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Formal charge is a hypothetical charge given to every atom in a covalent molecule considering that the bond pair is shared equally between the atoms.
To calculate formal charge on an atom, total number of valence electrons in an isolated atom is substracted with the sum of bonding and non-bonding electrons in the bonded atom.
Formal Charge = Valence electrons - ( total bonding electrons + total non-bonding electrons ).
Remember, formal charge is very useful in asserting a lewis structure stable that other lewis structure of same compound.
Oxidation state is also a hypothetical charge given to every atom in a covalent molecule considering that the bond pair is shifted towards the more electronegative atom.
To calculate oxidation state of an atom in a molecule, one should shift the bond pair of electrons to more electronegative atom and give appropriate partial charges to each atom. The net charge obtained at the end will be the net oxidation state of the considered atom.
Oxidation state helps us predicting an oxidation or reduction reaction and it has nothing to do with the stability of a particular structure.
For more details, try watching khan's academy video on youtube on this topic. You are going to have many doubts clear.
Hope this helps.
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