Assertion (A): The equilibrium constant for cyanohydrin formation is `=10^(13)` times greater for cyclo-hexanone than for cyclophentanone.
Reason (R ): For a five-membered ring, reactions are more favourable when a ring C changes from `sp^(3)` to `sp^(2)` because eclipsing interactions are removed.

Options

A. If both (A) and (R ) true and (R ) is the correct explanation of (A).
B. If both (A) and (R ) are true but (R ) is not correct explanation of (A).
C. If (A) is true but (R ) is false.
D. If (A) is false but (R ) is true.

Answer

To solve the question, we will analyze both the assertion (A) and the reason (R) provided in the question step by step.

### Step 1: Understanding the Assertion (A)
The assertion states that the equilibrium constant for cyanohydrin formation is \(10^{13}\) times greater for cyclohexanone than for cyclopentanone.

- **Cyanohydrin Formation**: This reaction involves the addition of HCN to a carbonyl compound (like cyclohexanone or cyclopentanone) to form a cyanohydrin.
- **Equilibrium Constant (K)**: A larger equilibrium constant indicates that the formation of the product (cyanohydrin) is favored over the reactants (cyclohexanone or cyclopentanone).

### Step 2: Analyzing Cyclopentanone vs. Cyclohexanone
- **Cyclopentanone**: In this five-membered ring, the transition from sp² (carbonyl carbon) to sp³ (cyanohydrin carbon) leads to eclipsed interactions. This instability makes the formation of the cyanohydrin less favorable, resulting in a smaller equilibrium constant.
- **Cyclohexanone**: In this six-membered ring, the formation of the cyanohydrin results in a more stable staggered conformation, as the hydroxyl (OH) group can occupy an axial position while the cyanide (CN) group occupies an equatorial position. This stability leads to a much larger equilibrium constant.

### Conclusion for Assertion (A)
Thus, the assertion that the equilibrium constant for cyanohydrin formation is \(10^{13}\) times greater for cyclohexanone than for cyclopentanone is correct.

### Step 3: Understanding the Reason (R)
The reason states that reactions in a five-membered ring are more favorable when a ring carbon changes from sp³ to sp² because eclipsing interactions are removed.

- **Eclipsing Interactions**: In cyclopentanone, the formation of the cyanohydrin leads to eclipsed interactions, which are energetically unfavorable. This instability hinders the reaction's progression.
- **Transition from sp³ to sp²**: As the carbonyl carbon transitions from sp² to sp³ during the reaction, it encounters eclipsed interactions, making the reaction less favorable.

### Conclusion for Reason (R)
The reason provided is also correct, as it explains why the reaction is less favorable in cyclopentanone due to eclipsing interactions.

### Final Conclusion
Both the assertion (A) and the reason (R) are correct, and the reason is a correct explanation of the assertion. Therefore, the answer is option (E).

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