Breaking apart the O and the C bonded into carbon dioxide might occur at what temperature and why?

If I were to heat the molecules to 2000 degrees Fahrenheit, would the carbon and oxygen would break their double bond?

Certainly at some temperature — at some energy level — those bonds will be disturbed and vibrating enough to break, or shake, the atoms apart.

At that break-apart temperature, there will be carbon and oxygen atoms moving freely and no remaining carbon dioxide.

Then the oxygen, having been given all that energy, will be trying very hard to join up with some other atom or molecule to form a more stable compound.

At some equilibrium temperature that combining will take occur and carbon dioxide will be the product. If held at that temperature in our closed system, we would observe the break down and re-combination processes going on as long as the temperature was maintained steady.

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