J.R. S. answered 04/01/21
Ph.D. University Professor with 10+ years Tutoring Experience
First, you must balance the half reactions.
We'll do the reduction half reaction first:
MnO4- ==> Mn2+
MnO4- ==> Mn2+ + 4H2O ... balanced for O
MnO4- + 8H+ ==> Mn2+ + 4H2O ... balanced for H
MnO4- + 8H+ + 5e- ==> Mn2+ + 4H2O ... balance for charge, O, and H and Mn (BALANCED REACTION)
Next, we'll do the oxidation half reaction:
SO32- ==> SO42-
SO32- + H2O ==> SO42- ... balanced for O
SO32- + H2O ==> SO42- + 2H+ ... balanced for H
SO32- + H2O ==> SO42- + 2H+ + 2e- ... balanced for charge, O, H, and S (BALANCED REACTION)
MnO4- + 8H+ + 5e- ==> Mn2+ + 4H2O ... balanced reduction
SO32- + H2O ==> SO42- + 2H+ + 2e- ... balance oxidation
To equalize electrons, we must multiply reduction reaction by 2 and oxidation reaction by 5 to get...
2MnO4- + 16H+ + 10e- ==> 2Mn2+ + 8H2O ... balanced reduction
5SO32- + 5H2O ==> 5SO42- + 10H+ + 10e- ... balanced oxidation
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2MnO4- + 6H+ + 5SO32- => 2Mn2+ + 3H2O + 5SO42- combined reactions = BALANCED EQUATION