Balance the following by ion electron method in acidic medium.
`CIO_(3)^(ө)+I_(2)rarrIO_(3)^(ө)+CI^(ө)`

Explanation

(a) Ion electron method Write the skeleton equation for the given reaction.
`MnO_(4)^(-)(aq)+SO_(2)(g)toMn^(2+)(aq)+HSO_(4)^(-)(aq)`.
Find out the elements which undergo change in O.N.

Divide the given skeleton into two half equations.
Reduction half equation: `MnO_(4)^(-)(aq)toMn^(2+)(aq)`
Oxidation half equation : `SO_(2)(g)toHSO_(4)^(-)(aq)`
To balance reduction half equation
In acidic medium, balance H and O-atoms
`MnO_(4)^(-)(aq)+8H^(+)(aq)+5e^(-)toMn^(2+)(aq)+H_(2)O(l)`
To balance the complete reaction
`({:(2MnO_(4)(aq)+16H^(+)(aq)+10e^(-)toMn^(2+)(aq)+8H_(2)O(l)),(5SO_(2)(g)+10H_(2)O(l)to5HSO_(4)^(-)(aq)+15H^(+)(aq)+10e^(-)):})/(2MnO_(4)^(-)(aq)+5SO_(2)(g)+2H_(2)O(l)+H^(+)(aq)to2Mn^(2+)(aq)+5HSO_(4)^(-)(aq))`
(b) Oxidation number method Write the skeleton equation for the given reaction.
`N_(2)H_(4)(l)+ClO_(3)^(-)(aq)toNO(g)+Cl^(-)(g)`
O.N. increases by 4 per N-atom

Multiply `NO` by 2 because in `N_(2)H_(4)` there are 2N atoms
`N_(2)H_(4)(l)+ClO_(3)^(-)(aq)to2NO(g)+Cl^(-)(aq)`
Total increase in O.N. of `N=2xx4 = 8(8e^(-) "lost")`
Total decrease in O.N. of `Cl=1xx6=6(6e^(-) "gain")`
Therefore, to balance increase of decrease in O.N. multiply `N_(2)H_(4)` by 3. 2NO by 3 and `ClO_(3),Cl^(-)` by 4
`3N_(2)H_(4)(l)+4ClO_(3)^(-)(aq)to6NO(g)+4Cl^(-)(aq)`
Balance O and H-atoms by adding `6H_(2)O` to RHS
`3N_(2)H_(4)(l)+4ClO_(3)^(-)(aq)to6NO(g)+4Cl^(-)(aq)+6H_(2)O(l)`
( c) Ion electron method Write the skeleton equation for the given reaction.
`Cl_(2)O_(7)(g)+H_(2)O_(2)(aq)toClO_(2)^(-)(aq)+O_(2)(g)`
Find out the elements which undergo a change in O.N.

Divide the given skeleton equation into two half equations.
Reduction half equation : `Cl_(2)O_(7)toClO_(2)^(-)`
Oxidation half equation : `H_(2)O_(2)toO_(2)`
To balance the reduction half equation
`Cl_(2)O_(7)(g)+6H^(+)(aq)+8e^(-)to2ClO_(2)^(+)(aq)+3H_(2)O(l)`
To balance teh oxidation half equation
`H_(2)O_(2)(aq)toO_(2)(aq)+2H^(+)2e^(-)`
To balance the complete reaction
`({:(Cl_(2)O_(7)(g)+6H^(+)(aq)+8e^(-)to2ClO_(2)^(-)(aq)+3H_(2)O(l)),(" "4H_(2)O_(2)(aq)to4O_(2)(g)+8H^(+)(aq)+8e^(-)):})/(Cl_(2)O_(7)(g)+4H_(2)O_(2)(aq)to2ClO_(2)^(-)(aq)+3H_(2)O(l)+4O_(2)(g)+2H^(+)+(aq))`
This represents the balanced redox reaction