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Redox Reactions

Question
CBSEENCH11006782

Permanganate (VII) ion, MnO subscript 4 superscript minus in basic solution oxidises iodide ion, I- to produce molecule iodine (I2) and manganese (IV) oxide (MnO2). Write a balanced ionic equation to represent redox reaction. 

Solution
The skeleton ionic equation is
MnO subscript 4 superscript minus left parenthesis aq right parenthesis space plus space straight I to the power of minus left parenthesis aq right parenthesis space space space rightwards arrow space space space MnO subscript 2 left parenthesis straight s right parenthesis space plus space space straight I subscript 2 left parenthesis straight s right parenthesis
1. Write the oxidation and reduction half-reactions by observing the changes in oxidation number and writing these separately. 
             Oxidation half reaction:
                -1               0
                I-(aq)  rightwards arrow  I2(s)
              Reduction half reaction:
                +7               +4
               MnO subscript 4 superscript minus left parenthesis aq right parenthesis space space rightwards arrow space space space MnO subscript 2 left parenthesis straight s right parenthesis
2. Balance the oxidation half reaction
(i) Balance 1 atoms by multiplying I- by 2
                       -1                  0
                       2 straight I to the power of minus left parenthesis aq right parenthesis space space rightwards arrow space space space space straight I subscript 2 left parenthesis straight s right parenthesis
(ii) Add 2 electrons towards R.H.S. to balance the charges on iodine atoms
                     2 straight I to the power of minus left parenthesis aq right parenthesis space space space rightwards arrow space space straight I subscript 2 left parenthesis straight s right parenthesis space plus space 2 straight e to the power of minus
space space space space space space space space space space space space space space space space left square bracket Balanced space oxidation space half space reaction right square bracket
3. Balancing the reduction half reaction
    (i) Add 3 electrons towards L.H.S. to balance the charge on Mn
                     MnO subscript 4 superscript minus left parenthesis aq right parenthesis space plus space 3 straight e to the power of minus space space rightwards arrow space space space MnO subscript 2 left parenthesis straight s right parenthesis
     (ii) Balance O atoms by adding two H2O molecules towards R.H.S.
             MnO subscript 4 superscript minus left parenthesis aq right parenthesis space plus space 3 straight e to the power of minus space space rightwards arrow space space space MnO subscript 2 left parenthesis straight s right parenthesis space plus space 2 straight H subscript 2 straight O left parenthesis straight l right parenthesis
     (iii) Balance H atoms by adding four H+ towardS
      L.H.S.
               MnO subscript 4 superscript minus left parenthesis aq right parenthesis space plus space 4 straight H to the power of plus left parenthesis aq right parenthesis space plus space 3 straight e to the power of minus space space rightwards arrow space space space MnO subscript 2 left parenthesis straight s right parenthesis space plus space 2 straight H subscript 2 straight O left parenthesis straight l right parenthesis
Since the reaction takes place in a basic solution, therefore for four H+ ions, we add four OH- ions to both sides of the equation.
MnO subscript 4 superscript minus left parenthesis aq right parenthesis space plus space 4 straight H to the power of plus left parenthesis aq right parenthesis space plus space 4 OH to the power of minus left parenthesis aq right parenthesis space plus space 3 straight e to the power of minus space space rightwards arrow space
space space space space space space space space space space space space space space space space space space space MnO subscript 2 left parenthesis straight s right parenthesis space plus space 2 straight H subscript 2 straight O left parenthesis straight l right parenthesis space plus space 4 OH to the power of minus left parenthesis aq right parenthesis
or
space MnO subscript 4 superscript minus left parenthesis aq right parenthesis space plus space 2 straight H subscript 2 straight O left parenthesis straight l right parenthesis plus 3 straight e to the power of minus space rightwards arrow space MnO subscript 2 left parenthesis straight s right parenthesis space plus space 4 OH to the power of minus 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 space space space space space space space space
[Balanced reduction half reaction]
4. Multiply balanced oxidation half-reaction by 3 and balanced reduction half-reaction by 2 and add both the half reactions.
space 6 straight I to the power of minus left parenthesis aq right parenthesis space plus space 3 MnO subscript 4 superscript minus left parenthesis aq right parenthesis space plus space 4 straight H subscript 2 straight O left parenthesis straight l right parenthesis space space rightwards arrow space space
space space space space space space space space space space space 3 straight I subscript 2 left parenthesis straight s right parenthesis space plus space 2 MnO subscript 2 left parenthesis straight s right parenthesis space plus space 8 OH to the power of minus left parenthesis aq right parenthesis
This is a balanced equation.