Balance the equation by lon-electron method
(i) `MnO_(4)^(-) + Fe^(2+) to Mn^(2+)+ Fe^(3+)` (In acidic medium)

Explanation

Write the oxidation number of all the atoms.
`overset(+7-2)(MnO_(4)^(-))+" "Fe^(+2)rarrMn^(+2)+Fe^(+3)`
Change in oxidation number has occurred in Mn and Fe.
`{:(overset(+7)(MnO_(4)^(-))rarroverset(+2)(Mn^(+2))," ..................(1) (Decrement in oxidation number by 5)"),(Fe^(+2)rarrFe^(+3)," ..................(2) (Increment in oxidation number by 1)"):}`
To make increase and decrease equal, eq. (2) is multiplied by 5.
`MnO_(4)^(-)+5Fe^(+2)rarrMn^(+2)+5Fe^(+3)`
To balance oxygen, `4H_(2)O` are added to R.H.S. and to balance hydrogen, `8H^(+)` are added to L.H.S.
`MnO_(4)^(-)+5Fe^(+2)+8H^(+)rarrMn^(+2)+5Fe^(+3)+4H_(2)O`
This is the balanced equation.