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Redox Reactions

Question
CBSEENCH11006785

Balance the following equation in basic medium by ion-electron method and oxidation number method and identify the oxidising agent and the reducing agent.
Cl subscript 2 straight O subscript 7 left parenthesis straight g right parenthesis space plus space straight H subscript 2 straight O subscript 2 left parenthesis aq right parenthesis space space rightwards arrow space space space ClO subscript 2 superscript minus left parenthesis aq right parenthesis space plus space straight O subscript 2 left parenthesis straight g right parenthesis space plus space straight H to the power of plus

Solution

(A) Ion-electron method: 
1. Write the oxidation and reduction half-reaction by observing the changes in oxidation numbers.
Oxidiation half reaction:
        -1                      0
   straight H subscript 2 straight O subscript 2 left parenthesis aq right parenthesis space space rightwards arrow space space space straight O subscript 2 left parenthesis straight g right parenthesis
Reduction half-reaction:
       +7                  +3
      Cl subscript 2 straight O subscript 7 left parenthesis straight g right parenthesis space space space rightwards arrow space space space space ClO subscript 2 superscript minus left parenthesis aq right parenthesis
2. Balancing the oxidation half reaction
    (i) Add 2 electrons towards R.H.S. to balance the charges
                straight H subscript 2 straight O subscript 2 left parenthesis aq right parenthesis space space space rightwards arrow space space space straight O subscript 2 left parenthesis straight g right parenthesis space plus space 2 straight e to the power of minus
   (ii) Add 2 OH- ions towards L.H.S to balance the charges
         straight H subscript 2 straight O subscript 2 left parenthesis aq right parenthesis space plus space 2 OH to the power of minus left parenthesis aq right parenthesis space rightwards arrow space space straight O subscript 2 left parenthesis straight g right parenthesis space plus space 2 straight e to the power of minus
(iii) Balance O atoms by adding two H2O molecules towards H
          straight H subscript 2 straight O subscript 2 left parenthesis aq right parenthesis space plus space 2 OH to the power of minus left parenthesis aq right parenthesis space rightwards arrow space space space straight O 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 2 straight e to the power of minus
space space space left parenthesis Balanced space oxidation space half space reaction right parenthesis
3. Balancing the reduction half reaction
   left parenthesis straight i right parenthesis Balance space Cl space atoms space by space multiplying space ClO subscript 2 superscript minus space by space 2
space space space space Cl subscript 2 straight O subscript 7 left parenthesis straight g right parenthesis space space rightwards arrow space space space 2 ClO subscript 2 superscript minus left parenthesis aq right parenthesis
left parenthesis ii right parenthesis space Add space 8 space electrons space towards space LHS space to space balance space the space charge
space space space space space space Cl subscript 2 straight O subscript 7 left parenthesis straight g right parenthesis space plus space 8 straight e to the power of minus space space rightwards arrow space space space 2 ClO subscript 2 superscript minus left parenthesis aq right parenthesis
left parenthesis iii right parenthesis space Add space six space OH to the power of minus space towards space straight R. straight H. straight S. space to space balance space the space charges
space space space space space Cl subscript 2 straight O subscript 7 left parenthesis straight g right parenthesis space plus space 8 straight e to the power of minus space rightwards arrow space space 2 ClO subscript 2 superscript minus left parenthesis aq right parenthesis space plus space 6 OH to the power of minus left parenthesis aq right parenthesis
  space left parenthesis iv right parenthesis space Balance space straight O space atoms space by space adding space three space straight H subscript 2 straight O space
molecules space towards space straight L. straight H. straight S.
Cl subscript 2 straight O subscript 7 left parenthesis straight g right parenthesis space plus space 3 straight H subscript 2 straight O plus space 8 straight e to the power of minus space space rightwards arrow space space 2 ClO subscript 2 superscript minus left parenthesis aq right parenthesis space plus space 6 OH to the power of minus left parenthesis aq right parenthesis
space space space left parenthesis Balanced space reduction space half space reaction right parenthesis
 4. Multiply balanced oxidation half-reaction by 4 and add it to the balanced reduction half-reaction.
4 straight H subscript 2 straight O subscript 2 left parenthesis aq right parenthesis space plus space 8 OH to the power of minus left parenthesis aq right parenthesis space plus space Cl subscript 2 straight O subscript 7 left parenthesis straight g right parenthesis space plus space 3 straight H subscript 2 straight O left parenthesis straight l right parenthesis space space rightwards arrow space space
space 2 ClO subscript 2 superscript minus left parenthesis aq right parenthesis space plus space 6 OH to the power of minus left parenthesis aq right parenthesis plus space 4 straight O subscript 2 left parenthesis straight g right parenthesis space plus space 8 straight H subscript 2 straight O left parenthesis straight l right parenthesis
or space space Cl subscript 2 straight O subscript 7 left parenthesis straight g right parenthesis space plus space 4 straight H subscript 2 straight O subscript 2 left parenthesis aq right parenthesis space plus space 2 OH to the power of minus left parenthesis aq right parenthesis
space space space space space rightwards arrow space space space space space space 2 ClO subscript 2 superscript minus left parenthesis aq right parenthesis space plus space 4 straight O subscript 2 left parenthesis straight g right parenthesis space plus space 5 straight H subscript 2 straight O left parenthesis straight l right parenthesis
(B) Oxidation number method            
 (i) The skeleton equation along with oxidation number of each atom is
+7 -2          +1 -1                 +3               0
Cl subscript 2 straight O subscript 7 left parenthesis straight g right parenthesis space plus space straight H subscript 2 straight O subscript 2 left parenthesis aq right parenthesis space space space rightwards arrow space space space ClO subscript 2 superscript minus space left parenthesis aq right parenthesis space plus space straight O subscript 2 left parenthesis straight g right parenthesis space plus space straight H to the power of plus
(ii) The ON of O atom increases by 1 per atom while that of CI decreases by 4 per atom.

Thus Cl2O7(g) acts as an oxidising agent while H2O2(aq) as the reducing agent
Total increase in O.N. of H2O2 = 2 X 1=2
Total decrease in O.N. of Cl2O7 = 4 x 2 = 8
(iii) Equalise the increase/decrease in O.N. by multiplying H2O2 and O2 by 4.
Cl subscript 2 straight O subscript 7 left parenthesis straight g right parenthesis space plus space 4 straight H subscript 2 straight O subscript 2 left parenthesis aq right parenthesis space space rightwards arrow space space ClO subscript 2 superscript minus left parenthesis aq right parenthesis space plus space 4 straight O subscript 2 left parenthesis straight g right parenthesis
(iv) Balance Cl atoms by multiplying ClO subscript 2 superscript minus space by space 2
    Cl subscript 2 straight O subscript 7 left parenthesis straight g right parenthesis space plus space 4 straight H subscript 2 straight O subscript 2 left parenthesis aq right parenthesis space space space rightwards arrow space space space 2 ClO subscript 2 superscript minus left parenthesis aq right parenthesis space plus space 4 straight O subscript 2 left parenthesis aq right parenthesis
(v) Balance O atoms by adding three straight H subscript 2 straight O towards R.H.S.
           space Cl subscript 2 straight O subscript 7 left parenthesis straight g right parenthesis plus space 4 straight H subscript 2 straight O subscript 2 left parenthesis aq right parenthesis rightwards arrow space 2 ClO subscript 2 superscript minus left parenthesis aq right parenthesis space plus space 4 straight O subscript 2 left parenthesis straight g right parenthesis space plus space 3 straight H subscript 2 straight O left parenthesis straight l right parenthesis
(vi) Balance H atoms by adding two straight H subscript 2 straight O towards R.H.S. and two OHtowards L.H.S.
space Cl subscript 2 straight O subscript 7 left parenthesis straight g right parenthesis space plus space 4 straight H subscript 2 straight O subscript 2 left parenthesis aq right parenthesis space plus space 2 OH to the power of minus left parenthesis aq right parenthesis space space rightwards arrow
space space space space space space space space space space space space space space space space space space space 2 ClO subscript 2 superscript minus left parenthesis aq right parenthesis plus space 4 straight O subscript 2 left parenthesis straight g right parenthesis space plus space 5 straight H subscript 2 straight O left parenthesis straight l right parenthesis
This is the balanced redox equation.