state.

This question tests the 'Hidden Variable' of the Arrhenius pre-exponential factor ( $A$ ) and its thermodynamic equivalent, the entropy of activation ( $\Delta S^\ddagger$ ).

By explicitly holding $E_a$ constant, the student is forced to recognize that bulky groups (like tert-butyl) restrict the solid angle of nucleophilic attack.

This geometric constraint drastically reduces the probability of a favorable collision orientation, thereby lowering $A$ and making the reaction kinetically inert despite a surmountable energetic barrier.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Chemical Kinetics - Class 12
Concept	Arrhenius Pre-exponential Factor
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free