Arrange the following carbocations in the increasing order of stability with respect to their labels.…

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

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).

Asked in: AP EAMCET 2020 (18 Sep Shift 2)

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