Arrange the given carbocations in order of increasing stability and explain the order:
(##_Q01.png" width="80%">
`CH_(2)=CH-overset(oplus)(C)H_(2)(II),CH_(3)overset(oplus)(C)H_(2)(III), CF_(3)overset(oplus)(C)H_(2)(IV)`

Explanation

The order of increasing stability of these carbocation is :
`underset((IV))(CH_(3)overset(oplus)(C)H_(2))ltunderset((III))(CH_(3)overset(oplus)(C)H_(2))ltCH_(2)underset((II))(=)CH-overset(oplus)(C)H_(2)lt (##CHY_CHE_ORG_XI_P2_U12_E04_005_S01.png" width="80%">
Being an aromatic one `[(4n+2)pi-"electron system,where" " " n=1]`, the carbocation (I) is the most stable carbocation. The carbocation (II) is effectively resonance stabilised. So, its stability is greater than that of (III) and (IV) (which are not resonance - stabilised) but less than that of (I). The carbocation (III) is stabilised by +I and hyperconjugative effect of the methyl group and its stability is less than (II). The carbocation (IV) is destabilised by the stronger -I effect of the `-CF_(3)` group, so it is the least stable one.