Jacob, if I look at your formula it seems that you could move the C_N bond to the left. Then O would have 2 bonds, the C on the left would still have 4, the N would have 3 and the O on the right has 2. The C on the right only has 3 bonds, though. Suppose you put an electron dot above it, as we do with Lewis structures, to show an electron looking for a pair. You may know that a structure like this is sometimes called a radical, and radicals like to pair up and turn their electrons into a pair. NO2 does the same thing; it pairs up to make a dimer, N2O4.
Your compound's "empirical formula" is C2O2N because when you analyze it and weigh the C, O and N, the atom ratios fit that formula. You proposed a nice structure to go with that formula but you also know something else: each O has 6 electrons in the outer shell and each C has 4 electrons so you can also make electron pairs with C's and O's, but N has 5 electrons so there will always be an electron left over in C-O-N compounds unless you have an even number of N's. If you say that the "molecular formula" has to be a multiple of the "empirical formula" to solve that problem, then you can write the molecular formula as (C2O2N)2n where "n" is any number. Other structures than the dimer may work for you.
You said that you "made" C2O2N. Did you make the formula or did you do an experiment and make some stuff? If you made stuff, what did it look and feel like?
