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I am confused between these two concepts. My book gives $\ce{O2}$ as an example of a radical inhibitor and peroxide as an example of an initiator. But I don’t know why this is so? Both have $\ce{O-O}$ bonds so what is the difference?

Also aren’t all radical initiators in some sense? Aren’t radicals in general reactive and that they always create more radicals?

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The confusing thing about initiators and inhibitors of radical reactions is that both are often radicals.

But it isn't being a radical that is important: it is what happens when that radical reacts in the reaction conditions. If the radical reacts with another radical to give something that is no longer capable of propagating the radical reaction, it is an inhibitor. If it reacts to give more radicals it is an initiator.

Which compounds can do the job of either depends a lot on the specific reaction.

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A radical inhibitor, as the name itself says, inhibits the formation of radicals. It reacts to "wipe out" radicals. $\ce{O2}$ is one such chemical. A radical initiator on the other hand is a substance that generates radicals, as in the case of $\ce{H2O2}$, which forms radicals via the cleavage of the $\ce{O-O}$ bond.

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