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A formal charge is just the charge on each specific atom in the molecule, the formal charges of the atoms should add up to the charge of the whole molecule. The purpose of the formal charges is to see the stability of the structures I think. The structure is more favored and stable if the central atom has a formal charge of 0. The farther away from 0 the formal charges get the more unfavorable it is.
Formal charge is the charge of a certain atom when it is bonded with other atoms in a molecule. A positive formal charge means that there are less electrons than there are protons in an atom, while a negative formal charge means there are more electrons than there are protons. In either case, the atom is imbalanced in its charge and therefore makes the molecule less stable. A formal charge that adds up to the charge of the whole ion, or to 0 in the case of a neutral molecule, makes the ion or molecule very stable; this is why it's important to draw Lewis structures in that way. My TA even told me that having formal charges add up to the total charge of the ion, or to 0 for a molecule, is more important than following the octet rule for each atom. So, there will be cases where atoms in a molecule may not have a full octet of electrons in a Lewis structure, but it is okay as long as the formal charge of each atom is 0. I hope this helped!
Although I do agree with the post before, I have found that in some cases, getting a 0 Formal Charge is not possible. Sometimes a molecule may be more stable when it is in a -1 or +1 charge simply because this is the same charge for either side. This would mostly be the case for molecules consisting of the same element.
My TA told me about a general guideline to follow when trying to figure out the best Lewis structures. When the molecule consists of atoms down and to the right of carbon, generally you would try to optimize the formal charges of each atom. For bonds between atoms down and to the left of boron, you would focus more on the octet rule. However, he emphasized that this is a general guideline, and there are exceptions to this pattern.
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