Fluorine is more electronegative than chlorine even then, p-flurobenzoic acid is weaker acid than p-chlorobenzoic acid explain ?

Since halogens are more electronegative than carbon and also possesses lone pair electrons , therefore they exert both -I and +R effects . Now in F , the lone pair of electrons are present in 2p-orbitals but in Cl , they are present in 3p-orbitals . Since 2p- orbitals of fluorine and carbon are almost  equal size , therefore , the +R effect is more pronounced in p- flurobenzoic acid than p-chlorobenzoic acid.

 
Thus in p- flurobenzoic acid +R effect is out weight the -I effect but in p-chlorobenzoic acid, it is the -I effect which is out weight  the +R effect. Hence p- flurobenzoic acid is weaker acid than p-chlorobenzoic acid.

Trifluoroethyl carbocation is less stable than trifluromethyl carbocation why ?

In case of trifluroethylcarbocation the highly electronegative fluorine atom , withdraws shared pair electrons between C-F bonds towards itself to great extent and intensifies positive charge on carbon. Greater the intensification of charge more is the instability.theirfore this carbocation is destabilised.

In case of trifluroethylcarbocation carbocation, the unshared paired of electrons in P - Orbital of each of the fluorine can be shifted into vacant Orbital of carbon atom of carbocation via P-P overlap.

It's leads to dispersal of charge and provide stability to the carbonation.

Stability of Heteroatomic carbocations:

The carbocaton contaning hetero atoms adjacent to positive carbon of cation such as oxygen, nitrogen and sulphur etc which are more electronegative than carbon, you might expect that they would by definition be electron withdrawing groups that destabilize carbocations.

But there is opposite effect, if the oxygen, nitrogen or sulphur atom is present at adjacent to carbocation, the overall effect is carbocation stabilization.

This is due to the fact that although these heteroatoms are electron withdrawing groups by induction, they are electron donating groups by resonance, and it is this resonance effect which is more powerful.

ILLUSTRATIVE EXAMPLE(1): Give the correct Stability of given carbocation .

SOLUTION: Sulphur containing carbocation is more stable because lone pair of sulphur atom show more resonating effect due to least electronegativity as compared to nitrogen as well as oxygen atom similarly  nitrogen show more resonance than oxygen atom

Conceptual Facts:

(1) If number of conjugation increases stability of carbocation increases ...

(2) We known that on increasing conjugation stability increases. their is exception in option (A) their is three nitrogen may involving in resonance but  actually not, 

 Because positive carbon does not involved in resonance due to bridge head carbon. we known according to Bredt,s rule bridge carbon cannot for duble bond.

Hence correct stability order is  (B) > (C) >> (A): 

(3)  Similarly 

Hence correct stability order is  (B) > (C) >> (A): 

ILLUSTRATIVE EXAMPLE(3): Give the correct Stability of given carbocation.

SOLUTION: (1):  (C) > (B) > (A)     and    (2):   (C) > (B) > (A)  

ILLUSTRATIVE EXAMPLE(4): Give the correct Stability of given carbocation.

SOLUTION: (1):  (D) > (B) > (C) > (A)     and    (2):  (D) > (B) > (C) > (A)  

Other important examples:

IIT UPDATE:

QUESTION(1)

SOLUTION: (D)

Dancing resonance or Sigma Resonance:

Dancing resonance is a special stability mechanism which increases stability of carbocations attached directly to the three membered rings. For example Cyclopropylmethyl Carbocation.

In cyclopropane all the carbon is sp3 hybridized and the bond angle for the same should be 109 degree 28′ but the actual bond angle is 60 due to which angle strain develops. So in order to minimize the strain p orbital bents due to which it acquires partial sigma and partial pi bond character which behave like pi bond. And resonance take place between sigma and vacant p-orbitals hence called P-orbitals overlapping or sigma resonance.

We know by Drago’s rule bond angle is directly proportional to the s-character while inversely proportional to p-character.  

Dancing resonance is a hypothetical phenomenon which is reduces strain of the ring, hence the carbocation is more stable.  CH₂⁺ has a vacant p orbital and a very effective overlapping takes place between p-orbital and electron density of cyclopropane, due to this its stability is very high. There is a conjugation between the sigma bond and positive charge.

The exceptional stability of cyclopropane methyl cation can be explained by the concept of dancing resonance concept. The stability of additional cyclopropyl group , is result of more conjugation between the bent orbital of cyclopropyl ring and cationic carbon.

The most stable carbocation known till date in organic chemistry is explain by Dancing resonance.

ILLUSTRATIVE EXAMPLE: Why is the Tropylium carbocation less stable than the tricyclopropylmethyl carbocation?

Why is the Tropylium carbocation less stable than the tricyclopropylmethyl carbocation?

Tropylium is highly stable due to conjugated system, that being resonance stabilized and the number of canonical forms of tropylium is more. But it is less stable than tricyclopropylmethyl carbocation because tricyclopropylmethyl carbocation undergoes a strong  stability mechanism factor that is sigma resonance or dancing resonance  (sigma-tropic rearrangement ).