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Redox Reactions

Question
CBSEENCH11006780

Balance the following redox reactions by ion-electron method:
MnO subscript 4 superscript minus left parenthesis aq right parenthesis space plus space SO subscript 2 left parenthesis straight g right parenthesis space rightwards arrow space space Mn to the power of 2 plus end exponent left parenthesis aq right parenthesis space plus space HSO subscript 4 superscript minus left parenthesis aq right parenthesis space left parenthesis in space acidic space solution right parenthesis

Solution

The skeleton equation is:
    MnO subscript 4 superscript minus left parenthesis aq right parenthesis space plus space SO subscript 2 left parenthesis straight g right parenthesis space space rightwards arrow space space space Mn to the power of 2 plus end exponent left parenthesis aq right parenthesis space plus space HSO subscript 4 superscript minus left parenthesis aq right parenthesis
(i) Separation of the equation in two half reactions. 
    Write the O.N. of the atoms involved in the equation. 
             +7-2      +4-2            +2            +1 + 6-2
            left parenthesis MnO subscript 4 right parenthesis to the power of minus space plus space SO subscript 2 space space rightwards arrow space space space left parenthesis Mn right parenthesis to the power of 2 plus end exponent space space plus space left parenthesis HSO subscript 4 right parenthesis to the power of minus
(ii) Identify the atoms which undergo change in O.N.
             +7             +4          -2            - 6
       left parenthesis MnO subscript 4 right parenthesis to the power of minus space plus space SO subscript 2 space space space rightwards arrow space space left parenthesis Mn right parenthesis to the power of 2 plus end exponent space plus space left parenthesis HSO subscript 4 right parenthesis to the power of minus
(iii) Find out the species involved in the oxidation and reduction half reactions.

Oxidation half reaction:
                              SO subscript 2 space rightwards arrow space space space HSO subscript 4 superscript minus
Reduction half reaction:
                       MnO subscript 4 superscript minus space space space space rightwards arrow space space space Mn to the power of 2 plus end exponent
Balancing the oxidation half reaction:
    The oxidation half reaction is:
                     SO subscript 2 space rightwards arrow space space space HSO subscript 4 superscript minus
(i) As the increase in O.N. is 2, therefore add two electrons on the product side to balance change in O.N.
SO subscript 2 space space space rightwards arrow space space space HSO subscript 4 superscript minus space plus space 2 straight e to the power of minus
(ii) Balance O atoms by adding two H2O molecules on the reactant side and balance H atoms by adding three H+ on the product side. 
        SO subscript 2 space plus space 2 straight H subscript 2 straight O space space space rightwards arrow space space space HSO subscript 4 superscript minus space plus space 3 straight H to the power of plus space plus space 2 straight e to the power of minus        ...(1)
Balancing the reduction half reaction:
The reduction half reaction is:
            MnO subscript 4 superscript minus space space rightwards arrow space space space Mn to the power of 2 plus end exponent
(i) As the decrease in O.N. is 5, therefore, add 5e- on the reactant side. 
                  MnO subscript 4 superscript minus plus 5 straight e to the power of minus space space rightwards arrow space space Mn to the power of 2 plus end exponent
(ii) Balance O atoms by adding four H2O molecules on the product side and balance H atoms by adding eight H+ on the reactant side. 
               MnO subscript 4 superscript minus space plus space 8 straight H to the power of plus space plus space 5 straight e to the power of minus space space space rightwards arrow space space space Mn to the power of 2 plus end exponent space plus space 4 straight H subscript 2 straight O space space space space... left parenthesis 2 right parenthesis
Adding the two half reactions.
In order to equate the electrons, multiply equation (1) by 5 and equation (2) by 2. Add the two equations.
            SO subscript 2 space plus space 2 straight H subscript 2 straight O space space space rightwards arrow space space space space HSO subscript 4 superscript minus space plus space 3 straight H to the power of plus space plus space 2 straight e to the power of minus right square bracket space cross times space 5
MnO subscript 4 superscript minus space plus space 8 straight H to the power of minus space plus space 5 straight e to the power of minus space space space rightwards arrow space space space space Mn to the power of 2 plus end exponent space plus space 4 straight H subscript 2 straight O right square bracket space cross times space 2
minus negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative
2 MnO subscript 4 superscript minus left parenthesis aq right parenthesis space plus space 5 SO subscript 2 left parenthesis straight g right parenthesis space plus space 2 straight H subscript 2 straight O left parenthesis straight l right parenthesis space plus space straight H to the power of plus left parenthesis aq right parenthesis
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space rightwards arrow space 5 HSO subscript 4 superscript minus left parenthesis aq right parenthesis space plus space 2 Mn to the power of 2 plus end exponent left parenthesis aq right parenthesis