Relative Stabilities of Carbocations

Free radicals, carbocations and carbanions are not stable species and exist as intermediates in chemical reactions.

1. Classifications of carbocations

• Carbocations are classified according to the number of alkyl substituents that are bonded to the positively charged carbon.
• A primary (1^o) carbocation has one alkyl substituent, a secondary (2^o) carbocation has two alkyl substituents and a tertiary (3^o) carbocation has three alkyl substituents.

2. Stability of carbocations 

• The stability of carbocations depends on the number of alkyl groups that are bonded to the positively charged carbon.
• The stability of a carbocations increases as the number of alkyl groups bonded to the positively charged carbon increases. 
• Thus, tertiary carbocations are more stable than secondary carbocations, and secondary carbocations are more stable than primary carbocations.

   

• Alkyl groups are electron donating group which increase the electron density inductively on the positive charge carbon (or decrease the electron deficiency on the positive charge carbon).

    

 3. Additional explanations about how do alkyl groups decrease the electron deficiency on the positive charge carbon

• The positive charge on a carbon signifies an empty p orbital. The figure shows that in the ethyl cation, the orbital of an adjacent C–H σ bond can overlap with the empty p orbital. No such overlap is possible in the methyl cation. Movement of electrons from the σ bond orbital toward the vacant p orbital of the ethyl cation decreases the charge on the sp² carbon and causes a partial positive charge to develop on the carbon bonded by the σ bond. Therefore, the positive charge is no longer localised solely on one atom, but is spread out over a greater volume of space.
• This dispersion of the positive charge stabilises the carbocation because a charged species is more stable if its charge is spread out (delocalised) over more than one atom. Delocalisation of electrons by the overlap of a σ bond orbital with an empty p orbital is called hyperconjugation.  

  

  Stabilisation of a carbocation by hyperconjugation: The electrons of an adjacent C-H bond in the ethyl cation spread into the empty p orbital. Hyperconjugation cannot occur in a methyl cation.

    
• Hyperconjugation occurs only if the σ bond orbital and the empty p orbital have the proper orientation. The proper orientation is easily achieved because there is free rotation about a carbon-carbon σ bond. In the case of the tert-butyl cation, nine C–H σ bond orbitals can potentially overlap with the empty p orbital of the positively charged carbon. The isopropyl cation has six such orbitals, and the ethyl cation has three. Therefore, there is greater stabilisation through hyperconjugation in the tertiary tert-butyl cation than in the secondary isopropyl cation and greater stabilisation in the secondary isopropyl cation than in the primary ethyl cation. 

   

Read more about George A. Olah for his work on the chemistry of carbocations, that earned him the 1994 Nobel Prize in Chemistry.