Why does the correct lewis structure of Co2 involve a double bond between each of the oxygen atoms and the carbon atom

Because both carbon and oxygen are demanded to obey the octet's rule.

Explanation:

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In this case, recalling the Lewis dot structure of CO₂ which is basically:

We know oxygen has six valance electron whereas carbon four valence electrons, it means that oxygen needs two electrons in order to attain eight electrons and carbon needs four electrons for the same purpose. In such a way, as carbon dioxide contains one carbon atom and two oxygen atoms we infer that each oxygen is providing two electrons for a total of four to allow the carbon obey the octet as well as oxygen and this is attained via two double bonds.

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explanation: