Question

What is the observed order of the stability of the carbocation ${-\left({\mathrm{CH}}_3\right)}_3{C}^{+}>,{}_{2}C{H}^{+}\mathit{,}\mathit{}C{H}_{3}C{H}_2^{+}\mathit{}and\mathit{}{\mathrm{CH}}_3^{+}$

Answer 1

Carbocation

• A carbocation (formerly called carbonium ion) is a cationic reaction intermediate species with a carbon atom that bears a positive charge and is two electrons short for completing its octet.

Stability order of the carbocation

• The order of the stability can be explained on the basis of the positive inductive effect and hyperconjugation effect.

[Note: Positive inductive effect is the electron releasing nature of the groups or atoms and is denoted by +I. Hyperconjugation is the delocalization of electrons by the overlap of a $\mathrm{\sigma }$ bond orbital with a $\mathrm{\pi }$or p-orbital.]

Positive inductive effect

• According to the positive inductive effect, the alkyl groups show an electron-releasing inductive effect (+I effect) in the direction of the positive charge in a carbocation.
• Through the +I effect, an alkyl group disperses the positive charge and thus stabilizes the carbocation.
• The greater the number of alkyl groups attached to the positive carbon, the greater the dispersal of the charge and consequently, the greater the stability of the carbocation.
• Thus, the t-butyl cation with three methyl groups attached to the positive carbon would be more stable than the isopropyl cation with two methyl groups.
• Likewise, the isopropyl cation with two methyl groups would be more stable than the ethyl group with only one methyl group.
• The methyl cation with no alkyl group attached to the positive carbon would be the least stable among them.

Hyperconjugation effect

• According to the hyperconjugation effect, the greater the number of $\mathrm{\alpha }-$hydrogens attached to ht positive carbon, the greater will be the stabilization of the carbocation.
• For carbocations, the number of $\mathrm{\alpha }-$hydrogens and the number of hyper conjugative structures decreases in the order:$3°>2°>1°>{\mathrm{CH}}_3^{+}$
• So the order of stabilization will decrease in the same order.
• Therefore, the observed order of stability of the carbocation is ${\left({\mathrm{CH}}_3\right)}_{\mathbf{3}}{\mathit{C}}^{\mathbf{+}}\mathbf{>}{\left(C{H}_3\right)}_{\mathbf{2}}\mathit{C}{\mathit{H}}^{\mathbf{+}}\mathbf{>}\mathit{C}{\mathit{H}}_{\mathbf{3}}\mathit{C}{\mathit{H}}_{\mathbf{2}}^{\mathbf{+}}\mathbf{>}{\mathbf{CH}}_{\mathbf{3}}^{\mathbf{+}}$