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When I attempted to draw this, I put two double bonds on a C, so it looked like C=C=N for that part of the structure. I was told a triple bond between the C and N would be preferred, removing the double bond between the C's. Is this a general rule that an atom doesn't want multiple double bonds to other atoms, or is this just a specific situation for this molecule?
The lewis structure with 3 bonds between C and N is preferred because of formal charge. If were two bonds between C and C, the carbon on the end would have more than an octet. The formal charge of Nitrogen is 0 because it has 3 bonds and one lone pair.
As for your double bond question, the only time I can think of where you wouldn't want adjacent double bonds is for carbon rings (because that would result in more than an octet for the carbon atoms involved).
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