The correct option is A 6Fe3O4+2MnO−4+H2O→9Fe2O3+2MnO2+2OH−
The unbalanced redox equation is as follows:
Fe3O4+MnO−4→Fe2O3+MnO2
Balance all atoms other than H and O.
2Fe3O4+MnO−4→3Fe2O3+MnO2
The oxidation number of Fe changes from 2.67 to 3. The change in the oxidation number of 1 Fe atom is 0.33. Total change in the oxidation number for 6 C atoms is 2.
The oxidation number of Mn changes from +7 to 4. The change in the oxidation number of Mn is 3.
The increase in the oxidation number is balanced with decrease in the oxidation number by multiplying Fe3O4 and Fe2O3 with 3 and by multiplying MnO−4 and MnO2 with 2.
6Fe3O4+2MnO−4→9Fe2O3+2MnO2
O atoms are balanced by adding 1 water molecule on RHS.
6Fe3O4+2MnO−4→9Fe2O3+2MnO2+H2O
Hydrogen atoms are balanced by adding 2 H+ atoms on the LHS.
6Fe3O4+2MnO−4+2H+→9Fe2O3+2MnO2+H2O
Since the reaction occurs in basic medium, add 2 hydroxide ions on both sides of the equation.
6Fe3O4+2MnO−4+2H++2OH−→9Fe2O3+2MnO2+H2O+2OH−
On LHS, 2 H+ ions combine with 2 OH− ions to form 2 water molecules out of which 1 water molecule cancels with 1 water molecule on RHS.
6Fe3O4+2MnO−4+H2O→9Fe2O3+2MnO2+2OH−
This is the balanced chemical equation.