Question

Which pair among the following compounds have equal number of hyperconjugation:

• A. I, II, III
• B. I, III, V
• C. II, V
• D. II, III, V

Hint:

For carbocations, {number of hyperconjugative structures = number of \(\alpha\)-hydrogens}. Always count hydrogens on carbons directly attached to the positively charged carbon.

Answer 1

The Correct Option is A

Concept:
The number of hyperconjugative structures in a carbocation is equal to the number of \(\alpha\)-hydrogen atoms (hydrogens attached to carbon atoms directly bonded to the positively charged carbon).
Step 1: Count \(\alpha\)-Hydrogens for Each Structure
(I)
The positively charged carbon is secondary and is attached to two alkyl groups. Total \(\alpha\)-hydrogens \(= 6\).
(II)
The carbocation is at a bridgehead carbon bonded to two equivalent ring carbons. Total \(\alpha\)-hydrogens \(= 6\).
(III)
The carbocation is also bonded to two equivalent alkyl carbons in a fused ring system. Total \(\alpha\)-hydrogens \(= 6\).
(IV)
The carbocation has a different substitution pattern giving a different number of \(\alpha\)-hydrogens. Hence, hyperconjugation count is not equal to (I), (II), or (III).
(V)
The carbocation has a different alkyl environment and number of \(\alpha\)-hydrogens differs.
Step 2: Compare Results
Compounds (I)
, (II)
, and (III)
have the same number of \(\alpha\)-hydrogens and hence the same number of hyperconjugative structures.
Final Conclusion:
Correct pair(s) with equal hyperconjugation: \[ \boxed{\text{I, II, III}} \]