Question

The correct order of the rate of reaction of the following reactants with nucleophile by \( \mathrm{S_N1} \) mechanism is: 
(Given: Structures I and II are rigid) 

• A. \( \text{III}<\text{I}<\text{II}<\text{IV} \)
• B. \( \text{I}<\text{II}<\text{III}<\text{IV} \)
• C. \( \text{II}<\text{I}<\text{III}<\text{IV} \)
• D. \( \text{IV}<\text{III}<\text{II}<\text{I} \)

Hint:

For \( \mathrm{S_N1} \) reactions, carbocation stability governs the rate; resonance stabilization dominates over hyperconjugation.

Answer 1

The Correct Option is C

Step 1: Key factor in \( \mathrm{S_N1} \) reaction.
The rate of an \( \mathrm{S_N1} \) reaction depends on the stability of the carbocation formed after the leaving group departs.
Step 2: Analyze each structure.
Structure II: Due to rigid bicyclic framework, carbocation formation is highly strained and least stable.
Structure I: Slightly less strained than II, but still rigid, hence carbocation is unstable.
Structure III: Forms a tertiary carbocation which is stabilized by hyperconjugation.
Structure IV: Forms a triphenylmethyl carbocation which is highly stabilized due to resonance with three phenyl rings.
Step 3: Arrange in increasing order of stability (and hence rate).
\[ \text{II}<\text{I}<\text{III}<\text{IV} \]
Final Answer: \[ \boxed{\text{II}<\text{I}<\text{III}<\text{IV}} \]