Balance the following equation by ion electron method in the acidic medium.
`Cr_(2)O_(7)^(2-)+C_(2)O_(4)^(2-)+H^(+)toCr^(3+)+CO_(2)+H_(2)O`

Explanation

Step 1. The given equation is
`MnO_(4)^(2-)+H_(2)OtoMnO_(4)^(-)+MnO_(2)+OH^(-)`
Step 2. Writing the oxidation number of atoms, we have
`overset(+6-2)(MnO_(4)^(2-))+overset(+1-2)(H_(2)O)tooverset(+7-2)(MnO_(4)^(-))+overset(+4-2)(MnO_(2))+overset(-2+1)(OH^(-))`
In this equation, on the right hand side, Mn is appearing in two oxidation states +7 and +4. This implies that a part of `MnO_(4)^(2-)` ions is oxidised into `MnO_(4)^(-)` ions (O.N. increased from +6 to +7) and the remaining `MnO_(4)^(2-)` ions are reduced into `MnO_(2)` (O.N. decreased from +6 to +4).
Step 3. Therefore, the half reactions can be written as follows.
`MnO_(4)^(2-)toMnO_(4)^(-)` (oxidation half reaction)
`MnO_(4)^(2-)toMnO_(2)` (reduction half reaction)
Step 4. (a) Balancing of oxidation half reaction :
(i) The Mn atoms are balanced.
(ii) Oxygen atoms are already balanced. Equation does not contain any H atom.
(iii) The charge can be balanced by adding one electron on the right
`MnO_(4)^(2-)toMnO_(4)^(-)+e^(-)`
This is the balanced oxidation half reaction.
(b) Balancing reduction half reaction :
(i) The Mn atoms are balanced
(ii) Since the reaction proceeds in basic medium, oxygen atoms can be balanced by adding `H_(2)O` ions on the right.
`MnO_(4)^(2-)toMnO_(2)+2OH^(-)`
Hydrogen atoms can be balanced by adding two `H_(2)O` molecules on the left and two more OH ions on the right.
`MnO_(4)^(2-)+2H_(2)OtoMnO_(2)+2OH^(-)+2OH^(-)`
or `MnO_(4)^(2-)+2H_(2)O+2e^(-)toMnO_(2)+4OH^(-)`
(iii) The charge can be balanced by adding two electrons on the left.
`MnO_(4)^(2-)+2H_(2)O+2e^(-)toMnO_(2)+4OH^(-)`
This is the balanced reduction half reaction.
Step 5. The electrons in the two balanced half reactions can be cancelled as shown below.
`{:([MnO_(4)^(2-)toMnO_(4)^(-)+e^(-)]xx2),(MnO_(4)^(2-)+2H_(2)O+2e^(-)toMnO_(2)+4OH^(-)),(bar(2MnO_(4)^(2-)+MnO_(4)^(2-)+2H_(2)Oto2MnO_(4)^(-)+MnO_(2)+4OH^(-))),(or3MnO_(4)^(2-)+2H_(2)Oto2MnO_(4)^(-)+MnO_(2)+4OH^(-)):}`
This is the final balanced equation in basic medium.