What is the correct order of decreasing stability of following cations?
Factor Affecting stability of carbocation
Since, carbocation is an electron deficient species. So, any electron releasing group will increase the stability of carbocation and the electron withdrawing group will decrease the stability of carbocation.
Analysing the given structures
This carbocation has six α-hydrogen. So, it is stabilised by hyperconjugation (+H effect) using these alpha hydrogens. Also, it involves stabilization through +I effect of two methyl groups.
This carbocation is stabilised by positive mesomeric effect (i.e,+M effect). This carbocation will be most stable because mesomeric effects are more stabilising as compared to hyperconjugation.
This carbocation has five α-hydrogen. So, it is stabilised by hyperconjugation (via+H effect) using these five alpha hydrogens. but −I effect of OCH3 group will destabilize the carbocation. Hence, less number of alpha hydrogens and electron withdrawing inductive effect will make this carbocation less stable than other two carbocations.
As we already know, mesomeric effect is stronger than the inductive and hyperconjugation effect. So, carbocation (II) will be more stable than carbocation (I).
Hence, order of stability of carbocation is: II>>I>III
So, correct answer is option (A).