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Think of it like this, Carbon has 5 Valence electrons and you must obey the octect rule. the 1st C has 5 , and the 2nd C has 5, thats 10 total. so you would need a double bond inbetween these 2 Carbons in order to sucessfully obey the octet rule. Therefore, C-C can only be double bonded. Although in organic chains C-C can be single, double, or triple bonded.

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