Question

Rate the following carbocations in increasing order of stability:

Answer 1

The carbocation is a cation of carbon in which the central carbon atom bearing the positive charge is $\text{s}{{\text{p}}^{\text{3}}}$ hybrid and forms three bonds with three substituents. This is formed as the reaction intermediate in the unimolecular substitution ${{\text{S}}_{\text{N}}}\text{1}$ reactions.

Complete Stepwise Solution:
Among the above carbocations, the third fourth one is least stable while the most stable one is the second one. The order of stability of the carbocations is as follows:
II > I > III > IV.
The reason being, the presence of three phenyl groups as the substituents attached to the positive carbon atom causes an extended conjugated structure which stabilizes the carbocation. The second carbocation has three methyl groups that stabilize the central carbon with their positive inductive effect. The third one has one methyl group to stabilize the carbocation while the last one, which is the phenyl carbocation is the least unstable due to the fact that the carbon atoms in an aromatic system on losing the electron pair, loses their conjugation or resonance that stabilizes their structure and hence, the stability is lost.

Note:
The stability of the central carbon atom bearing the positive charge depends on a number of factors which are as follows:
The inductive effect of the substituents – Presence of electron donating substituents such as the alkyl groups, increases the electron availability on the central atom and stabilizes it while the presence of the electron withdrawing group makes the carbon atom more unstable.
Effect of resonance – the presence of substituents with alternate double and single bonds or aromatic rings can lead to extended conjugation which provides stability to the carbon atom.