How do you balance redox reactions in basic solution?

This is a lengthy response, so be warned: in basic solution, redox equations are balanced as though they were in acid, and OH⁻ is used to convert to base at the end.

AN EXAMPLE

In basic solution, balance the following equation: MnO₄⁻ + CN⁻ → MnO₂ + CNO⁻

Resolution:

Divide the equation into two half-reactions, as follows: MnO₄⁻ → MnO₂ CN⁻ → CNO⁻.

Step 2: Align every atom except for H and O. Completed

Step3: Add H₂O to the deficient side to balance O. MnO₄⁻ → MnO₂+ 2H₂O CN⁻+ H₂O → CNO⁻

In step four, add H⁺ to the deficient side to balance H. MnO₄⁻+ 4H⁺ → MnO₂+ 2H₂O CN⁻+ H₂O → CNO⁻ + 2H⁺

Step 5: Add electrons to the more positive side to balance the charge. MnO₄⁻+ 4H⁺ + 3e⁻ → MnO₂+ 2H₂O CN⁻+ H₂O → CNO⁻ + 2H⁺ + 2e⁻

Step 6: The first half-reaction is multiplied by two, and the second half-reaction is multiplied by three. This gives the lowest common multiple of the electrons transferred, which in this case is six.

3 × [CN⁻+ H₂O → CNO⁻ + 2H⁺ + 2e⁻] 2 × [MnO₄⁻+ 4H⁺ + 3e⁻ → MnO₂+ 2H₂O]

Step 7: Combine the two half-reactions, eliminating terms that are similar.

3CN + 2H + 2MnO₄⁻ → 2MnO₂ + 3CNO⁻ + H₂O

This is the acid solution's balanced equation, which we now need to convert to the base solution.

Step 8: In order to cancel the H in the redox equation and cancel like terms, add enough multiples of the equations H⁺ + OH⁻ → H₂O or H₂O → H⁺ + OH⁻.

2MnO₄⁻+ 3CN⁻+ 2H⁺ → 2MnO₂ + 3CNO⁻ + H₂O 2H₂O → 2H⁺ + 2OH⁻

3CN + H₂O + 2MnO₄⁻ → 2MnO₂ + 3CNO⁻ + 2OH⁻

Step 9: Verify that the atoms are in balance. The following are listed from left to right: 2 Mn, 9 O, 3 C, 3 N, and 2 H.

Step 10: Verify the charges balance. 2- + 3- = 5- On the left; 3- + 2- = 5- On the right.

Equation 2MnO₄⁻+ 3CN⁻+ H₂O → 2MnO₂ + 3CNO⁻ + 2OH⁻ is balanced.

1. Identify the oxidation and reduction half-reactions.
2. Balance the elements in each half-reaction, excluding oxygen and hydrogen.
3. Balance oxygen atoms by adding water molecules to the side lacking oxygen.
4. Balance hydrogen atoms by adding hydrogen ions to the side lacking hydrogen.
5. Balance charge by adding electrons to the side with a higher positive charge.
6. Multiply each half-reaction to ensure the electrons cancel out.
7. Add the balanced half-reactions, canceling out common terms.
8. Check that mass and charge are balanced.
9. If in a basic solution, add hydroxide ions to both sides to neutralize hydrogen ions, then simplify the equation.