Question

A carbocation is a group of atoms with a positively charged carbon atom having six electrons in a valence shell after sharing. Carbocations are formed in the heterolysis of a bond and are planar species. Stability of the carbocation is determined by inductive effect, hyperconjugation and resonance effect. Greater the number of contributing structures more is the stability of a carbocation. Electron releasing groups (+I effect) increases the stability of a carbocation whereas the electron withdrawing groups (-I effect) have an opposite effect.
Which of the following is the most stable carbocation?
(A)- $\overset{+}{\mathop{C}}\,{{H}_{3}}$
(B)- $C{{H}_{3}}\overset{+}{\mathop{CH}}\,C{{H}_{3}}$
(C)- $C{{H}_{3}}\overset{+}{\mathop{C}}\,{{H}_{2}}$
(D)- $C{{H}_{3}}-\overset{+}{\mathop{C}}\,(C{{H}_{3}})-C{{H}_{3}}$

Answer 1

The presence of electron-donating substituents on the carbocation enhances the stability. Also, the hydrogens on the adjacent carbon, create partial double bonds in the contributing structures, which further increase the stabilisation of the carbocation.

Complete step by step solution:
Firstly, the given carbocations can be classified into primary, secondary and tertiary carbocation on the basis of the number of methyl groups attached to the central carbon atom (that is, positively charged).
The stability of the carbocation depends on the inductive effect and hyperconjugation due to the substituents attached to it, which produces more contributing structures for its stabilization.
In the given carbocations, the methyl groups attached show positive inductive effect, which increases the electron density over the central carbon atom, dispersing the positive charge over a larger space and thus makes the carbocation more stable.
Whereas, through the hyperconjugation, that is, the presence of hydrogens on the adjacent $\alpha$- carbon, partial double bond character is formed. Thus, increasing the stability of the carbocation.
So, in carbocation (A), having only hydrogens attached to it, shows no inductive effects or hyperconjugation. Hence, the least stable.
In carbocation (B), having two methyl groups attached to the central carbon, shows positive inductive effect along with the presence of six hyperconjugative hydrogens on the adjacent carbons.
Similarly, in carbocation (C) and (D) with one and three methyl groups respectively, have three and nine hyperconjugative hydrogens on the adjacent carbons respectively. Also, carbocation (D) has the maximum positive inductive effect by the three methyl groups.
Thus, we have the order of the stability of the given carbocations as follows:
$C{{H}_{3}}-\overset{+}{\mathop{C}}\,(C{{H}_{3}})-C{{H}_{3}}$ > $C{{H}_{3}}\overset{+}{\mathop{CH}}\,C{{H}_{3}}$ > $C{{H}_{3}}\overset{+}{\mathop{C}}\,{{H}_{2}}$ > $\overset{+}{\mathop{C}}\,{{H}_{3}}$

Therefore, the carbocation which is most stable is option (D)- $C{{H}_{3}}-\overset{+}{\mathop{C}}\,(C{{H}_{3}})-C{{H}_{3}}$.

Note: In the given carbocations, there is no resonance seen because of the absence of the lone pairs of electrons or unsaturated bonds on the adjacent carbon. Thus, the inductive effect and the hyperconjugation are most effective in the given carbocations.