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Say I have the following carbocations:

enter image description here

The first is secondary; the second is resonance stabilized, but primary. Which is more stable and why?

I've been looking around in my textbooks and haven't been able to find a comparison. This site compares alkane and alkene intermediate stability, but only with the same degrees of substitution.

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    $\begingroup$ The effect of resonance stabilization totally beats the primary/secondary difference, so the answer is 2. $\endgroup$ – Ivan Neretin Sep 15 '15 at 19:04
  • $\begingroup$ @IvanNeretin According to this site, the effect is not as big as you might think. Those two cations have roughly the same stability. $\endgroup$ – bon Sep 16 '15 at 16:54
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There are two competing effects at work here; hyperconjugation, and resonance involving the double bond.

According to this website, a secondary alkyl cation and a primary allyl cation have roughly the same stability.

Carbocation Stability: $\ce{CH3+ < CH3CH2+ < (CH3)2CH+ ≈ CH2=CH-CH2+ < C6H5CH2+ ≈ (CH3)3C+}$

This is not really something you can predict from qualitative considerations - it is difficult to assess the strength of resonance versus hyperconjugation - but it requires experimental evidence, or detailed computer calculations to give a definitive answer.

In addition, the effect of adding more hyperconjugated groups is not linear. The difference in stability between tertiary and secondary alkyl cations is bigger than that between primary and secondary cations - tertiary alkyl cations are actually pretty stable.

Lastly, (thanks to @permeakra for pointing this out) the stability of carbocations in influenced by the environment which they are in. In particular, different solvents affect the stability of different cations to a varying degree and so the above order of stability should be taken as a rough guideline, not a hard and fast rule.

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    $\begingroup$ I would also add that the relative stability may be affected by solvent, so any such row should be threated with caution. Specifically, I bet that conjugated systems gain relative stability boost in nonpolar solvents. $\endgroup$ – permeakra Sep 16 '15 at 18:01
  • $\begingroup$ @permeakra Yes this is a good point that I missed. $\endgroup$ – bon Sep 16 '15 at 18:25

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