The determination of the oxidation number (or oxidation state) of chemical compounds can be made by following a few simple rules. The rules are presented in order with the previous rule superseding the next.

1. The oxidation number of an atom is zero in a neutral substance that contains atoms of only one element. Thus, the atoms in O₂, O₃, P₄, S₈, and aluminum metal all have an oxidation number of 0.

2. The oxidation number of simple ions is equal to the charge on the ion. The oxidation number of sodium in the Na⁺ ion is +1, for example, and the oxidation number of chlorine in the Cl^- ion is -1.

3. The oxidation number of hydrogen is +1 when it is combined with a nonmetal as in CH₄, NH₃, H₂O, and HCl.

4. The oxidation number of hydrogen is -1 when it is combined with a metal as in. LiH, NaH, CaH₂, and LiAlH₄.

5. The metals in Group IA form compounds (such as Li₃N and Na₂S) in which the metal atom has an oxidation number of +1.

6. The elements in Group IIA form compounds (such as Mg₃N₂ and CaCO₃) in which the metal atom has a +2 oxidation number.

7. Oxygen usually has an oxidation number of -2. Exceptions include molecules and polyatomic ions that contain O-O bonds, such as O₂, O₃, H₂O₂, and the O₂^2- ion.

8. The elements in Group VIIA often form compounds (such as AlF₃, HCl, and ZnBr₂) in which the nonmetal has a -1 oxidation number.

9. The sum of the oxidation numbers in a neutral compound is zero.

H₂O: 2(+1) + (-2) = 0

10. The sum of the oxidation numbers in a polyatomic ion is equal to the charge on the ion. The oxidation number of the sulfur atom in the SO₄^2- ion must be +6, for example, because the sum of the oxidation numbers of the atoms in this ion must equal -2.

SO₄^2-: (+6) + 4(-2) = -2

11. Elements toward the bottom left corner of the periodic table are more likely to have positive oxidation numbers than those toward the upper right corner of the table. Sulfur has a positive oxidation number in SO₂, for example, because it is below oxygen in the periodic table.

Definitions: The atom oxidized is the atom whose oxidation number increases.  The atom reduced isthe atom whose oxidation number decreases. Half reactions show the gain or loss of electrons by one atom (oxidized or reduced).  The oxidizing agent is the reactant containing the atom reduced. The reducing agent is the reactant containing the atom oxidized. Balancing an oxidation-reduction reaction: Find the number of electrons gained and lost by the agents. Select coefficients in front of them so that the numbers of electrons gained and lost are equal.

Problem: Assign the oxidation numbers of the atoms in the following compounds.

(a) Al₂O₃        (b) XeF₄         (c) K₂Cr₂O₇   (d) BaO₂     (e) (NH₄)₂MoO₄  (f)Na₃Co(NO₂)₆      (g) CS₂

Arrange the following compounds in order of increasing oxidation state for the carbon atom.

(a) CO            (b) CO₂           (c) H₂CO        (d) CH₃OH    (e) CH₄

1. Balance the following reaction by the half-reactions method in both acidic and basic media:

CN^-(aq)  +  MnO₄^-(aq) → CNO^-(aq)  +  MnO₂(s)

i) Assign oxidation numbers to each element.

ii) Divide the reaction into half reactions: Oxidation and Reduction.

iii) Balance the non-oxygen and hydrogen elements:

iv) Balance the Oxygen atoms by adding H₂O:

v) Balance the Hydrogen atoms by adding H⁺:

vi) Balance the charge on both sides by adding e^- to the side with the greater positive charge:

vii) Multiply the two half reactions by coefficients so that the e^-‘s cancel:

viii) Add the two reactions back together and cancel ions etc. that appear in equal amounts on both sides of the reaction:

viiii) Convert the resulting reaction to basic media using H⁺ + OH^- = H₂O:

For each reaction below, identify the atom oxidized, the atom reduced, the oxidizing agent, the reducing agent, the oxidation half reaction, the reduction half reaction, and then balance the equation by the method of oxidation-reduction showing all electrons transfers.

1) Mg + HCl <=> MgCl₂ + H₂

2) Fe + V₂O₃ <=> Fe₂O₃ + VO

3) KMnO₄ + KNO₂ + H₂SO₄ <=> MnSO₄ + H₂O + KNO₃ + K₂SO₄

4) K₂Cr₂O₇ + SnCl₂ + HCl <=> CrCl₃ + SnCl₄ + KCl + H₂O 

5) KMnO₄ + NaCl + H₂SO₄ <=> Cl₂ + K₂SO₄ + MnSO₄ + H₂O + Na₂SO₄

6) K₂Cr₂O₇ + H₂O + S <=> SO₂ + KOH + Cr₂O₃ 

7) KClO₃ + C₁₂H₂₂O₁₁ <=> KCl + H₂O + CO₂

8) H₂C₂O₄ + K₂MnO₄ <=> CO₂ + K₂O + Mn₂O₃ + H₂O

9) Mn(NO₃)₂ + NaBiO₃ + HNO₃ <=> HMnO₄ + Bi(NO₃)₃ + NaNO₃ + H₂O

10) H₂C₂O₄ + KMnO₄ <=> CO₂ + K₂O + Mn₂O₃ + H₂O