Carbocation stability order

Question

I was wondering whether the following order (from here) is correct:

In the first inequality, why did 9 hyperconjugations dominated resonance effect of benzene ring?
In the last inequality doesn't the 2 hyperconjugations of vinylic carbocation overpower the methyl carbocation?

In middle there is:
allyl = secondary

Why is there an equality here when resonance dominates inductive effect?

The vinyl group exerts a -I effect that destabilises the positive charge and makes it more unstable than the methyl carbocation. — Binary Geek, Mar 10 '15 at 10:07
related http://chemistry.stackexchange.com/questions/10509/instability-of-vinylic-and-arylic-carbocations?rq=1 — Mithoron, Mar 20 '15 at 11:30
also http://chemistry.stackexchange.com/questions/19027/inductive-effect-and-hyperconjugation-one-elephant-different-parts?lq=1 — Mithoron, Mar 20 '15 at 12:48
I'm not sure about this but I don't think vinylic hydrogens participate in hyperconjugation. — Binary Geek, Mar 20 '15 at 14:55
@BinaryGeek I think they do. Do you have some link for stability orders? — pikachu, May 20 '15 at 08:55
@pikachu Vinyl hydrogens can't participate in hyperconjugation because they don't have the correct geometry to allow the orbital interactions. — bon, Sep 17 '15 at 11:17
Also related: https://chemistry.stackexchange.com/q/74943/4945 — Martin - マーチン, Jan 15 '18 at 11:11

score 2 · Answer 1 · answered Mar 21 '15 at 20:41

2

About the first two, it's an exception to the rule that resonance dominates hyperconjugation.

About the last inequality, the vinyl cation is sp hybridized which means it is highly electronegative, and a positive charge on it will be very unstable.

About the middle inequality, the benzyl carbocation (with five resonance structures) is more stable than allyl carbocation (two resonance structures). You may verify this here.

answered Mar 21 '15 at 20:41

Ayush Pateria

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Would you have a source for the claim "sp hybridized which means it is highly electronegative"? – Jori Mar 22 '15 at 11:53
https://books.google.co.in/books?id=gY-Sxijk_tMC&pg=PA16#v=onepage&q&f=false – Ayush Pateria Mar 22 '15 at 12:02
You got the middle equality wrong . Look at the highlighted text . I had asked for allyl and secondary . Thanks for the other parts . – pikachu Mar 23 '15 at 06:47
What will the stability order of $2^{\circ}$ and $3^{\circ}$ benzylic carbocation in comparison to tertiary carbocation? – Apurvium Apr 22 '20 at 09:44

score -1 · Answer 2 · answered Dec 02 '15 at 21:28

As for the 1st two:

Consider the 3 R's as independent(I am just explaining) ,each pushing a part of the electron cloud in its bond towards the central carbon through inductive effect as well as Hyper-conjugation. So in a way each R is reinforcing each other and an overall combined stability is achieved.

However consider the resonating structures of Benzyl carbocation. If you research a bit deeper , you will find that of all the 4 resonating structures possible, the form that is given ( + on the external carbon) contributes to almost 90% of the original stable structure. This is because, if you take any other resonating structure( say + charge on a carbon inside the ring ), you will find that the structure is quite unstable and very highly tends to resort back to the + charge outside the ring ( after all, breaking a Benzene ring isn't very favorable) . So in a way , the resonating structures do not 'reinforce' each other so "Resonance" does not stabilize the way it is expected to do (as in case of similar resonating structures)

Talking of the last inequality:

The "Hyper-conjugation" that you mentioned wouldn't play the role here as you imagine. You might- have overlooked the fact that vinyl cation is least stable MOSTLY because it has a very high tendency to get converted to another structure, namely the left carbon(in your diagram) with a + charge and the right one with a lone pair. This is because ,then it will have many more hyper-conjugations to get stable. This is what makes vinyl carbocation least stable, it very very rarely ever exists or tries to exist in this particular form.

As for the middle equality,

Yes, in a way your doubt is right. (Since there is an equivalent resonance structure in the left one (as given) and that is a powerful one!!).However the thing you have missed while comparing the 2nd one is the fact that "Inductive" effect plays a 'minor' role in contributing to the stability of the secondary carbocation.The 'Major' role is played by the 7 "Hyper-conjugations" which is no less than a single resonance. Of course 1 hyperconjugation is less than 1 resonance but basic intuition will tell you that 7 hyperconjugations will have a fair chance to cope with 1 resonance.

For discussion of the structure of the vinyl cation see here. Your analysis is completely wrong I'm afraid. — bon, Dec 02 '15 at 23:51
They are not wrong, per se, just poorly worded. I do take some issue with this statement though Resonance" does not stabilize the way it is expected to do. The benzyl cation has extensive resonance stabilization which accounts for the fact that it is far more stable than otherwise expected. It's just that tertiary alkyl cations are a little bit more stable. — bon, Dec 03 '15 at 10:18
But ,is a compound having non equivalent resonating structures as stable as another which has stable resonating structures? @bon — Qwerty, Dec 03 '15 at 15:18
What do you mean? Stable is only a relative term. Non equivalent resonance structures can still be stable compared to a different structure. — bon, Dec 03 '15 at 18:28
Am I wrong in saying whatever I have said in the second paragraph except the last part of the last line(on which you raised a question)? — Qwerty, Dec 03 '15 at 21:00

Carbocation stability order

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