Chemistry Carbocation Stability: Attracting Inductive vs Mesomeric Effects

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The discussion centers on the stability of carbocations, specifically addressing the stability of the fourth carbocation due to the influence of the carbonyl group. While the carbonyl group exerts an attracting inductive effect that destabilizes the carbocation, resonance with the C=O bond does not provide sufficient stabilization, as it results in a less stable structure with a positive charge on the electronegative oxygen. Consequently, the fourth carbocation is confirmed to be less stable than the first, which is an allyl cation known for its stability. The stability comparison with the second and third carbocations, which are secondary and tertiary alkyl carbocations, remains uncertain without further context. Overall, the discussion highlights the complexities of carbocation stability influenced by both inductive and mesomeric effects.
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Homework Statement
determine the stability of these following carbocations
Relevant Equations
x
1618329858219.png

Hi,
Sorry in advance if the vocab is incorrect, I'm translating this from french.
In the correction, it's written that the 4th carbocation is the less stable due to the attracting inductif effect of the carbonyle group.
But isn't this carbocation stabilised by the mesomer effect of the C=O bond? And if it isn't stabilised by the mesomer effect can you please explain to me why?
And in case it is, how do we determine the stability between the 1st and 4th carbocation?
Thank you so much!
 
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The carbonyl group is polarised due to the resonance C=O ↔ C+-O-. The carbocation is destabilised by being next to a δ+ carbon.
Resonance with the carbonyl group is possible, but it would give a structure C=C-O+, which is less stable because it has the + charge on the more electronegative O atom.
So 4 is definitely less stable than 1. Whether it's less stable than 2 or 3 I'm not so sure.
 
#1 is an allyl cation. A good organic textbook will have an explanation of allyl group stability. The other two are secondary and tertiary alkyl carbocations, and a good textbook should also explain their order of stability.
 
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