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Given that $\ce{CO2}$ is comprised of carbon and oxygen, why isn't it a flammable gas?

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    $\begingroup$ What has burned can never burn. $\endgroup$ – Ivan Neretin Nov 18 '16 at 5:33
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    $\begingroup$ fully oxidized. $\endgroup$ – gannex Nov 18 '16 at 7:33
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If I understand what you are saying, then the issue is that the carbon and oxygen have already reacted. Carbon dioxide is thus not flammable because it is the fully oxidized product of the combustion between oxygen and carbon.

"Made of" has multiple meanings. You're confusing the meaning of physical mixture (flammable) with the chemical composition of a compound (not flammable).

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