Which of the following is the correctly balanced equation for the redox reaction of MnO_4^- + Cl^- → MnO_2 + Cl_2 in basic solution?

• A. 2 MnO_4^- + 2 Cl^- + 4 OH^- → 2 MnO_2 + Cl_2 + 2 H_2O
• B. MnO_4^- + Cl^- + OH^- → MnO_2 + Cl_2 + H_2O
• C. 2 MnO_4^- + 10 Cl^- + 8 OH^- → 2 MnO_2 + 5 Cl_2 + 4 H_2O
• D. MnO_4^- + 2 Cl^- + 2 OH^- → MnO_2 + Cl_2 + H_2O

Answer: (C)

Verified step by step guidance

1. Identify the oxidation and reduction half-reactions in the given redox reaction. Here, permanganate ion (MnO_4^-) is reduced to manganese dioxide (MnO_2), and chloride ion (Cl^-) is oxidized to chlorine gas (Cl_2).
2. Write the half-reactions separately, including the electrons to balance the changes in oxidation states. For example, balance Mn and Cl atoms first, then balance oxygen by adding OH^- (since the solution is basic), and balance hydrogen by adding H_2O.
3. Balance the electrons lost in the oxidation half-reaction with the electrons gained in the reduction half-reaction by multiplying each half-reaction by appropriate coefficients so that the number of electrons cancels out when the half-reactions are added.
4. Add the two half-reactions together, canceling out species that appear on both sides (such as electrons and water molecules if possible), to get the overall balanced redox equation in basic solution.
5. Verify that the number of atoms of each element and the charges are balanced on both sides of the final equation, ensuring the equation is correctly balanced.