Answer and Explanation
MnO4- + Fe → Mn2+ + Fe3+
we need to balance the redox reaction in order to find the coefficient of H+
1. Identify the oxidation number of every atom.
to find the oxidation number let us take MnO4- as an example
MnO4- = -1 charge.
we know that oxygen has a -2 charge and there are 4 oxygen atoms in the molecule so 4 x -2 = -8
we see from the molecule that we have a net -1 charge so the Mn must be in the +7 oxidation state
so that +7 -8 = -1
Left hand side:
Fe = +2; Mn = +7; O = -2
Right hand side:
Fe = 0; Mn = +2
2. we separate the reaction to half reactions, oxidation reaction and reduction reaction and we add electrons to balance the reaction and H and O to balance out the other elements and charge
oxidation: MnO4- + 8H+ + 5e- → Mn2+ + 4H2O
reduction: Fe(s) → Fe3+(aq) + 3e
we multiply the redox reaction by the coefficient of the oxidation reaction and the oxidation reaction by the coefficient of the reduction reaction to get :
3MnO4- + 24H+ + 15e- → 3Mn2+ + 12H2O
5Fe(s) → 5Fe3+(aq) + 15e
now that we have the have reaction we add then together to get the net reaction
3MnO4- + 5Fe(s) + 24H+ + 15e- → 3Mn2+ + 12H2O + 5Fe3+(aq) + 15e
we simplify the reaction by cancelling out common terms of left and right hand side
3MnO4- + 5Fe(s) + 24H+ → 3Mn2+ 5Fe3+(aq) + 12H2O
we can see that everything balanced on the equation
therefore, the coefficient of H+ is 24