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Can total formal charge of a molecule be found, not only by summarizing individual atom's formal charges, but also by seeing how many electrons have been added on top of the total number of electrons the free atoms would have?
What you are describing is how we determine the charge of a polyatomic ion (a molecule with an overall charge). I don't think this is generally referred to as finding the formal charge of the molecule, it's just called finding the charge of the polyatomic ion.
Adding up the formal charges of the atoms of a molecule should give you the overall oxidation number if that's what you mean, but NOT the net formal charge. You will need to calculate the individual formal charges of each atom in order to understand if they have the correct configuration of electrons and if a certain atom is not wanting or discarding electrons to have a stable structure. This makes it easier to compare Lewis structures in a more precise way. Having a net formal charge is not something we have heard of before.
I think what you're referencing can help you when drawing Lewis structures/ diagrams, but it doesn't really serve as a reliable way to calculate formal charge. The number of "added" electrons will help you recognize if there is a net charge to be aware of, which is really important because it changes the amount of electrons in the diagram. But when you're looking at formal charge you should have already included those electrons, so your formal charge calculations are kind of independent of those extra electrons. If it helps you check to make sure you're using the right number of electrons that is totally fine, but I would make sure to use the traditional way of finding formal charge so you don't mix anything up.
I agree with the above posts. I think using the formal charge equation is the best way to determine the total formal charge because it will ensure that you calculate the formal charges of each individual atom correctly. It will also ensure that you assign the correct formal charge to each individual atom, which is important if you are asked to identify the most favorable lewis structure.
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