1
Example Balance the reaction in acidic solution
CuS (s) + NO 3− (aq) → Cu2+ (aq) + SO 24− (aq) + NO (g)
1. Write two half-rxns:
CuS (s) → Cu2+ (aq) + SO 24− (aq)
NO 3− (aq) → NO (g)
2. Balance elements other than H and O: Balanced
3. Balance oxygen by inserting H2O
CuS (s) + 4H2O (l) → Cu2+ (aq) + SO 42− (aq)
NO 3− (aq) → NO (g) + 2H2O (l)
4. Balance hydrogen by inserting H+
CuS (s) + 4H2O (l) → Cu2+ (aq) + SO 24− (aq) + 8H+ (aq)
NO 3− (aq) + 4H+ (aq) → NO (g) + 2H2O (l)
5. Balance charge by inserting e −
CuS (s) + 4H2O (l) → Cu2+ (aq) + SO 24− (aq) + 8H+ (aq) + 8e − (oxidation)
NO 3− (aq) + 4H+ (aq) + 3e − → NO (g) + 2H2O (l) (reduction)
6. Make the number of e − in the two half-rxns the same
3CuS (s) + 12H2O (l) → 3Cu2+ (aq) + 3SO 42− (aq) + 24H+ (aq) + 24e −
8NO 3− (aq) + 32H+ (aq) + 24e − → 8NO (g) + 16H2O (l)
7. Addition of the two half-rxns
3CuS (s) + 12H2O (l) + 8NO 3− (aq) + 32H+ (aq) + 24e − → 3Cu2+ (aq) + 3SO 24− (aq) +
24H+ (aq) + 24e − + 8NO (g) + 16H2O (l)
3CuS (s) + 8NO 3− (aq) + 8H+ (aq) → 3Cu2+ (aq) + 8NO (g) + 3SO 24− (aq) + 4H2O (l)
Check: Mass balance Cu: 3 3, S: 3 3, N: 8 8, H: 8 8, O: 24 24
Charge balance -8+8=0 +6-6=0
2
Example Balance the reaction in basic solution
Ag (s) + HS − (aq) + CrO 24− (aq) → Ag2S (s) + Cr(OH)3 (s)
1. Write the two half-rxns
Ag (s) + HS − (aq) → Ag2S (s)
CrO 24− (aq) → Cr(OH)3 (s)
2. Balance the elements other than H and O
2Ag (s) + HS − (aq) → Ag2S (s)
CrO 24− (aq) → Cr(OH)3 (s)
3. Balance O by inserting H2O
2Ag (s) + HS − (aq) → Ag2S (s)
CrO 24− (aq) → Cr(OH)3 (s) + H2O (l)
4. Balance H by inserting H2O on the side that is deficient in hydrogen and an
equal amount of OH − on the other side (basic solution)
2Ag (s) + HS − (aq) + OH − (aq) → Ag2S (s) + H2O (l)
CrO 24− (aq) + 5H2O (l) → Cr(OH)3 (s) + H2O (l) + 5OH − (aq)
5. Balance charge by inserting e −
2Ag (s) + HS − (aq) + OH − (aq) → Ag2S (s) + H2O (l) +2e − (oxidation)
CrO 24− (aq) + 5H2O (l) +3e − → Cr(OH)3 (s) + H2O (l) + 5OH − (aq) (reduction)
6. Make the number of e − in the two half-rxns the same
6Ag (s) + 3HS − (aq) + 3OH − (aq) → 3Ag2S (s) + 3H2O (l) +6e −
2CrO 24− (aq) + 10H2O (l) +6e − → 2Cr(OH)3 (s) + 2H2O (l) + 10OH − (aq)
7. Addition of the two half-rxns
6Ag (s) + 3HS − (aq) + 3OH − (aq) + 2CrO 42− (aq) + 10H2O (l) +6e − → 3Ag2S (s) +6e −
+2Cr(OH)3 (s) + 2H2O (l) + 2OH − (aq)
6Ag (s) + 3HS − (aq) + 2CrO 24− (aq) + 5H2O (l) → 3Ag2S (s) + 2Cr(OH)3 (s) +
7OH − (aq)
Check: Mass balance Ag: 6 6, S: 3 3, Cr: 2 2, H: 13 13, O: 13 13
Charge balance -7 -7