Question

Arrange the following carbocations in increasing stability order \[ A.\ \mathrm{CH_3^+} \] \[ B.\ 1^\circ \] \[ C.\ 2^\circ \] \[ D.\ 3^\circ \] Choose the correct answer from the options given below:
• \( \mathrm{B < A < C < D} \)
• \( \mathrm{A < B < C < D} \)
• \( \mathrm{D < C < B < A} \)
• \( \mathrm{C < B < A < D} \)

• A. \( \mathrm{B < A < C < D} \)
• B. \( \mathrm{A < B < C < D} \)
• C. \( \mathrm{D < C < B < A} \)
• D. \( \mathrm{C < B < A < D} \)

Hint:

Carbocation stability order: \[ \mathrm{CH_3^+ < 1^\circ < 2^\circ < 3^\circ} \] Reason:
• \(+I\) effect
• Hyperconjugation More alkyl groups mean greater stabilization.

Answer 1

The Correct Option is B

Concept: A carbocation is a positively charged carbon species in which carbon possesses only six electrons in its valence shell. General representation: \[ \mathrm{R_3C^+} \] Carbocations are electron deficient species and hence are generally unstable. Their stability depends mainly upon:
• Inductive effect
• Hyperconjugation
• Resonance stabilization Alkyl groups stabilize carbocations through:
• \(+I\) (electron donating inductive effect)
• Hyperconjugation Greater the number of alkyl groups attached to the positively charged carbon, greater is the stability.

Step 1: Understand methyl carbocation \( \mathrm{CH_3^+} \). Methyl carbocation is: \[ \mathrm{CH_3^+} \] This carbocation has:
• No alkyl group attached.
• No hyperconjugation.
• Very high electron deficiency. Therefore, it is the least stable carbocation. Thus: \[ \boxed{\mathrm{CH_3^+} \text{ is least stable}} \]

Step 2: Understand primary carbocation (\(1^\circ\)). A primary carbocation has one alkyl group attached to the positively charged carbon. Example: \[ \mathrm{CH_3CH_2^+} \] This carbocation receives:
• Small electron donation through inductive effect.
• Limited hyperconjugation. Hence, it is more stable than methyl carbocation. Therefore: \[ \mathrm{CH_3^+ < 1^\circ} \]

Step 3: Understand secondary carbocation (\(2^\circ\)). A secondary carbocation has two alkyl groups attached. Example: \[ \mathrm{(CH_3)_2CH^+} \] Now:
• Two alkyl groups donate electron density.
• Hyperconjugation increases significantly. Hence, secondary carbocation is more stable than primary carbocation. Thus: \[ 1^\circ < 2^\circ \]

Step 4: Understand tertiary carbocation (\(3^\circ\)). A tertiary carbocation has three alkyl groups attached. Example: \[ \mathrm{(CH_3)_3C^+} \] This carbocation receives maximum stabilization through:
• Strong \(+I\) effect
• Maximum hyperconjugation Therefore, tertiary carbocation is the most stable among the given species. Thus: \[ 2^\circ < 3^\circ \]

Step 5: Write the complete increasing order. Combining all observations: \[ \boxed{ \mathrm{CH_3^+ < 1^\circ < 2^\circ < 3^\circ} } \] Using symbols: \[ \boxed{ A < B < C < D } \]

Step 6: Match with the given options. The correct option is: \[ \boxed{(2)} \] Additional Understanding: Carbocation stability increases because alkyl groups help disperse the positive charge. More alkyl groups: \[ \Rightarrow \text{ More electron donation} \] \[ \Rightarrow \text{ Lower electron deficiency} \] \[ \Rightarrow \text{ Greater stability} \] Final Conclusion: The increasing order of carbocation stability is: \[ \boxed{ A < B < C < D } \] Hence, the correct answer is: \[ \boxed{(2)} \]