Balance the following Relox reaction by ion-electron method an acidie medium.
`{:(Cr_2" "O_7^(2-)+SO_2 to Cr^(3+)+SO_4^(2-)),((aq)" "(g)" "(aq)" "(aq)):}`.

Explanation

`Cr_(2)O_(7)^(-2)+SO_(2)to Cr^(+3)+SO_(4)^(-2)`
Reduction half cell-
`Cr_(2)O_(7)^(-2)to Cr^(+3)`
`Cr_(2)O_(7)^(-2)to 2Cr^(+3)` (Cr balanced)
`Cr_(2)O_(7)^(-2)to 2Cr^(+3)+7H_(2)O` (oxygens balanced)
`Cr_(2)O_(7)^(-2) +14H^+to 2 Cr^(+3)+7H_(2)O` (Hydrogens balanced)
Oxidation half cell
`SO_(2)to SO_(4)^(-2)`
`SO_(2)+2H_(2)Oto SO_(4)^(-2)` (Oxygens balanced)
`SO_(2)+2H_(2)Oto SO_(4)^(-2)+4H^(+)`
(Hydrogens balanced)
`SO_(2)+2H_(2)O to SO_(4)^(-2)+4H^(+)+2e^(-)`
(Charge balanced)
Oxidation half cell
`Fe^(+2)to Fe^(+3)`
`Fe^(+2)to Fe^(+3)+e^(-)` (charge balanced)
`2[Fe^(+2)to Fe^(+3)+e^(-)]`
`underline(Cr_(2)O_(7)^(-2)+14H^(+)+6e^(-)to 2Cr^(+3)+7H_(2)O underset(("charge balanced"))` `(overset(Cr_(2)O_(7)^(-2)14H^(+)+6e^(-)to 2Cr^(+3)+7H_(2)O)underline(3SO_(2)+6H_(2)O to 3 SO_(4)^(-2)+12H^(+)+6e^(-)))/underline(Cr_(2)O_(7)^(-2)+3SO_(2)+2H^(+)to 2Cr^(+3)+3 SO_(4)^(-2)+H_(2)O)`