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A formal charge is the charge assigned to an atom in a molecule, assuming the electrons in a chemical bond are shared equally between the atoms. You know how to calculate it, but the purpose of it is to determine which of the Lewis structures it the most stable/correct. The lower the formal charge, the more stable the structure.
Assigning formal charge allows you to determine the most stable and accurate lewis structure for the compound. There can be multiple valid/correct ways to draw a Lewis structure for something, but the lowest energy model (which you use formal charges to find) will be a better representation of what the compound actually looks like.
The point of formal charge is to make sure you are drawing the most stable and hence most likely version of a molecule you would see in nature. For example, if you draw a molecule one way and the formal charges of two atoms are 2+ and 2- they cancel out. However, if you draw the molecule another way you find the formal charges of two atoms are 1+ and 1-. In both cases the formal charges cancel out but in the case where the charges are 1+ and 1- there is less overall formal charge within the molecule which means it is more stable.
Formal charge allows us to find the most likely molecular structure when there are multiple valid Lewis structures. Among the valid Lewis structure, the structure with FC closest to 0 is the most likely arrangement of atoms. It is super important to note that this is not the same as resonance or electron delocalization. The difference in FC actually corresponds to structural differences, in using FC to compare structure, we can determine the most likely molecular structure.
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