Arrange the following carbocations in the increasing order of stability with respect to their labels. \(\begin{array}{c|c} \hline \text { Label } & \text { Carbocation } \\ \hline 1 & \left(\mathrm{CH}_3\right)_2 \mathrm{CH}^{+} \\ \hline 2 & \mathrm{CH}_3^{+} \\ \hline 3 & \left(\mathrm{CH}_3\right)_3 \mathrm{C}^{+} \\ \hline 4 & \mathrm{CH}_3-\mathrm{CH}_2^{+} \\ \hline \end{array}\)

• Correct answer
  A

  \(2 < 4 < 1 < 3\)
• B

  \(1 < 2 < 3 < 4\)
• C

  \(4 < 3 < 2 < 1\)
• D

  \(2 < 4 < 3 < 1\)

Solution

Stability of carbocation \(\propto\) number of hyperconjugative structure \(\propto\) number of \(\alpha-\mathrm{H}\) atoms (1) \(\stackrel{\alpha}{\mathrm{C}} \mathrm{H}_3-\stackrel{\oplus}{\mathrm{C}} \mathrm{H}-\stackrel{\alpha}{\mathrm{C}} \mathrm{H}_3\), Hyperconjugative structure \(=6\) (2) \(\stackrel{\oplus}{\mathrm{C}} \mathrm{H}_3\), Hyperconjugative structure \(=0\) (3)
Hyperconjugative structure \(=9\) (4) \(\stackrel{\alpha}{\mathrm{C}} \mathrm{H}_3-\stackrel{\oplus}{\mathrm{C}} \mathrm{H}_2\), Hyperconjugative structure \(=3\) So, stability of carbocations \(2 < 4 < 1 < 3\) (option a).

Hence, the correct answer is option: 'A'.