NOTE: This is NOT the same as balancing a regular chemical reaction! Please see the related question to the bottom of this answer for how to balance a normal chemical reaction. This is for oxidation-reduction, or redox reactions ONLY!
These instructions are for how to balance a reduction-oxidation, or redox reaction in aqueous solution, for both acidic and basic solution. Just follow these steps! I will illustrate each step with an example. The example will the dissolution of copper(II) sulfide in aqueous nitric acid, shown as the following
unbalanced reaction:
CuS
(s) + NO
3-(aq) ---> Cu
2+(aq) + SO
42-(aq) + NO
(g)Step 1:
Write two unbalanced half-reactions, one for the species that is being oxidized and its product, and one for the species that is reduced and its product.
Here is the unbalanced half-reaction involving CuS:
CuS
(s) ---> Cu
2+(aq) + SO
42-(aq) And the unbalanced half-reaction for NO
3- is:
NO
3-(aq) --> NO
(g)Step 2:
Insert coefficients to make the numbers of atoms of all elements except oxygen and hydrogen equal on the two sides of each half-reaction. In this case, copper, sulfur, and nitrogen are already balanced in the two half-reaction, so this step is already done here.
Step 3:
Balance oxygen by adding H2O to one side of each half-reaction. CuS + 4 H
2O ---> Cu
2+ + SO
42- NO
3- --> NO + 2 H
2O
Step 4:
Balance hydrogen atoms. This is done differently for acidic versus basic solutions.
For acidic solutions: Add H3O+ to each side of each half-reaction that is "deficient" in hydrogen (the side that has fewer H's) and add an equal amount of H2O to the other side.
For basic solutions: add H2O to the side of the half-reaction that is "deficient" in hydrogen and add an equal amount of OH- to the other side. Note that this step does not disrupt the oxygen balance from Step 3. In the example here, it is in acidic solution, and so we have:
CuS + 12 H2O ---> Cu2+ + SO42- + 8 H3O+
NO
3- + 4 H
3O
+ --> NO + 6 H
2O
Step 5:
Balance charge by inserting e- (electrons) as a reactant or product in each half-reaction.
Oxidation: CuS + 12 H2O ---> Cu2+ + SO42- + 8 H3O+ + 8 e-
Reduction: NO3- + 4 H3O+ + 3 e- --> NO + 6 H2O
Step 6:
Multiply the two half-reactions by numbers chosen to make the number of electrons given off by the oxidation step equal to the number taken up by the reduction step. Then add the two half-reactions. If done correctly, the electrons should cancel out (equal numbers on the reactant and product sides of the overall reaction). If H3O+, H2O, or OH- appears on both sides of the final equation, cancel out the duplication also. Here the oxidation half-reaction must be multiplied by 3 (so that 24 electrons are produced) and the reduction half-reaction must by multiplied by 8 (so that the same 24 electrons are consumed).
3 CuS + 36 H
2O ---> 3 Cu
2+ + 3 SO
42- + 24 H
3O
+ + 24 e
- 8 NO
3- + 32 H
3O
+ + 24
e- ---> 8 NO + 48 H
2O
Adding these two together gives the following equation:
3 CuS + 36 H
2O + 8 NO
3- + 8 H
3O
+ ---> 3 Cu
2+ + 3 SO
42- + 8 NO + 48 H
2O
Step 7:
Finally balancing both sides for excess of H2O (On each side -36) This gives you the following overall balanced equation at last:
3 CuS(s) + 8 NO3-(aq) + 8 H3O+(aq) ---> 3 Cu2+(aq) + 3 SO42-(aq) + 8 NO(g) + 12 H2O(l)