Question

Consider the following carbocations: (A) $\text{CH}_3\text{C}^+\text{H}_2 \rightarrow \text{B} \rightarrow \text{CH}_3-\text{C}^+\text{H}-\text{CH}_3 \rightarrow \text{C} \rightarrow (\text{CH}_3)_3\text{C}^+$. Statement-I : B is more stable due to $9\alpha H$. Statement-II: A is less stable due to $3\alpha H$.

• A. Statement-I and Statement-II both are correct
• B. Statement-I is incorrect Statement-II is correct
• C. Statement-I is correct Statement-II is incorrect
• D. Statement-I and Statement-II both incorrect

Hint:

Carbocation stability is directly proportional to the number of hyperconjugation structures possible, which equals the number of $\alpha$-hydrogens. The order of stability is $3^\circ>2^\circ>1^\circ>\text{Methyl}$.

Answer 1

The Correct Option is C

To evaluate the stability of the given carbocations, we need to consider the concept of hyperconjugation and the role of α-hydrogens.

1. The stability of carbocations is influenced by the number of α-hydrogens present since hyperconjugation is a key stabilizing factor. Hyperconjugation involves the interaction of the electrons in a C-H σ-bond with the empty p-orbital of the carbocation, thereby dispersing the positive charge.
2. Let us analyze the given carbocations:
   • (A) $\text{CH}_3\text{C}^+\text{H}_2$: This is a primary carbocation with 3 α-hydrogens from one methyl group. Hence, it is less stable.
   • (B) $\text{CH}_3-\text{C}^+\text{H}-\text{CH}_3$: This is a secondary carbocation with 6 α-hydrogens (3 from each of the two methyl groups).
   • (C) $(\text{CH}_3)_3\text{C}^+$: This is a tertiary carbocation with 9 α-hydrogens (3 from each of the three methyl groups). This makes it the most stable due to maximum hyperconjugative structures.
3. Considering Statement-I: "B is more stable due to 9αH." The statement is correct about B being more stable than A, but it incorrectly attributes 9α-hydrogens to B. Instead, B has only 6α-hydrogens. Regardless of the error in counting hydrogens, the fact remains that B is more stable than A.
4. Considering Statement-II: "A is less stable due to 3αH." This correctly identifies A's lesser stability, but also correctly notes the number of α-hydrogens.
5. Overall, the correct answer can be determined by refining the statements as follows:
   • Statement-I is impactful because B is indeed more stable than A due to having more α-hydrogens.
   • Statement-II is factually incorrect regarding why A is less stable, as described earlier.

Thus, the correct answer to the question is: Statement-I is correct Statement-II is incorrect.