To correctly determine the oxidation numbers of atoms there are certain rules that prove helpful and that should be followed.
The most important rule is that elements have an oxidation state of 0. This is due to the fact that elements are neutral atoms with a 0 charge. Secondly, an ion that exists by itself (monatomic) has an oxidation number equal to its ionic charge. If you have an oxygen atom, as an example, its oxidation state would be zero because it is a neutral element. However, if you have an oxygen ion, its oxidation number is equal to its ionic charge of -2. This leads on to the third rule which states that oxygen always has an oxidation number of -2, except in peroxides where it is -1.
Fourthly, hydrogen has an oxidation state of +1, except when it is in a binary compound with a metal where it is (-1). Halogens in group 5 always have an oxidation state of -1, with the exception of binary compounds with another halogen or with oxygen.
The finale and perhaps most important and simple rule to remember is that any compound has an oxidation state of 0. So when you add up all the oxidation numbers in a compound, you know they should add up to 0.
Some examples might help the understanding of this topic. Suppose that we wanted to find the oxidation numbers in perchloric acid HClO4. We know that oxygen has (-2), but there are 4 oxygen atoms present, so the total charge from oxygen is 4(-2)=-8. Hydrogen we know has a charge of +1 with nonmetals, so by doing simple computation we get the oxidation state of chlorine from -8+1 +Cl= 0. The oxidation number of chlorine is thus +7. We could set up this equation because the compound itself is in a neutral state with an oxidation number of 0.
So what is the use of oxidation numbers? They become very useful in describing oxidation-reduction reactions. By assigning specific numbers to each element during a reaction, we can know exactly how the electrons were transferred. We can then classify different atoms as an oxidizing or reducing agent.
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