Question

The most stable carbocation among the following is:

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is D

Carbocation stability is primarily dictated by the degree of substitution (tertiary>secondary>primary) and enhanced by hyperconjugation (number of $\alpha$-hydrogens) and resonance (if present).

Analysis of Each Carbocation:

(1) $CH3     | CH_3-CH+-CH-CH_3       |      CH_3$

This is a secondary carbocation ($ \text{2}^\circ $), with the positively charged carbon bonded to two other carbons. It possesses 7 $\alpha$-hydrogens.

(2) $+ CH_3-CH-CH_2-CH-CH_3             |            CH_3$

This is also a secondary carbocation ($ \text{2}^\circ $), with the positively charged carbon bonded to two other carbons. It has 4 $\alpha$-hydrogens.

(3) $  +   CH_2   / \  |   | CH_2-CH_2  \ /   CH_2$

This is a primary carbocation ($ \text{1}^\circ $), with the positively charged carbon bonded to one other carbon within the cyclohexane ring. It has 2 $\alpha$-hydrogens.

(4) $   CH_3      |     +   C  / \ CH_2 CH_2 |   | CH_2 CH_2  \ /$

This is a tertiary carbocation ($ \text{3}^\circ $), with the positively charged carbon bonded to three other carbons (one methyl and two from the cyclohexane ring). It has 3 $\alpha$-hydrogens from the methyl group. The hydrogens on the adjacent cyclohexane carbons are not considered direct $\alpha$-hydrogens for hyperconjugation with the carbocation center.

Stability Comparison:
The stability order is tertiary ($ \text{3}^\circ $)>secondary ($ \text{2}^\circ $)>primary ($ \text{1}^\circ $).

Consequently, carbocation (4), being tertiary, is the most stable among the options, irrespective of the $\alpha$-hydrogen counts in the secondary carbocations.

Final Answer:
The most stable carbocation is: $ \boxed{(4)} $