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The problem asks you to draw the Lewis structure for ONF. So, the structure has N as the central atom, with a double bond between O and N and a single bond between N and F. But why can't you put the double bond between N and F and the single bond between O and N?
Going off the explanation above, when you are drawing Lewis structures it's best to think about the octet rule, in which every element has 8 e- in the outer most shell (through sharing valence e- in this case). But, there are a few exceptions (the slides mention the exceptions as H, He, Li, and Be) and we later learned that in the section about resonance P, S, and Cl are exceptions to the octet rule.
You can also try checking the formal charge. If we were to put a double bond between the N and the F, and a single bond between the N and the O, the formal charge for F would be +1, and the formal charge for O would be -1. This is worse than the zero formal charges across the board when the double bond is between the O and the N, and the single bond is between the N and the F. Therefore, the latter is more stable and accepted.
Continuing from this, how would we know which atom would be the central atom? The book stated that "usually" the central atom would be listed first, but for ONF this clearly was not the case... how could we tell from the "usually" and exceptions?
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