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Which is the most stable free radical among the given species?
(1) $\ce{CH2=CH-CH2^.}$ (allyl radical)
(2) $\ce{C6H5-CH2^.}$ (benzyl radical)
(3) $\ce{(H3C)3C^.}$ (t-butyl radical)
(4) $\ce{C2H5^.}$ (ethyl radical)

The book claims the answer to be the allyl radical, option 1. But how can we definitely say that the allylic free radical is more stable, compared to the benzyl radical (option 2) which is also resonance-stabilised, or the tertiary radical (option 3) which has more hyperconjugative donation from α-hydrogen atoms?

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  • $\begingroup$ I just want to say your book is correct. In simple words in this case benzyl free radical has resonance but the mesomeric effect is not transmitted to the free radical simply because it does not have a LONE PAIR of electrons. And besides Benzene has a -I effect thus further withdrawing the electrons and making the free radical unstable. (Coz obviously it needs electrons) $\endgroup$ Jan 2 '20 at 5:51
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This is a tough question. I think it might even be unfair to ask such a question on a test in non-advanced classes. In advanced classes it could make an interesting topic of discussion, but I'm still not sure that the "real" answer is known.

What can be said is that due to resonance, both the allylic and benzylic radicals are more stable than the t-butyl or ethyl radicals which are not resonance stabilized. You can see from the following diagram that you can draw two resonance structures for the allyl radical.

Resonance structures of allyl radical

For the benzyl radical you can draw even more resonance structures.

Resonance structures of benzyl radicals

Superficially, this might suggest that the benzylic radical is more stable than the allyl radical. This was the "answer" and reasoning provided here.

However, if you do some thermochemical calculations (as done here), you arrive at the opposite conclusion that the allyl radical is roughly 2 kcal/mol more stable than the benzyl radical. The number of resonance structures alone is not a perfect indicator of stability.

For me, that is a pretty small difference in energy, and I think it would be fair to answer that the allyl and benzyl radicals have comparable stabilities.