Balance the following ionic equations
(i) `Cr_2O_7^(2-) +H^(+)I^(-) rarr Cr^(3+)+I_(2)+H_(2)O`
(ii) `Cr_2O_(7)^(2-) +Fe^(2+)+H^(+)rarrCr^(3+)+Fe^(3+)+H_2O`
(iii) `MnO_(4)^(-) +SO_(3)^(2-)+H^(+)rarrMn^(2+)+SO_4^(2-)+SO_(4)^(2-)+H_2O`
(iv) `MnO_(4)^(-) +H^(+)+Br^(-) rarr Mn^(2+)+Br_(2)+H_(2)O`

Explanation

(i)
Dividing the equation into two half reactions :
Oxidation half reaction : `I^(-) rarrI_(2)`
Reduction half reaction : `Cr_(2)O_(7)^(2-) rarrCr^(3+)`
Balancing oxidation and reduction half reactions separately as :
Oxidation half reaction
`I^(-) rarr I_2`
`2I^(-) rarr I_2`
`2I^(-) rarr I_2+2e^(-) " "...(i)`
Reduction half reaction
`Cr_(2)O_(7)^(2-) rarr Cr^(3+)`
`Cr_(2)O_(7)^(2-)rarr2Cr^(3+)`
`Cr_2O_(7)^(2-) +6e^(-) rarr 2Cr^(3+)+7H_2O" "...(ii)`
`" "("acidic medium")`
To balance the electrons multiply eq(i) by 3 and add to eq (ii)
`Cr_(2)O_(7)^(2-) +14H^(+)+6I^(-) rarr 2Cr^(3+)+3I_(2)+7H_2O`
(iii)
Dividing the equation into two half reactions :
Oxidation half reaction : `SO_(3)^(2-) rarr SO_(4)^(2-)`
Reduction half reaction : `MnO_(4)^(-) rarr Mn^(2+)`
Balancing oxidation and reduction half reactions separately as :
Oxidation half reation
`SO_(3)^(2-) rarr SO_4^(2-)`
`SO_3^(2-) rarr SO_(4)^(2-) +2e^(-)`
Since the reaction occurs in acidic medium,
`SO_3^(2-) rarr SO_4^(2-) +2e^(-) +2H^(+)`
`SO_3^(2-) +H_2O rarr SO_4^(2-) +2H^(+) +2e^(-) .....(i)`
Reduction half reaction
`MnO_4^(-) rarr Mn^(2+)`
`MnO_4^(-) +5e^(-) rarr Mn^(2+)`
`MnO_4^(-) +8H^(+) +5e^(-) rarr Mn^(2+)`
`MnO_4^(-) +8H^(+) +5e^(-) rarr Mn^(2+) +4H_2O" "....(ii)`
To balance the electrons , multiply eq. (i) by 5 and eq (ii) by 2 and add
`2Mn_4^(-) +5SO_(3)^(2-) +6H^(+) rarr 2Mn^(2+)+5SO_4^(2-) +3H_2O`
(iv)
Dividing the equation into two half reactions :
Oxidation half reaction : `Br^(-) rarr Br_2`
Reduction half reaction : `MnO_4^(-) rarr Mn^(2+)`
Balancing oxidation and reduction half reaction separately as :
Oxidation half reaction
`Br^(-) rarr Br_2`
`2Br^(-) rarr Br_2`
`2Br^(-) rarr Br_2+2e^(-) " "...(i)`
Reduction
`MnO_4^(-) rarr Mn^(2+)`
`MnO_4^(-) +5e^(-) rarr Mn^(2+)`
`MnO_4^(-) +8H^(+) +5e^(-) rarr Mn^(2+)`
`MnO_4^(-) +8H^(+) +5e^(-) rarr Mn^(2+)+4H_2O" "...(ii)`
To balance the electrons, multiply eq (i) by 5 and eq (ii) by 2 and add
`2MnO_4^(-) +10Br^(-) +16 H^(+) rarr 2Mn^(2+)+5Br_2+8H_2O`