Reduction Half reaction : \(Cr _2 O _7^{2-}+6 e ^{-} \longrightarrow 2 Cr ^{3+}\)

Oxidation Half reaction: \(SO _3^{2-} \longrightarrow SO _4^{2-}+2 \overline{ e } \times 3\)

Overall reaction : \(Cr _2 O _7^{2-}+3 SO _3^{2-} \longrightarrow 2 Cr ^{3+}+3 SO _4^{2-}\)

- To balance 'O' atoms, adding \(H _2 O\) on LHS

\(Cr _2 O _7^{2-}+3 SO _3^{2-} \longrightarrow 2 Cr ^{3+}+3 SO _4^{2-}+4 H _2 O\)

- To balance 'H' atoms, adding \(H ^{+}\)on \(RHS\)

\(Cr _2 O _7^{2-}+3 SO _3^{2-}+8 H ^{+} \longrightarrow 2 Cr ^{3+}+3 SO _4^{2-}+4 H _2 O\)

\(\therefore \quad a =1\)

\(b =3\)

\(c =8\)