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When carbon combusts with oxygen, is this considered a redox reaction since the oxygen atoms gain electrons and the carbon atoms lose them?

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In general, yes. If the reaction involves oxygen going from the oxidation state of zero in $\ce{O_2}$ to an oxidation state of -2, then there is oxidation and the reaction is a redox reaction.

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Could you elaborate a bit? When you say "in general", does that mean that there are some special cases? If so, you may want to add them to your answer, it'll make it more interesting... –  ManishEarth Nov 3 '12 at 4:49
    
@ManishEarth There's nothing 'in general' about it. a combustion reaction requires an oxidizer; therefore it is always a redox reaction. (Late comment, I know.) –  bobthechemist Jul 28 '13 at 2:12
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