Balance the following equations in basic medium by ion-electron method and oxidation number methods and identify the oxidising agent and the reducing agent.
(a) `P_(4)(s) + OH^(-) (aq) rarr PH_(3) (g) + HPO_(2)^(-) (aq)`
(b) `N_(2)H_(4)(I) + ClO_(3)^(-) (aq) rarr NO(g) + Cl^(-) (g)`
(c) `Cl_(2)O_(7) (g) + H_(2)O_(2) (aq) rarr ClO_(2)^(-) (aq) + O_(2)(g) + H^(+)`

Explanation

`(a)P_(4)+OH^(-)to PH_(3)+HPO_(2)^(-)`
Reduction half cell
`P_(4)to PH_(3)`
`P_(4)to 4PH_(3)`
`P_(4)+12H_(2)Oto 4PH_(3)+12 OH^(-)("H balanced")`
`overset(P_(4)+12H_(2)O+12e^(-)to 4PH_(3)+12OH^(-))underline(3P_(4)+24 OH^(-)to 12H_(2)PH_(2)^(-)+12e^(-))/underline(4P_(4)+12H_(2)O+12e^(-)to 12H_(2)PO_(2)^(-)+4PH_(3))`
(b) Oxidation half cell
`P_(4)to H_(2)PO_(2)^(-)`
`P_(4)to 4H_(2)PO_(2)^(-)(".P. balanced")`
`P_(4)+8H_(2)O to 4H_(2)PO_(2)^(-)`("Oxygen balanced")
`P_(4)+8H_(2)O+8OH^(-)to 4H_(2)PO_(2)^(-)+8H_(2)O underset(("Hydrogen balanced"))`
`P_(4)+8OH^(-)to 4H_(2)PO_(2)^(-)+4e^(-)underset(("Charge balanced")`
Oxidation half cell
`N_(2)H_(4)to NO`
`N_(2)H_(4)to 2NO`
`N_(2)H_(4)+2H_(2)Oto 2NO`
`N_(2)H_(4)+2H_(2)O+8OH^(-)to 2 NO+8H_(2)O`
` N_(2)H_(4)+8OH^(-)to 2 NO +6H_(2)O`
`N_(2)H_(4)+8OH^(-)to 2 NO + 6H_(2)O+8e^(-)`
`ClO_(3)^(-)` is oxidant
`N_(2)H_(4)` is reductant
(c) `Cl_(2)O_(7)+H_(2)O_(2)to ClO_(2)^(-)+O_(2)+H^(+)`
Rrduction half cell
`Cl_(2)O_(7)to ClO_(2)^(-)`
`Cl_(2)O_(7)to 2ClO_(2)^(-)`
`Cl_(2)O_(7)to 2ClO_(2)^(-)+3H_(2)O`
`Cl_(2)O_(7)+ 6H_(2)Oto 2ClO_(2)^(-)+3H_(2)O+6OH^(-)`
`Cl_(2)O_(7)+3H_(2)O to 2ClO_(2)^(-)+6OH^(-)`
`Cl_(2)O_(7)+3H_(2)O +8e^(-)to 2ClO_(2)^(-)+6OH^(-)`
` overset(Cl_(2)O_(7)+3H_(2)O+8e^(-)to 2ClO_(2)^(-)+6 OH^(-))(4H_(2)O_(2)+8OH^(-)to 4O_(2)+8H_(2)O+8e^(-))/underline(Cl_(2)O_(7)+4H_(2)O_(2)+2OH^(-)to ClO_(2)^(-)+4O_(2)+5H_(2)O)`
`Cl_(2)O_(7)` is oxidant
`H_(2)O_(2)` is reductant
Oxidation half cell
`H_(2)O_(2)to O_(2)+H^(+)`
`H_(2)O_(2)to O_(2)+2H^(+)`
`H_(2)O_(2)+2(OH)to O_(2)+2H_(2)O`
`H_(2)O_(2)+2(OH^(-))to O_(2)+2H_(2)O+2e^(-)`