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no, Co2 does not burn. carbon monoxide has a blue flame and carbon produces a broad but yellow spectrum, hydrogen is white, though not very bright. A number of metals burrn also like someone mentioned, sodium, lithium, magnesium, iron, aluminium, and nonmetallics: phosphorus, sulphur. But they sublime, because the burning temperature is above their boiling point and it takes a very hot starter, like magnesium, which ignites easily and produces ~3000°C, or yoi can use sometimes just a propane flame or so especially with fine material.

However these temperatures are too high for just making heat and the they are too rare.

I believe you can do reactions with carbon dioxide when it is supercritical, but I think they are endothermic. Carbon monoxide can be combined with hydrogen and a zinc and some other metal catalyst with it to get methanol, with a small amount of CO2.

A mix of hydrogen and carbon monoxide is called "fuel gas" and it can be used to synthesise all kinds of hydrocarbons by varying ratios and conditions and catalysts. You get it by destructive distillation of coal, heat but not enough oxygen.

carbon monoxide has a blue flame

Yes, CO burns 8-).

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