Steps for Determination of Oxidation Numbers

1. The oxidation number of the atoms in their elemental state is zero. This includes polyatomic elements such as H2, O2, O3,P4, and S8.
2. The oxidation number of an atom in a monatomic ion is equal to the charge on the ion.
3. The sum of the oxidation numbers of the atoms in a neutral compound is zero.
4. In a polyatomic ion, the sum of the oxidation numbers of the atoms is equal to the charge on the ion.
5. Hydrogen has an oxidation number of +1 in compounds, unless it is combined with metals, in which case it has an oxidation number of -1.
6. Oxygen usually has an oxidation number of -2 in its compounds. There are some exceptions:

a. Oxygen has an oxidation number of -1 in peroxide
b. Oxygen has an oxidation number of - ½ in superoxides.
c. When combined with fluorine in OF2, oxygen has an oxidation number of +2.

7. The position of the element in the periodic table helps to assign its oxidation number:

a. Group I elements have oxidation numbers of +1.
b. Group II elements have oxidation numbers of +2.
c. Group III elements have oxidation numbers of +3.
d. Group V elements have oxidation numbers of -3 in binary compounds with metals.
e. Group VI elements below oxygen have oxidation numbers of -2 in binary compounds with metals, with H, or with NH4+.
f. Group VII elements have oxidation numbers of -1 in binary compounds with metals, with H, with NH4+, or with a heavier halogen.

Assign oxidation numbers to each element in the following compounds: (a) N2O4, (b) NH3, (c) HNO3, (d) NO3-

N2O4

oxygen's oxidation number is -2,  there are 4 O resulting a total of -8,
the sum of the oxidation numbers has to be 0, therefore the total of nitrogen's oxidation numbers has to be +8
there are two nitrogens, so they are each +4

HNO3

hydrogen oxidation number is +1
oxygen oxidation number is -2 with three oxygen providing a total of -6
combined oxygen's and hydrogen's oxidation numbers total to -5
the sum of oxidation numbers for HNO3has to be 0 therefore nitrogen's oxidation number is +5

NH3

hydrogen's is oxidation number is +1, there are 3 H giving a sum of +3
the sum of the oxidation numbers has to be 0
therefor, nitrogen's oxidation number is -3

NO3-

oxygen's oxidation number is is -2, and there are 3 of them providing a total of -6
the total of the oxidation numbers has to combined to -1
therefor nitrogen is +5