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I know the general Lewis dot structure of carbon dioxide is the one where there are two double bonds connecting oxygens to carbon.

However the question is, does $\ce{CO2}$ have resonance structures?

We could have moved one of the bonds (pi bond in this case) to the other $\ce{O-C}$ bond, leaving us with a single bond and a triple bond forming $\ce{CO2}$.

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It is almost always possible to draw resonance structures. In case of $\ce{CO2}$ you could imagine a resonance structure in which the carbon doesn't have an electron octet and a positive charge and one of the oxygen atoms carrying a negative charge.
You could also draw one in which the carbon is only connected via a single bound to each oxygen and carrying two positive charges while the two oxygens carry a negative charge each.

You might come up with more of those structures.

So the question you really wanna ask is whether these resonance structures have any real contribution to the actual bonding state of $\ce{CO2}$ and for that you will see that all of the described strucutures are highly unfavourable due to their energetic state. Therefore the normal Lewis-notation of $\ce{CO2}$ decribes the real bonding state pretty well as all other resonance structures don't contribute much.

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    $\begingroup$ I'm just confused. There was an IB chemistry test that asked for which of the following compounds have resonance structures. However, it said that CO2 did not count as a compound having resonance structure. $\endgroup$ – Stone Dec 10 '17 at 12:38
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    $\begingroup$ The they most likely meant resonance structure that actually contribute to the structure and bounding state of the molecule. In that case (as mentioned above) CO2 does indeed not have a resonance structure. $\endgroup$ – Raven Dec 10 '17 at 13:50
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    $\begingroup$ Every single molecule can be described with more then one contributor to structure chemistry.stackexchange.com/questions/32306/… $\endgroup$ – Mithoron Dec 11 '17 at 20:14

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