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Question
Write balanced chemical equation for the following reactions:
Permanganate ion \[\ce{(MnO^{-}4)}\] reacts with sulphur dioxide gas in acidic medium to produce \[\ce{Mn^{2+}}\] and hydrogen sulphate ion.
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Solution
\[\ce{2MnO^{-}4 + 5SO2 + 2H2O + H+ -> 5HSO^{-}4 + 2Mn^{2+}}\]
Balancing by ion-electron method:
\[\ce{\overset{+7}{Mn}\overset{-2}{O}^{-}4 + \overset{+4}{S}\overset{-2}{O2} -> \overset{+2}{Mn}^{2+} + \overset{+1}{H}\overset{+6}{S}\overset{-2}{O}^{-}4}\] (Skeletal equation)
Oxidation half: \[\ce{SO2 -> HSO^{-}4}\]
Reduction half: \[\ce{MnO^{-}4 -> Mn^{2+}}\]
Oxidation half: \[\ce{SO2 -> HSO^{-}4 + 2e-}\]
\[\ce{SO2 + 2H2O -> HSO^{-}4 + 3H^{+} + 2e-}\] ......(i)
(Add \[\ce{2H2O}\] molecules to balance \[\ce{O}\] atoms)
Reduction half:
\[\ce{MnO^{-}4 + 5e- -> Mn^{2+}}\]
\[\ce{MnO^{-}4 + 8H^{+} + 5e- -> Mn^{2+} + 4H2O}\] ......(ii)
(Add \[\ce{4H2O}\] molecules to balance \[\ce{O}\] atoms and \[\ce{H}\] atoms)
Add oxidation and reduction half
\[\ce{[SO2 + 2H2O -> HSO^{-}4 + 3H+ + 2e-] × 5}\]
\[\ce{[MNO^{-}4 + 8H+ + 5e- -> Mn^{2+} + 4H2O] × 2}\]
\[\ce{2MNo^{-}4 + 5SO2 + 2H2O + H+ -> 5HSO^{-}4 + 2Mn^{2+}}\]
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