The document describes the oxidation number method for balancing redox reactions. It provides two examples showing the steps: 1) Assign oxidation numbers and identify changes 2) Determine the ratio that balances the changes 3) Use the ratio to balance the reactants and products 4) Balance other elements by inspection The first example balances the reaction of aluminum with manganese dioxide to form aluminum oxide and manganese. The second example balances the reaction of ammonia with oxygen to form nitrogen dioxide and water.

1. BALANCING REDOX REACTIONS
Oxidation Number Method

2. OXIDATION NUMBER METHOD
Redox reactions can be balanced using:
a) Half Reactions
b) Oxidation numbers
Goal: To balance the electrons that
are gained and lost
NOTE: When half-reactions are not provided, and a reaction
does not occur in either acidic or basic solution, then the
oxidation number method can be used to balance a redox
reaction

3. OXIDATION NUMBER METHOD
Example #1
1. Assign oxidation numbers to each element.
2. Identify the increase and decrease in oxidation numbers.
3. Determine the smallest whole-number ratio of the oxidized and reduced elements so that the total increase in oxidation
numbers equals the total decrease in oxidation numbers.
4. Use the determined ratio from step 3 to balance the oxidized and reduced reactants.
5. Balance the other elements/compounds by inspection.
6. Add H2O, H+, and OH- as needed to balance reactions in acidic or basic solution (recall the half-reaction method rules)
Al(s) + MnO2(s)  Al2O3(s) + Mn(s)
0 +4 -2 +3 -2 0

4. OXIDATION NUMBER METHOD
Example #1
1. Assign oxidation numbers to each element.
2. Identify the increase and decrease in oxidation numbers.
3. Determine the smallest whole-number ratio of the oxidized and reduced elements so that the total increase in oxidation
numbers equals the total decrease in oxidation numbers.
4. Use the determined ratio from step 3 to balance the oxidized and reduced reactants.
5. Balance the other elements/compounds by inspection.
6. Add H2O, H+, and OH- as needed to balance reactions in acidic or basic solution (recall the half-reaction method rules)
+3
Al(s) + MnO2(s)  Al2O3(s) + Mn(s)
0 +4 -2 +3 -2 0
-4

5. OXIDATION NUMBER METHOD
Example #1
1. Assign oxidation numbers to each element.
2. Identify the increase and decrease in oxidation numbers.
3. Determine the smallest whole-number ratio of the oxidized and reduced elements so that the total increase in oxidation
numbers equals the total decrease in oxidation numbers.
4. Use the determined ratio from step 3 to balance the oxidized and reduced reactants.
5. Balance the other elements/compounds by inspection.
6. Add H2O, H+, and OH- as needed to balance reactions in acidic or basic solution (recall the half-reaction method rules)
+3
Al(s) + MnO2(s)  Al2O3(s) + Mn(s)
0 +4 -2 +3 -2 0
-4
Ratio = 4:3
Each Al atom loses 3, .: 4 Al loses 12
Each Mn atom gains 4, .: 3 Mn gains 12

6. OXIDATION NUMBER METHOD
Example #1
1. Assign oxidation numbers to each element.
2. Identify the increase and decrease in oxidation numbers.
3. Determine the smallest whole-number ratio of the oxidized and reduced elements so that the total increase in oxidation
numbers equals the total decrease in oxidation numbers.
4. Use the determined ratio from step 3 to balance the oxidized and reduced reactants.
5. Balance the other elements/compounds by inspection.
6. Add H2O, H+, and OH- as needed to balance reactions in acidic or basic solution (recall the half-reaction method rules)
+3
4 Al(s) + 3 MnO2(s)  Al2O3(s) + Mn(s)
0 +4 -2 +3 -2 0
-4
Ratio = 4:3

7. OXIDATION NUMBER METHOD
Example #1
1. Assign oxidation numbers to each element.
2. Identify the increase and decrease in oxidation numbers.
3. Determine the smallest whole-number ratio of the oxidized and reduced elements so that the total increase in oxidation
numbers equals the total decrease in oxidation numbers.
4. Use the determined ratio from step 3 to balance the oxidized and reduced reactants.
5. Balance the other elements/compounds by inspection.
6. Add H2O, H+, and OH- as needed to balance reactions in acidic or basic solution (recall the half-reaction method rules)
+3
4 Al(s) + 3 MnO2(s)  2Al2O3(s) + 3Mn(s)
0 +4 -2 +3 -2 0
-4
Ratio = 4:3

8. OXIDATION NUMBER METHOD
Example #1
1. Assign oxidation numbers to each element.
2. Identify the increase and decrease in oxidation numbers.
3. Determine the smallest whole-number ratio of the oxidized and reduced elements so that the total increase in oxidation
numbers equals the total decrease in oxidation numbers.
4. Use the determined ratio from step 3 to balance the oxidized and reduced reactants.
5. Balance the other elements/compounds by inspection.
6. Add H2O, H+, and OH- as needed to balance reactions in acidic or basic solution (recall the half-reaction method rules)
4 Al(s) + 3 MnO2(s)  2Al2O3(s) + 3Mn(s)

9. OXIDATION NUMBER METHOD
Example #2
1. Assign oxidation numbers to each element.
2. Identify the increase and decrease in oxidation numbers.
3. Determine the smallest whole-number ratio of the oxidized and reduced elements so that the total increase in oxidation
numbers equals the total decrease in oxidation numbers.
4. Use the determined ratio from step 3 to balance the oxidized and reduced reactants.
5. Balance the other elements/compounds by inspection.
6. Add H2O, H+, and OH- as needed to balance reactions in acidic or basic solution (recall the half-reaction method rules)
NH3(g) + O2(g)  NO2(g) + H2O(l)
-3 +1 0 +4 -2 +1 -2

10. OXIDATION NUMBER METHOD
Example #2
1. Assign oxidation numbers to each element.
2. Identify the increase and decrease in oxidation numbers.
3. Determine the smallest whole-number ratio of the oxidized and reduced elements so that the total increase in oxidation
numbers equals the total decrease in oxidation numbers.
4. Use the determined ratio from step 3 to balance the oxidized and reduced reactants.
5. Balance the other elements/compounds by inspection.
6. Add H2O, H+, and OH- as needed to balance reactions in acidic or basic solution (recall the half-reaction method rules)
+7
NH3(g) + O2(g)  NO2(g) + H2O(l)
-3 +1 0 +4 -2 +1 -2
-2

11. OXIDATION NUMBER METHOD
Example #2
1. Assign oxidation numbers to each element.
2. Identify the increase and decrease in oxidation numbers.
3. Determine the smallest whole-number ratio of the oxidized and reduced elements so that the total increase in oxidation
numbers equals the total decrease in oxidation numbers.
4. Use the determined ratio from step 3 to balance the oxidized and reduced reactants.
5. Balance the other elements/compounds by inspection.
6. Add H2O, H+, and OH- as needed to balance reactions in acidic or basic solution (recall the half-reaction method rules)
+7
NH3(g) + O2(g)  NO2(g) + H2O(l)
-3 +1 0 +4 -2 +1 -2
-2
Ratio = 4:7
Each N atom loses 7, .: 4 N loses 28
Each O atom gains 2  each O2 gains 4, .: 7 O2 gains 28

12. OXIDATION NUMBER METHOD
Example #2
1. Assign oxidation numbers to each element.
2. Identify the increase and decrease in oxidation numbers.
3. Determine the smallest whole-number ratio of the oxidized and reduced elements so that the total increase in oxidation
numbers equals the total decrease in oxidation numbers.
4. Use the determined ratio from step 3 to balance the oxidized and reduced reactants.
5. Balance the other elements/compounds by inspection.
6. Add H2O, H+, and OH- as needed to balance reactions in acidic or basic solution (recall the half-reaction method rules)
+7
4 NH3(g) + 7 O2(g)  NO2(g) + H2O(l)
-3 +1 0 +4 -2 +1 -2
-2
Ratio = 4:7
Each N atom loses 7, .: 4 N loses 28
Each O atom gains 2  each O2 gains 4, .: 7 O2 gains 28

13. OXIDATION NUMBER METHOD
Example #2
1. Assign oxidation numbers to each element.
2. Identify the increase and decrease in oxidation numbers.
3. Determine the smallest whole-number ratio of the oxidized and reduced elements so that the total increase in oxidation
numbers equals the total decrease in oxidation numbers.
4. Use the determined ratio from step 3 to balance the oxidized and reduced reactants.
5. Balance the other elements/compounds by inspection.
6. Add H2O, H+, and OH- as needed to balance reactions in acidic or basic solution (recall the half-reaction method rules)
+7
4 NH3(g) + 7 O2(g)  4 NO2(g) + 6H2O(l)
-3 +1 0 +4 -2 +1 -2
-2
Ratio = 4:7
Each N atom loses 7, .: 4 N loses 28
Each O atom gains 2  each O2 gains 4, .: 7 O2 gains 28

14. OXIDATION NUMBER METHOD
Example #2
1. Assign oxidation numbers to each element.
2. Identify the increase and decrease in oxidation numbers.
3. Determine the smallest whole-number ratio of the oxidized and reduced elements so that the total increase in oxidation
numbers equals the total decrease in oxidation numbers.
4. Use the determined ratio from step 3 to balance the oxidized and reduced reactants.
5. Balance the other elements/compounds by inspection.
6. Add H2O, H+, and OH- as needed to balance reactions in acidic or basic solution (recall the half-reaction method rules)
4 NH3(g) + 7 O2(g)  4 NO2(g) + 6H2O(l)

15. OXIDATION NUMBER METHOD
Example #3: In acidic solution
1. Assign oxidation numbers to each element.
2. Identify the increase and decrease in oxidation numbers.
3. Determine the smallest whole-number ratio of the oxidized and reduced elements so that the total increase in oxidation
numbers equals the total decrease in oxidation numbers.
4. Use the determined ratio from step 3 to balance the oxidized and reduced reactants.
5. Balance the other elements/compounds by inspection.
6. Add H2O, H+, and OH- as needed to balance reactions in acidic or basic solution (recall the half-reaction method rules)
Cu(s) + NO3-(aq)  NO2(g) + Cu2+(aq)
0 +5 -2 +4 -2 +2

16. OXIDATION NUMBER METHOD
Example #3: In acidic solution
1. Assign oxidation numbers to each element.
2. Identify the increase and decrease in oxidation numbers.
3. Determine the smallest whole-number ratio of the oxidized and reduced elements so that the total increase in oxidation
numbers equals the total decrease in oxidation numbers.
4. Use the determined ratio from step 3 to balance the oxidized and reduced reactants.
5. Balance the other elements/compounds by inspection.
6. Add H2O, H+, and OH- as needed to balance reactions in acidic or basic solution (recall the half-reaction method rules)
+2
Cu(s) + NO3-(aq)  NO2(g) + Cu2+(aq)
0 +5 -2 +4 -2 +2
-1

17. OXIDATION NUMBER METHOD
Example #3: In acidic solution
1. Assign oxidation numbers to each element.
2. Identify the increase and decrease in oxidation numbers.
3. Determine the smallest whole-number ratio of the oxidized and reduced elements so that the total increase in oxidation
numbers equals the total decrease in oxidation numbers.
4. Use the determined ratio from step 3 to balance the oxidized and reduced reactants.
5. Balance the other elements/compounds by inspection.
6. Add H2O, H+, and OH- as needed to balance reactions in acidic or basic solution (recall the half-reaction method rules)
+2
Cu(s) + NO3-(aq)  NO2(g) + Cu2+(aq)
0 +5 -2 +4 -2 +2
-1
Ratio = 1:2
Each Cu atom gains 2, .: 1 Cu gains 2
Each N atom loses 1, .: 2 N loses 2

18. OXIDATION NUMBER METHOD
Example #3: In acidic solution
1. Assign oxidation numbers to each element.
2. Identify the increase and decrease in oxidation numbers.
3. Determine the smallest whole-number ratio of the oxidized and reduced elements so that the total increase in oxidation
numbers equals the total decrease in oxidation numbers.
4. Use the determined ratio from step 3 to balance the oxidized and reduced reactants.
5. Balance the other elements/compounds by inspection.
6. Add H2O, H+, and OH- as needed to balance reactions in acidic or basic solution (recall the half-reaction method rules)
+2
Cu(s) +2 NO3-(aq)  NO2(g) + Cu2+(aq)
0 +5 -2 +4 -2 +2
-1
Ratio = 1:2
Each Cu atom gains 2, .: 1 Cu gains 2
Each N atom loses 1, .: 2 N loses 2

19. OXIDATION NUMBER METHOD
Example #3: In acidic solution
1. Assign oxidation numbers to each element.
2. Identify the increase and decrease in oxidation numbers.
3. Determine the smallest whole-number ratio of the oxidized and reduced elements so that the total increase in oxidation
numbers equals the total decrease in oxidation numbers.
4. Use the determined ratio from step 3 to balance the oxidized and reduced reactants.
5. Balance the other elements/compounds by inspection.
6. Add H2O, H+, and OH- as needed to balance reactions in acidic or basic solution (recall the half-reaction method rules)
+2
Cu(s) +2 NO3-(aq)  2 NO2(g) + Cu2+(aq)
0 +5 -2 +4 -2 +2
-1
Ratio = 1:2
Each Cu atom gains 2, .: 1 Cu gains 2
Each N atom loses 1, .: 2 N loses 2

20. OXIDATION NUMBER METHOD
Example #3: In acidic solution
1. Assign oxidation numbers to each element.
2. Identify the increase and decrease in oxidation numbers.
3. Determine the smallest whole-number ratio of the oxidized and reduced elements so that the total increase in oxidation
numbers equals the total decrease in oxidation numbers.
4. Use the determined ratio from step 3 to balance the oxidized and reduced reactants.
5. Balance the other elements/compounds by inspection.
6. Add H2O, H+, and OH- as needed to balance reactions in acidic or basic solution (recall the half-reaction method rules)
4H+ + Cu(s) +2 NO3-(aq)  2 NO2(g) + Cu2+(aq) + 2H2O
1. Write down the reactant and product and balance atoms other than oxygen and hydrogen.
2. Add H2O molecules to balance the oxygen atoms.
3. Add H+ ions to balance the hydrogen atoms.
4. Add electrons to balance the charge on both sides of the equation.

21. OXIDATION NUMBER METHOD
Example #3: In acidic solution
1. Assign oxidation numbers to each element.
2. Identify the increase and decrease in oxidation numbers.
3. Determine the smallest whole-number ratio of the oxidized and reduced elements so that the total increase in oxidation
numbers equals the total decrease in oxidation numbers.
4. Use the determined ratio from step 3 to balance the oxidized and reduced reactants.
5. Balance the other elements/compounds by inspection.
6. Add H2O, H+, and OH- as needed to balance reactions in acidic or basic solution (recall the half-reaction method rules)
4H+ + Cu(s) +2 NO3-(aq)  2 NO2(g) + Cu2+(aq) + 2H2O